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Digitized by the Internet Archive 
 in 2011 with funding from 
 The Library of Congress 
 
 http://www.archive.org/details/fundamentalsourcOOdure 
 
FUNDAMENTAL SOURCES 
 OF EFFICIENCY 
 
 BY 
 
 FLETCHER DURELL, Ph.D. 
 
 HEAD OF THE MATHEMATICAL DEPARTMENT OF THE LAWRENCEVILLE SCHOOL ; 
 AUTHOR OF A SERIES OF MATHEMATICAL TEXTBOOKS 
 
 PHILADELPHIA AND LONDON 
 
 J. B. LIPPINCOTT COMPANY 
 
 1914 
 

 COPYRIGHT, igi4, BY J. B. LIPFINCOTT COMPANY 
 
 PRINTED IN THE UNITED STATES OF AMERICA 
 
 DEC 22 1314 #2r* 
 i 
 
 ©CI.A388917 
 
To 
 
 My Wife 
 
PREFACE 
 
 The present work is an attempt to analyze the various forms and 
 sources of efficiency into a few elemental principles. It is felt that 
 the study of such primal elements will not only aid in the mastery of 
 efficiency in a given field, but will prevent this important idea from 
 assuming a narrow meaning and thus leading to limited or even, in 
 some respects, harmful results. 
 
 The above treatment of the subject also facilitates, on the one 
 hand, the use of efficiency principles in all the various details of 
 work and experience and, on the other, their application in the 
 formation of a general philosophy of life. 
 
 While the book has been cast in a form adapted to general read- 
 ing, groups of exercises have been inserted which, it is hoped, 
 will add to its value if it is used as a textbook in any institution 
 where the principles of efficiency are taught either generally or in 
 any specific field. 
 
 It is also believed that such a presentation of the principles of 
 efficiency may throw light on the problem of vocational and cultural 
 studies, and perhaps suggest how the study of the principles of 
 efficiency, as such, may be made a central study in educational 
 systems, helping to give both vocational and cultural values to 
 other more conventional studies. 
 
 The leading ideas contained in this book were suggested to the 
 author when reading the philosophy of Herbert Spencer more than 
 twenty years ago. The importance of investigating the elements 
 which constitute fitness, that is, efficiency, becomes evident as soon 
 as the principle of the survival of the fittest is recognized. While 
 all the principal ideas in the book were thus arrived at before the 
 present energetic movement toward efficiency in more or less con- 
 crete fields arose, new light and many important details have been 
 obtained from a reading of the publications of the Efficiency So- 
 ciety, and the works of writers like F. W. Taylor, Harrington 
 Emerson, and Hugo Miinsterburg. 
 
 The writer wishes to express his indebtedness to Ida Kruse 
 McFarlane and Charles William Cuno of the Department of Effi- 
 ciency, University of Denver, who have kindly read the manuscript 
 and made important suggestions concerning the same. 
 
CONTENTS 
 
 CHAPTER PAGE 
 
 I. DEFINITIONS AND FIRST PRINCIPLES i 
 
 II. REUSE 15 
 
 III. THE UNIT AND ITS MULTIPLIER 34 
 
 IV. THE GROUP 56 
 
 V. MULTIPLICATIVE GROUPS 70 
 
 VI. ORDERS OF MATERIAL 95 
 
 VII. EXTERNALITY in 
 
 VIII. UNIFORMITY AND DIVERSITY 130 
 
 IX. EXPENDITURES AND RESULTS v 152 
 
 X. SYMBOLISM 164 
 
 XI. DIRECTIVE 192 
 
 XII. KINEMATIC AND DYNAMIC 210 
 
 XIII. RHYTHM 230 
 
 XIV. DIALECTIC ! 249 
 
 XV. LIMITATION 265 
 
 XVI. ERROR AND PARADOX 281 
 
 XVII. COMBINATIONS OF EFFICIENTS. SUMMARY........ 301 
 
 XVIII. APPLICATIONS 309 
 
 APPENDIX A. The Categories and a Philosophy of Life 333 
 
 B. Historical Survey 350 
 
CHAPTER I 
 
 PRELIMINARY SURVEY. DEFINITIONS 
 
 Recent Advances in Efficiency 
 
 In the year 1900 a competent authority estimated that the cost, 
 of unskilled labor, such as digging dirt and carrying burdens, when 
 done by man unaided, was one thousand times as great as the cost: 
 of the same labor when done by the aid of the best steam engines. 
 But even since that statement was made, there has been remarkable- 
 progress. For instance the Diesel oil and tar engine, which is 
 three, or under some circumstances four times as efficient as the 
 steam engine, has been invented and come into use. 
 
 When he was a young man Harrington Emerson, on one oc- 
 casion, had an opportunity to watch the work of digging the Suez 
 Canal. He thus describes the crude way in which part of the dig- 
 ging was being done : "Many of the workers were girls digging up 
 the sand with their hands, throwing it into the rush basket each had 
 woven for herself, lifting the baskets to their heads, and carrying 
 the load of 20 or 30 pounds a hundred feet up the bank and dump- 
 ing it." He calls attention to the contrast of this method of exca- 
 vating and removing earth with that used in digging the Panama 
 Canal. At the latter place the digging has been done almost en- 
 tirely by steam scoops, each lifting two or more cubic yards of 
 dirt at a single stroke. The earth has, in some cases, been removed 
 for twenty miles by trains of cars, and the tracks on which these 
 cars ran, when a change in their position became necessary, were 
 moved in large sections at a single operation. Yet in the highly 
 efficient process of digging the Panama Canal, many improvements 
 were made from time to time. It was estimated that in this work 
 in the year 1912 a ton of dynamite was twice as effective as in the 
 year 1908. 
 
 Nor has the advance in the efficiency of skilled labor been less 
 noteworthy than that in such crude and fundamental work as dig- 
 ging dirt. For instance in the weaving of cotton fabrics, the use 
 of power machinery has increased the efficiency of a workman at 
 least eightfold. 
 
2 SOURCES OF EFFICIENCY 
 
 Primitive methods of agriculture, as compared with hunting and 
 fishing, increase the productivity of the land 200 times. Here 
 again, the use of machinery and other improved methods have 
 greatly increased the efficiency of man's labor. Thus "between the 
 years 1830 and 1896 the time of human labor required for the 
 production of a bushel of wheat was reduced from three hours to 
 ten minutes, and the cost of the human labor to produce this bushel 
 declined from 17% cents to 3^2 cents". 
 
 In the year 1866 the death rate of New York City was 34 per 
 thousand; in the year 1912 this rate had been reduced to 14.1 per 
 thousand. This means that twelve years have been added to the 
 length of the average human life in that city. Similar illustrations 
 might be given of increased efficiency in the various other depart- 
 ments of human activity. 
 
 Opportunities for Further Increases in Efficiency 
 
 In spite of the large advances which have been made, even a 
 slight examination shows that opportunities exist for large exten- 
 sions of the efficiencies which have been mentioned. Even in the 
 Diesel engine nearly two thirds of the fuel energy is wasted. Ow- 
 ing to losses in mining coal, and in converting coal energy into 
 electric light, only a little over one half of 1 per cent of the 
 energy latent in coal as it lies in the ground is utilized by man in 
 using coal as a source of light. 
 
 In the fundamental industry of. agriculture, an efficiency expert 
 like Harrington Emerson estimates the farms in the United States 
 as about 30 per cent efficient. At the Conservation Congress in 
 the year 191 1, the statement was made that one-third of the barn- 
 yard manure in the United States is wasted, and that this means 
 an annual loss of $800,000,000. In the World's Work in the year 
 1906, it was stated that "all authorities are now agreed that we 
 might double the yield of our principal crops". In his address to 
 the Pennsylvania Pilgrims, May 1913, President Van Hise of the 
 University of Wisconsin said : "We know enough about agriculture 
 so that the agricultural production of the country could be doubled 
 if the knowledge were applied. We know enough about disease so 
 that if the knowledge were utilized infectious and contagious disease 
 would be substantially destroyed in the United States — and that 
 within a score of years. We know enough about eugenics so that 
 if the knowledge were applied the defective classes would disap- 
 
PRELIMINARY SURVEY 3 
 
 pear within a generation. Similarly in other fields our knowledge 
 has expanded far beyond utilization." 
 
 Growing Need of Increased Efficiency 
 
 Not only do opportunities for increased efficiency thus exist, but 
 there is also an increasing need for the development and applica- 
 tion of such methods. On February 14, 1912, President Taft signed 
 the bill for the admission of Arizona as the forty-eighth and last 
 state in the Union. Henceforth the people .of the United States 
 must look forward primarily, not to new territory, but to the best 
 possible use of the resources now in their possession. The same 
 principles apply essentially to the world as a whole. The leading 
 nations have explored and taken possession of all the productive 
 parts of the earth's surface. By the use of steel and electricity 
 this process has recently been brought to a conclusion with great 
 suddenness. Henceforth the law of the survival of the fittest will 
 have a new and more crushing power. 
 
 Increasing Value of Efficiency 
 
 On the other hand improved methods of efficiency will now have 
 an ever increasing value for those who know how to master and 
 apply them. Of the 110,000 species of flowering plants known to 
 exist in the world, less than 1 per cent have been studied in any 
 adequate way and reduced to man's service. The non-flowering 
 plants and the animal life of the world has been studied and uti- 
 lized in an even smaller degree. Quite as great is the wealth 
 which man can make by his own exertions. Thus in the field of 
 chemistry, between the years 1883 and 1900 the number of carbon 
 compounds increased from 16,000 to 67,000. As yet but few of 
 these products have been fully studied and employed. Humus, be- 
 cause it improves the texture of the soil, conserves moisture, sup- 
 plies food to the growing plant, and is the home of the nitrogen 
 fixating bacteria, is one of the most important elements in agri- 
 culture. Yet notwithstanding the vast and manifold investigations 
 of science, the Encyclopedia Brittanica says concerning humus, 
 "little is known with regard to its chemical constitution". Hence 
 man's knowledge of the most efficient way to use humus is cor- 
 respondingly limited, and an important field here lies open by which 
 to obtain new power. 
 
 Improved methods of travel and communication bring each of the 
 
4 SOURCES OF EFFICIENCY 
 
 world's inhabitants into ever closer touch with its artistic treas- 
 ures, its literature, scenery, and history. Without proper methods 
 for its mastery, the vast mass of culture wealth thus made access- 
 ible, may become a burden or even a danger. With adequately 
 developed methods of assimilation, it becomes a near and instant 
 wealth to every person. 
 
 Hence supreme need and supreme opportunity alike spur on 
 mankind to a study of the science, art, and philosophy of achieving 
 results. It is desirable to analyze the concept of efficiency until 
 primal units of it are obtained which can be used in many ways 
 each day by the individual person, can be taught in the schools, 
 and developed into elaborate systems. 
 
 DEFINITIONS AND FIRST PRINCIPLES 
 Definition of Efficiency 
 
 An efficient process is one in which the available results exceed 
 the expenditure. Thus if a farmer expends $1000 in raising a 
 crop and receives $1500 for the crop, his work may be said to be 
 efficient. 
 
 Efficiency is the property of being efficient: that is, of producing 
 results in excess of expenditures. 
 
 The degree of efficiency of a process is the ratio of the available 
 result of the process to the expenditure. Thus in the above illu- 
 stration the degree of efficiency is $1500 -^ $1000, or 3/2. Often 
 "degree of efficiency" is shortened' to "efficiency", as when we say 
 that the efficiency of a process is 2, or twofold. 
 
 In case the degree of efficiency is less than one or unity, the given 
 process is one of loss or waste. Thus if a farmer spends $1000 in 
 raising a crop of wheat and receives only $800 for the crop, the 
 efficiency of the process is the fraction 4/5, serving to indicate the 
 degree of loss involved. 
 
 Principal Kinds of Efficiency 
 
 Relative efficiency is the degree of efficiency in a process in com- 
 parison with the efficiency in a like process taken as standard. Thus 
 if land which should produce 32 bushels of wheat per acre is being 
 made to yield only 24 bushels per acre, the efficiency of the process 
 of agriculture involved is 75 per cent. Or if one farmer raises 20 
 bushels of wheat per acre while another farmer raises 24 bushels 
 
DEFINITIONS 5 
 
 per acre on the same kind of land the efficiency of the second farmer 
 as compared with the first is 24 -r- 20, or 6/5. 
 
 In comparison with relative efficiency the first definition of effi- 
 ciency given is a definition of absolute or independent efficiency. 
 
 A case of homogeneous efficiency is one in which the material 
 expended and the results obtained are of the same kind. Illustra- 
 tions are the expenditure of money to obtain more money; or the 
 planting of grain to procure more grain of the same kind; or the 
 sacrifice of present happiness to obtain more happiness in the 
 future. 
 
 A case of heterogeneous efficiency is one in which the output 
 obtained is different in kind from the material expended. Particu- 
 lar instances are the burning of coal to produce light, or the taking 
 of strychnine in small doses to improve one's health. 
 
 It is important to note that the degree of a case of heterogeneous efficiency 
 cannot be expressed or measured directly. For the quantities com- 
 pared in any ratio must be of the same kind. Thus bushels cannot be 
 divided by dollars, nor light by coal, nor health by arsenic. Two ways, 
 however, exist by one or both of which the degree of a case of heterogeneous 
 efficiency may usually be expressed. The first of these methods consists in 
 transforming the given case into one of homogeneous efficiency and then 
 treating the result directly. Thus if money is expended to produce wheat 
 which is consumed on the farm and thereby results in health and happiness 
 the process is heterogeneous ; but if the wheat crop, instead of being consumed 
 on the farm, is converted into money, the process becomes homogeneous 
 and its efficiency can be expressed as the ratio of the sum of money received 
 to that expended. Similarly if the money received from the sale of light 
 be compared with that expended in producing the light, the efficiency involved 
 is determined numerically. 
 
 The second method of measuring heterogeneous efficiency is that of 
 expressing the efficiency in the relative form ; that is, comparing the output 
 in a given case with that in another case where the expenditure is the same, 
 the latter case being taken as a standard. Thus if the burning of a ton of 
 coal will produce a given number of units of light in one case, but will 
 produce twice as many units in another case, in the latter case the fuel 
 efficiency is twice what it is in the former. Or, to look at the matter from 
 a somewhat different point of view, if a given current of electricity on 
 passing through tungsten filaments will produce 2^ times as much light as 
 when passing through carbon filaments, the efficiency of the tungsten filament 
 is said to be 2 J /> times that of the carbon. Similarly if a given area of land 
 will support two persons who live by hunting and fishing, but when used 
 agriculturally will support 300 persons, the efficiency of the agricultural use 
 of the land as compared with its use for hunting is 150. 
 
6 SOURCES OF EFFICIENCY 
 
 Qualitative Efficiency 
 
 In some cases the results of a process are so abstract or complex 
 that it is not possible to reduce them to a numerical basis. Instances 
 are the expenditure of money to procure health or to save life. This 
 abstractness or complexity may characterize either the expenditure 
 or the results or both of these. As illustrations we have the sacri- 
 fice of home associations in order to make money in a foreign land, 
 or of health in order to obtain an education and power of social 
 service. Hence we may say in general that qualitative (or mass) 
 efficiency is efficiency whose existence is evident but which cannot 
 be expressed in an exact numerical form on account of the abstract- 
 ness or complexity of some of the elements involved. 
 
 Efficiency Relative to an Ideal 
 
 Certain important cases of relative efficiency call for special 
 mention. 
 
 The first is efficiency relative to an ideal or perfect standard. 
 Thus a perfect steam engine would be one which converts all the 
 energy latent in the coal consumed by it, into mechanical power. 
 No steam engine, however, can convert more than 18 per cent of its 
 fuel into power. Hence the fuel efficiency of a steam engine cannot 
 exceed 18 per cent. That of a small steam engine is frequently as 
 low as i per cent. There are indications that the amount of sugar 
 in a sugar beet cannot be made to exceed about 17.5 per cent. A 
 further increase seems to cause the vegetative processes of the beet 
 to degenerate and the whole organism to decay. If this view of 
 the matter is correct, with respect to the ideal beet the degree of 
 efficiency in a beet containing 10.5 per cent of sugar is 10.5 -r- 17.5, 
 or 60 per cent. Similarly if a pupil solves 8 problems out of 10 on 
 an examination paper, his efficiency is .80 with respect to the ideal 
 which consists of solving all of the problems. 
 
 Bogey and Competitive Efficiency 
 
 The second form of relative efficiency is that with respect to 
 some degree of efficiency taken as normal, or "bogey", under given 
 conditions. Thus if the thoroughly trained and equipped but 
 average workman is able to lay 2800 bricks per day, a workman 
 who lays 2240 bricks has an efficiency of 80 per cent; while one 
 who lays 3220 bricks has an efficiency of 115 per cent. This kind of 
 efficiency may be termed bogey efficiency. 
 
DEFINITIONS 7 
 
 In the third place we have what may be termed competitive 
 efficiency. By this is meant the degree of one's efficiency in com- 
 parison with that of one's immediate competitors. Thus if with a 
 given outlay of time and money one farmer produces only 1000 
 quarts of milk while his neighbors, with the same outlay, produce 
 1500, the competitive efficiency of the first farmer is 66}i per cent. 
 It is to be noted that the competitors involved in a given case may 
 fall below, equal, or exceed bogey efficiency. The importance of 
 the matter lies in the fact that, when a man's competitive efficiency 
 is small, he may be undersold, driven from business, or ruined com- 
 mercially. Efficiency of this kind which does not reach a certain 
 standard, is therefore often called inefficiency or absolute failure. 
 Competitive efficiency is recognized in such statements as "He has 
 made good", or "This is worth while". 
 
 Economy 
 
 Cases of efficiency may be relative in other ways as with respect 
 to the emphasis laid on expenditure or on output. For instance, in 
 a given case, it may be desirable to strive for that form of effi- 
 ciency which consists of diminishing the cost instead of that which 
 is characterized by an increase in the output. This form of effi- 
 ciency is usually termed economy. Or, in general, 
 
 Economy is a form of efficiency in which the output compared 
 with that in a standard case is unchanged but the expenditure is 
 diminished. Thus if a farmer who has been raising 1000 bushels 
 of wheat at a cost of $470 is enabled in a later year to produce this 
 same amount of wheat at a cost of $360, the process is primarily 
 one of economy. Hence, in general, efficiency means primarily an 
 increase in results ; economy, a diminution in expenses. Economy 
 is thus the inverse of efficiency. The proverb "A dollar saved is a 
 dollar made" illustrates the fact that economy and efficiency are two 
 aspects of the same thing. 
 
 It is frequently convenient to treat cases of relative efficiency as cases of 
 relative economy; that is, to estimate degrees of efficiency by a comparison 
 of costs instead of outputs. This is illustrated by comparing the cost of 
 raising a bushel of wheat on one farm with that on another. For example 
 if one farmer raises a bushel of wheat at a cost of 48 cents and his neighbor 
 at a cost of 40 cents, the efficiency of the first as compared with the second is 
 !$> or i > or 83 Ms per cent. It is to be carefully noted that in forming 
 •this ratio, the two costs are compared in the inverse order from that used in 
 determining the degree of efficiency by a comparison of two outputs. 
 
8 SOURCES OF EFFICIENCY 
 
 Infinite Efficiency 
 
 Important cases of efficiency are those in which the degree of 
 efficiency is immeasurably large (or infinite). As examples we 
 have all those cases where what is valueless when treated in one way 
 becomes useful when treated in some other way. For instance 
 some forms of lignite when burned directly are valueless for power 
 generating purposes, but become valuable when converted into gas 
 and used in a gas engine. Other and still more important cases are 
 those of the conversion of loss, waste, or defeat into results having 
 a positive value. An instance is that of saving life in a case where 
 death has hitherto resulted uniformly, as in certain kinds of surgical 
 operations. Another instance of infinite efficiency is that of using 
 two points to represent a straight line, or of the drawings called a 
 plan and elevation to represent a building. 
 
 Terms related to Efficiency 
 
 Usefulness means efficiency regarded as a broad qualitative fact 
 and with but slight emphasis on the quantitative elements involved. 
 
 Utility is the same as usefulness except that in utility results are 
 usually more concrete, or more definitely realized. 
 
 Efficacy (or effectiveness) is a form of efficiency in which em- 
 phasis is laid on the complete attainment of a specified end, com- 
 paratively small attention being paid to the cost involved. 
 
 It is convenient at times to denote cases of waste or loss by the 
 term negative efficiency. 
 
 Knowledge of Equivalence an Aid to Efficiency 
 
 Before concluding the discussion of cases of relative efficiency, a 
 word should be said as to the relation of efficiency processes to the 
 equivalence or invariant processes with which they are associated. 
 In certain respects the results of a process must be equivalent to 
 the data involved. Thus by the laws of the conservation of energy 
 and of matter, the amount of force and of matter in the entire 
 results of a process cannot differ from those in the data. Never- 
 theless in a given case the amount of those results, which are usable 
 or available for a given purpose, may differ from the amount availa- 
 ble in the data. Thus when a given amount of food is fed to one 
 kind of cow, more milk is often obtained than when the same amount 
 of food is fed to another variety of cow. In the present investiga- 
 tion we take this principle of profitable non-equivalence between 
 
DEFINITIONS 9 
 
 datum and result in certain processes as a fact or axiom and try 
 to take the utmost advantage of it. In the course of our investiga- 
 tion we shall find that equivalence laws and facts are useful in ob- 
 taining efficiency results. An illustration is the fact that when coal 
 is burned under the boiler of a steam engine only 15 per cent of the 
 power latent in the coal is converted into mechanical energy, the rest 
 being lost as friction in parts of the engine, or as heat which passes 
 up the chimney, or radiates from the parts of the engine. If, how- 
 ever, the coal is first converted into gas and then used in a gas 
 engine, the amount of useful energy obtained is often increased 
 threefold. A knowledge of the equivalences concerned has been 
 an important aid in obtaining this more efficient result. 
 
 COMPLEX CASES OF EFFICIENCY 
 
 Efficiency Factors Acting in Succession 
 
 An efficiency process may often be separated into a number of 
 parts acting in succession, each part acting upon the results of a 
 preceding part. The resultant efficiency of all the parts is then 
 obtained by taking the product of the respective efficiencies of the 
 different parts. By way of illustration we may consider a metal 
 cutting machine which has been run for 5 hours per day at a speed 
 of 10 revolutions per minute and which does its cutting by means 
 of a fine diamond point. If the machine is afterwards run 8 
 hours per day with a speed of 45 revolutions per minute and a round 
 nose tool with a cutting end 10 times as wide as the diamond point 
 is used for the cutting, the efficiency elements of time, speed, and 
 width of cut are increased 8/5, 9/2, and tenfold respectively. Hence 
 the efficiency of the new process, as compared with that of the old, 
 is f X f X 10, or 72. When elements of efficiency are combined 
 in this way, they may be regarded as acting tandem and the resultant 
 obtained called tandem or multiplicative efficiency. 
 
 Parallel Efficiency Factors 
 
 In other cases of resultant efficiency the elements concerned act 
 parallel to each other, and the degree of efficiency in the process as 
 a whole is equal to the average degree of efficiency of the compo- 
 nents. Thus if a farmer is raising four crops at the same time, all of 
 equal importance, and their respective efficiencies are .80, .90, .86, 
 .92, his efficiency for the year is the average of these rates, or .87. 
 In the same way the efficiency of a student is sometimes determined 
 
I0 SOURCES OF EFFICIENCY 
 
 by his average grade in all the subjects pursued by him. If however 
 the elements involved in a given case are of unequal importance, to 
 obtain the resultant efficiency it is necessary to multiply each ele- 
 mental efficiency by a number which indicates its weight or impor- 
 tance, to take the sum of all the products and divide the sum obtained 
 by the sum of all the weights. Thus if the respective efficiencies of 
 four crops raised by a farmer are .60, .90, .80, .71, and the second and 
 third crops are each twice, and the last three times as important as 
 the first, his resultant efficiency is jg±^><^g|g±3X7g Qr ??m 
 
 Tandem and Parallel Efficiencies Combined 
 
 In is evident that mixed cases of efficiency also occur, in the 
 sense that some of the elements involved act in tandem or multipli- 
 cative fashion in whole or part, and others are parallel or additive 
 in relation. For instance while the chief crops of a farmer during a 
 given year may be developed in parallel fashion, the operations in- 
 volved in raising one or more of the crops may act in multiplicative 
 succession. Thus the manner of preparing the seed bed affects 
 the development of the seed, care and efficiency in selecting the seed 
 influence all later processes, and so on. Also if the crops are 
 rotated from year to year the efficiency of any one crop influences 
 the efficiency of the crops which follow in succeeding years. This 
 may also result in certain multiplicative cross relations during any 
 one year. Thus large hay and corn crops will supply feed for 
 many cattle which in turn will supply a larger amount of fertilizer 
 for several later crops. 
 
 Another Method of Analyzing Efficiency Processes 
 
 Emphasis should be laid in this connection on what is for our 
 purpose a still more important method of analyzing an efficiency 
 process into constituent elements. To illustrate this method we take 
 the case of a particular crop raised by a farmer, as a crop of wheat. 
 The agriculturist obtains efficiency in preparing the seed bed of the 
 crop by several distinct means one of which, for instance, is the 
 group principle in the form of the gang plow and also of the extra 
 wide harrow. The group as a source of efficiency is also found in 
 the drill used in sowing the seed, and in the reaper used in harvest- 
 ing the grain. In some form, often in several forms, it is an aid 
 in the efficient marketing of the crop. Other general primal effi- 
 ciency principles are at work in the various concrete divisions of 
 
DEFINITIONS II 
 
 the process which have been enumerated. Even the division of the 
 process into such parts as fertilizing the ground, preparing the seed 
 bed, planting the seed, etc., for separate study, is an application of 
 one of these primary principles, viz. : that of the use of units, or of 
 diversity. Owing to their fundamental and inclusive nature, a thor- 
 ough grasp of these primal efficiency agencies will mean increased 
 efficiency in the various departments of life. These primary effi- 
 ciency principles will be taken up one by one in chapters which fol- 
 low and each investigated as closely as possible. Afterward they 
 will be considered to some extent in combination. 
 
 EXERCISE 1 
 
 Determine the degree of efficiency in each of the folloAving cases: 
 
 1. A farmer expended $2000 in raising a crop of corn and received $2800 
 for the crop. 
 
 2. A farmer spends $1200 in raising a crop of wheat and receives but 
 $1000 for the crop. 
 
 3. Land which should yield 80 bushels of corn per acre is producing but 
 56 bushels per acre. 
 
 4. By an expenditure of $800, 2,200 bushels of potatoes which sold for 
 80 cents a bushel were produced. 
 
 5. A machine capable of 400 revolutions per minute is making 250 revolu- 
 tions per minute. 
 
 6. It has been estimated that ten square miles of land used for hunting 
 and fishing will support 2 persons, while the same land when used agricultur- 
 ally will support 1000 persons. 
 
 7. In a certain town the light given by a 16 candle power carbon bulb 
 costs Ya cents per hour, while that given by a 32 candle power tungsten 
 bulb costs V 2 cent per hour. 
 
 8. On one field an expenditure of $800 produced a yield of 2000 bushels 
 of potatoes, and on another field $1200 produced 4200 bushels. 
 
 9. A field which, by following the best available methods, could have been 
 planted in 8 days, was aotually planted in 10 days. 
 
 10. It costs $4000 per annum to run a certain poultry establishment, and 
 the annual receipts average $4800. 
 
 11. A man who should work 8 hours per day, on account of ill health works 
 on the average 2 hours and 15 minutes per day. 
 
 12. A gold mine which cost $400,000 at first paid 8 per cent dividends, but 
 later when operated by improved methods paid dividends of 20 per cent. 
 
 13. Between the years 1840 and 1900 the per cent of sugar in the sugar 
 beet was increased from sVz to 13. 
 
 14. When coke is burned directly, 45 per cent of its energy is utilized. If 
 it is converted into water gas before it is consumed, 82 per cent of its 
 energy is utilized. 
 
12 SOURCES OF EFFICIENCY 
 
 15. At one time 61 hours of labor by one man were necessary to cultivate 
 one acre of wheat. At the present time this number of hours has been 
 reduced to 3. 
 
 16. When the Americans acquired the Philippine Islands, they found the 
 natives transporting mahogany logs at a certain place from the interior 
 to the seashore by such crude methods that it took 16 buffalos and 20 men 
 to transport one log a distance of one mile per day. An American taught 
 the Filipinos to suspend one end of a log from the axle of two large wheels, 
 and thus made it possible for 2 buffalos and 2 men to transport a log 
 20 miles in one day. If a day's work by a buffalo is taken as worth 50 cents, 
 and that by a man as worth the same, compute the efficiency of the second 
 process. 
 
 17. State which of the preceding instances are cases of relative efficiency. 
 Also which are cases of independent or absolute efficiency. 
 
 18. State which are cases of economy, and which O'f direct efficiency. 
 
 19. State which are cases of homogeneous and which of heterogeneous 
 efficiency. 
 
 Give an example of each of the following kinds of efficiency and determine 
 the degree of efficiency in each illustration given : 
 
 20. Economy 23. Homogeneous Efficiency 
 
 21. Direct Efficiency 24. Heterogeneous Efficiency 
 
 22. Relative Efficiency 25. Bogey Efficiency 
 
 26. Competitive Efficiency 
 
 27. Give an example of the transformation of a case of heterogeneous into 
 homogeneous efficiency. 
 
 28. At one time 40 hours of labor produced 2 tons of hay. Later 40 hours 
 of labor produced 20 tons of hay. Transform these statements so that 
 they shall express an economy instead of a direct efficiency. 
 
 29. At one time 100 hours of labor produced 48 bushels of oats. Later 
 by the use of improved methods 40 hours of labor were made to produce 
 180 bushels of oats. Transform these statements' so that the expenditure of 
 labor in the two cases is the same. Also so that the crop obtained is the 
 same. 
 
 30. Give an illustration of efficiency and transform it into an economy. 
 
 31. Give an illustration of economy and transform it into an efficiency. 
 
 Find the resultant degree of efficiency 
 
 32. In a process in which the efficiencies of the four constituent (tandem) 
 elements are 3, 2, 5, % respectively. 
 
 33. Are .60, .80, .90, .75 respectively. 
 
 34. Of a process where the five constituent (parallel) elements are 54, %, 
 Vz, 5-4, 5-2. 
 
 35. Where the three (parallel) elements are .60, .84, .72 respectively, and 
 the second and third elements each count twice as much as the first. 
 
DEFINITIONS 13 
 
 2.6. A metal cutting machine has been running 3% hours per day, and 
 making 18 revolutions per minute. If it should run 10 hours per day, 
 make 80 revolutions per minute, and use a cutting point 6 times wider than 
 that in use, how many fold would the efficiency of the machine be increased? 
 
 2.7. A farmer raises four crops with efficiencies of .Go, .80, .70, .50. If the 
 second and third crops are each twice, and the last three times as valuable 
 as the first, find his average efficiency for the year. 
 
 38. Give a numerical illustration of resultant efficiency composed of tandem 
 elements. 
 
 39. Also of one of parallel elements. 
 
 40. Also of one containing both tandem and parallel elements. 
 
 41. Ascertain the methods of judging milk cattle, horses, and a corn stalk 
 with ears, and determine whether each of these is a case of tandem or of 
 parallel efficiency. 
 
 42. By using an auxiliary instance in which the result equals the cost, 
 show that each case of absolute or independent efficiency may be regarded 
 as a case of relative efficiency. 
 
 43. Ascertain the original meaning of the word economy. Is this word 
 ever used in its original or some similar sense? 
 
 44. Give an example of infinite negative efficiency. 
 
 45. Give an illustration of a process which is efficient when judged by one 
 standard but is waste or loss when judged by another. 
 
 46. Give an illustration of reciprocal efficiency. 
 
 47. On a certain field 80 days labor by one man will produce a yield of 
 300 bushels of corn, while 90 days labor will produce a yield of 400 bushels. 
 Which method of cultivation is the more efficient and how much? 
 
 48. Which is the more fundamental test of efficiency in raising a given 
 crop in a given country, the yield per acre, or that per workman? Give 
 reasons for your answer. 
 
 49. Explain the meaning of the proverb "Strength saved is strength made." 
 Also of "Economy is wealth." 
 
 State the kind or kinds of efficiency involved in each of the following 
 instances; also compute the degree of efficiency wherever possible: 
 
 50. The office expenses of a given business were $2750 annually. After the 
 introduction of the card and loose leaf ledger system of keeping accounts, 
 the annual office expenses were reduced to $1600. 
 
 51. In Watt's steam engine 1/25 of the energy in coal was utilized. In 
 some modern steam engines 1/6 of this energy is utilized. 
 
 52. The employment in a productive way of capital which has been lying idle. 
 
 53. The efficiency of a given process should be 3/2 but is actually only 5/4. 
 
 54. By changing the seed used a farmer increased the yield of wheat per 
 acre on a given farm from 20 bushels to 24 bushels. 
 
 55. A series of separate pictures on a moving picture film when thrown 
 on the screen in succession gives the impression of a continuous whole. 
 
 56. By an expenditure of $20,000, gold worth $800 was obtained from 
 sea water. 
 
i 4 SOURCES OF EFFICIENCY 
 
 57. A given amount of grain and fodder when fed to beef cattle will 
 produce 4000 lbs. of beef, but when fed to milch cows will produce milk 
 which is equivalent in food value to 18,000 lbs. of beef. 
 
 58. Reciprocating steam engines on the average consume 4V2 lbs. of 
 coal per horse power per hour; turbine engines, 1 54 lbs. ; gas engines, i*/i lbs. 
 
 59. In a certain city the expenditure of $1,500,000 for a water filtration plant 
 reduced the annual death rate from 22 per thousand to 18 per thousand. 
 
 60. In fattening a beef steer it was found that the first 100 pounds of 
 increased weight in the animal were produced by 730 pounds of grain used as 
 food, and the last 100 pounds of weight required 1000 pounds of grain food. 
 
 61. The efficiency of a given business firm in buying is .80, in manufacturing 
 is .95, and in selling is .90. 
 
 62. The use of an improved textbook in a given school caused 30 per cent 
 more of the pupils to pass in the subject taught and saved the teacher much 
 time and effort. 
 
 63. On a certain railroad when operated by steam 90 lbs. of coal on the 
 average were burned to send a train of cars a distance of one mile. After 
 the railroad was electrified 50 lbs. of coal did this work. 
 
 64. In a certain year 9,000,000 agricultural workers in the United States 
 produced 600,000,000 bushels of wheat, while in Europe 6o,ooc,ooo farm 
 laborers produced 1,200,000,000 bushels of wheat. 
 
 65. In a certain neighborhood one farmer by spending $2,000 produces crops 
 worth $4,000. Another farmer by spending $2,000 produces $3,000. Com- 
 pute the absolute efficiency for each farmer. Also compute the relative 
 efficiency of the second farmer as compared with the first. 
 
CHAPTER II 
 
 REUSE 
 
 Illustrations of Reuse 
 
 A cook who has succeeded in inventing a new recipe frequently 
 saves herself much labor by preserving this recipe and using it 
 repeatedly. Often also the cook does mankind a service by giving 
 the recipe to other cooks to use. Similarly a man who has made a 
 successful speech may at times save himself much work by writing 
 out the speech and using it in whole or in part on other occasions. 
 
 The automobile is possible because the gas engine, the pneumatic 
 tire, and ball bearings, all invented in some other connection, have 
 been reused in combined form to produce the motor carriage. The 
 commission form of city government originated in Galveston after 
 the city had been devastated by a severe storm, and has since been 
 adopted by hundreds of other cities. 
 
 If we go back far enough in human history we find a primitive 
 manlike creature who' had been in the habit of picking up from 
 time to time any club that chanced in his way, and of using it as an 
 aid in killing wild animals for food. To this progenitor of man it 
 occurred at some time to keep a good club which he had found that 
 he might use it again and thus save himself the labor of searching 
 for other clubs. This act of his lifted his life to a new level of 
 efficiency and indeed constituted a distinct epoch in human progress. 
 
 For in this act and in the other instances given above we have 
 illustrations of a primary and fundamental principle of efficiency 
 which we may term reuse or repeated use. This is the first of the 
 specific efficiency principles which we shall study. 
 
 CLASSIFICATION 
 
 Cases of repeated use may be classified according to the character 
 of the objects which are used over and over again. 
 
 Classification according to Materials Reused 
 
 Material inorganic objects may be reused. Instances are the 
 repeated use of a spade, a gun, or a silver coin; of ammonia when 
 
 i5 
 
l6 SOURCES OF EFFICIENCY 
 
 used over and over again in an ice-making machine ; or of sea water, 
 which by being reoxygenated is used repeatedly in a vivarium, the 
 expense of obtaining a new supply of sea water each day being there- 
 by avoided. The basis of civilization is the soil which has been 
 cleared so that it can be reused in raising crops in successive years 
 and which, in advanced methods of cultivation, will even produce six 
 or seven crops in one season. Similarly all the material objects 
 which enter into the formation of tools and machinery, including 
 large objects like buildings, are reused. A noticeable case is the 
 reuse of a mold or pattern in manufacturing metallic objects. 
 
 Living organic objects are frequently reused in whole or part. 
 The amoeba improvises an arm or mouth out of its substance when 
 opportunity or need arises for the use of such a member. But 
 higher animals have organs and members which are grown once for 
 all and then reused. This repeated use often includes not merely 
 reuse for one given purpose but in many different ways. Thus the 
 human hand is used repeatedly not merely for the purpose of 
 grasping a specified object many times in succession, but as an 
 instrument by which to strike, push, pull, write, swim, gesture, give, 
 and to perform a variety of other acts. 
 
 The advantage in using domesticated animals instead of living 
 by the chase is largely the gain which comes from reuse. Thus if 
 a wild animal is killed and eaten it is used but once. Whereas if it 
 is kept and milked, or used as a beast of burden, or in breeding 
 other animals, it is used many times in succession. A similar ad- 
 vantage led to the change from torturing and killing men captured 
 in war, to keeping them as slaves. 
 
 In fact a high degree of social organization means that the mem- 
 bers of society are using and reusing each other in many ways daily. 
 
 Reuse of more Abstract Data » 
 
 Mental data are also capable of reuse. Thus by the aid of 
 memory and imagination, we reuse perceptions, feelings, and con- 
 cepts. We are thereby saved the labor of acquiring these data anew, 
 and, what is often of even greater importance, acquire a surplus 
 mental energy which we can use for higher purposes. An adequate 
 analysis would also show that we reuse mental data by means of the 
 reasoning faculty and by unconscious habit. One great source of 
 gain in doing work that is consecutive rather than broken and 
 fragmentary work is that in the former the initial act of the will 
 
REUSE 17 
 
 which starts a piece of consecutive work does not need to be 
 repeated but is, so to speak, used repeatedly and continuously till 
 the work is ended. Also in the process termed apperception, new 
 phenomena and experiences are stated in terms of the concepts 
 or units of knowledge which are already in the mind; that is, 
 the latter units are reused and the process of learning is thereby 
 economized. 
 
 Similarly the perceptions, feelings, thoughts, and ideas of other 
 persons may be reused by an individual. The volitions of the 
 teacher are reused by a class ; those of a general by an army ; and 
 those of any pace maker or leader by his followers. 
 
 Also larger, more objective and complex mental products may be 
 and are reused with fruitages correspondingly large and high in 
 the scale of values. Thus experience, education, theories, hypothe- 
 ses, and systems of thought of all kinds may be reused by different 
 individuals in a great variety of ways. For instance the alphabet 
 has been used by many nations and generations besides its inventors ; 
 and for many purposes which its inventors did not intend, as in 
 lettering diagrams in mathematics, or in expressing systems of 
 classification in science and logic. 
 
 In certain aspects work or energy can be reused. The savage in 
 using the same club repeatedly, reuses not only the object itself but 
 also the work done in searching for the club and in shaping it. This 
 principle applies in the reuse of all tools, machinery, and systems 
 of thought; to the imitation of other persons and the copying of 
 their work. In setting timepieces we reuse the work of the astrono- 
 mer who has accurately determined the time of day. In riding on 
 a railroad we reuse the work of the engineers and laborers who 
 constructed the road. Civil law is based on the reuse of precedents. 
 
 The Fuegians observed by Darwin kept the time of day, not by a 
 clock, but by having that old man in their midst in whom the 
 natural sense of time measurement was most accurate, strike a bell 
 at what he judged to be equal intervals. In this way the Fuegians 
 reused the work of nature in endowing this man with peculiar facul- 
 ties and his own work in developing these faculties. Similarly in 
 reusing various inventions we reuse the toil, or genius, or both, 
 which have made these discoveries and inventions possible. The 
 data thus reused become very extensive and complicated when traced 
 back in all their ramifications. 
 
18 SOURCES OF EFFICIENCY 
 
 Limitations in Reuse of Objects 
 
 It should be noted in this connection that not all objects can be 
 reused, nor can every object be reused in all ways. If a material 
 object has been once used and afterward has become inaccessible in 
 time or space, it cannot then be reused. Certain objects may be too 
 large, or too small, or otherwise unfit for reuse of a given kind. 
 Also an object which has been worn out, lost, or destroyed cannot 
 be used again. A ton of coal cannot be burned a second time. A 
 system may be beyond the comprehension of the person who seeks 
 to reuse it. In other words, the repeated use of things is often 
 prevented by subjective limitations in the user as well as by objective 
 limitations in the things themselves. This matter will be discussed 
 more fully in Chapter XV (p. 265). 
 
 Numerical Forms of Reuse 
 
 Instances of reuse may also be classified according to individual 
 forms in which they occur. 
 
 Thus certain cases of reuse may be characterized by a numerical 
 element prominent in them. For instance if a single object is 
 reused, the case may be described as unitary. Similarly if two, 
 three, or any number of data (denoted as n data) are reused in a 
 given case, the process involved may be termed dual, triple, or 
 n-fold reuse. Also, if a given object is reused one, two, or n times, 
 the corresponding processes may be denominated by a similar set 
 of numerical terms. 
 
 An important special case under this head may be termed dual 
 reciprocal reuse. As an illustration we have the fact that a hunter 
 reuses the power of smell in his dog, while the dog in effect reuses 
 the superior powers of vision and reasoning in the hunter. Each 
 blade of a pair of scissors reuses the other. Each of two friends 
 or two partners in any enterprise repeatedly uses the other. 
 
 If this method of reuse be extended to any number of agents 
 (that is, to n agents) it becomes what may be termed w-reciprocal 
 reuse. Thus a set of salesmen may all reuse the special devices 
 invented by any one of the set. So in any good organization, system, 
 society, or corporation, all the parts and members reuse the good or 
 virtue in any one part or member. 
 
REUSE 19 
 
 Spatial Forms of Reuse 
 
 Cases of reuse may also be characterized by some spatial or 
 quantitative element prominent in them. For example different 
 kinds of reuse may be local or comprehensive. A process or datum 
 may be reused in a near field as when the spectroscope is applied to 
 a new chemical substance in the laboratory ; or in a remote field, as 
 when the spectroscope is used in studying the stars. So a case of 
 reuse may be characterized by the transfer of the reused material 
 from a large domain to a small one, as when we use our knowledge 
 of the solar system in explaining the constitution of a molecule; or 
 vice versa. 
 
 Cases of reuse may also be described as one, two, or three 
 dimensional. For instance, a travelling crane moves back and forth 
 in a line (that is, along a beam), and is usable in its various posi- 
 tions. Hence this may be described as a case of linear reuse. 
 Similarly we have cases of circular and spiral reuse, or reuse ex- 
 panding from a point in a fanshaped, conical, or spherical way. 
 
 Marginal Reuse 
 
 Certain forms of the efficiency process under discussion may be 
 termed partial, differential, or marginal reuse. Thus if an engineer 
 should want to measure the distance from Washington to Albany, 
 and he already knew the distance from Washington to New York, 
 he could save himself labor by reusing his knowledge of the distance 
 from Washington to New York, and measuring only the distance 
 from New York to Albany. Similarly the astronomer diminishes 
 the work of determining the position of many stars and other bodies 
 on the celestial sphere by first measuring once for all with great 
 accuracy the position of certain fundamental stars, and then measur- 
 ing the distance of other objects from these primary stars. In doing 
 a large amount of work in this way the astronomer obviously reuses 
 many times the work done on the fundamental stars. 
 
 Similarly in the mastery and reuse of certain representative types 
 of organisms in biology, or of symbolisms in art, or of minds in 
 psychology, we are applying that principle of efficiency which we 
 have termed marginal or variant reuse. We have an even more 
 important case of it in the mastery and use of fundamental princi- 
 ples in ethics, religion, logic, and philosophy, and then applying 
 with slight variations this knowledge in various special fields. 
 
 In forming the plural of a word by annexing the letter s (see 
 
20 SOURCES OF EFFICIENCY 
 
 apples as formed from apple) instead of forming an entirely new 
 word, we save labor by means of marginal reuse. The same eco- 
 nomic principle is at work in the use of the various suffixes, prefixes, 
 and other modifiers of words employed in language. 
 
 An application of this principle in another field is found in the 
 use of the so-called universal machine; that is, a machine which 
 by slight modifications of its fundamental framework or of its 
 details, may be made to do the work of a variety of distinct 
 machines. A simple instance of like nature is the use of one brace 
 and a number of bits instead of several augers. A similar case is 
 the use of one tug boat and a number of barges instead of several 
 steamboats. In a steamboat the engine must be idle while the boat 
 is being loaded or unloaded; but in a tug boat the engine may be 
 kept in almost constant use in moving some barges while others are 
 loading or unloading. Hence one engine in a tug boat takes the 
 place of several engines in steamboats, or is relatively reused. If all 
 the bits mentioned above as used with a brace are replaced by a 
 single adjustable bit, the case becomes one of marginal reuse of 
 the second order. An important special case of marginal reuse is 
 what may be termed repair reuse. An instance of this is replacing 
 a broken mainspring in a watch by a new mainspring instead of 
 buying a new watch ; or having a pair of shoes half-soled instead of 
 buying a new pair. 
 
 Temporal Forms of Reuse 
 
 With respect to the category of time cases of reuse may be 
 characterized in a number of ways, as for instance by the adjectives 
 temporary or permanent. The most important special case in this 
 connection is what may be termed prophetic or anticipative reuse. 
 Thus if a man sees a small leak in a dam and stops it at once by 
 wheeling a small barrow of dirt to it, his work is reused in the sense 
 that it is a substitute for the much greater labor of rebuilding the 
 dam after it has been swept away. Similarly we have the proverb 
 that a stitch in time saves nine. What is called preventive medicine 
 is an instance of the same sort of efficiency. In fact a large part of 
 the virtue in farsightedness, forehandedness, and all wise planning 
 is of the same kind. So also care in laying a good foundation, or in 
 making a good start, partakes of the nature of prophetic reuse. 
 
REUSE 21 
 
 Other Special Forms of Reuse 
 
 Space and time together give rise to the idea of motion and order, 
 and to corresponding classes of reuse. Thus in the case of a travel- 
 ling library, the motion of the books is the means of their repeated 
 use, and the reuse involved may be described as motional. 
 
 Reuse obtained by means of the idea of order is illustrated by 
 the repeated use of a road obtained by travelling over the road in 
 opposite directions, or by the temporary conversion of a dynamo 
 into an electric motor by simply reversing its action. 
 
 When a given object or idea is propagated, spreads, or grows, the 
 element of force enters into the case in a special way. Cases of 
 this kind may perhaps be denominated as growth reuse. 
 
 With respect to the category of quality, instances of reuse may 
 be characterized, for example, as homogeneous or heterogeneous. 
 Thus a certain method of bracing the framework of bridges having 
 been invented, so long as it was reused in this kind of work only, it 
 constituted a case of homogeneous reuse. When it was later used 
 in making the framework of freight cars, it became a case of hetero- 
 geneous reuse. Almost all schoolhouses were originally built as 
 places to be used exclusively for the training of children. Recently 
 many such buildings have come to be used by adults also for various 
 social and cultural purposes, this latter application being a case of 
 heterogeneous reuse. Mr. Westinghouse having invented a system 
 of economical transmission of gas by high pressure mains, reused 
 this principle in devising an economical method of transmitting 
 electricity by means of high voltages on the principal wires. This 
 also is evidently a case of heterogeneous reuse. 
 
 Heterogeneous reuse may also be regarded as a kind of qualitative 
 marginal reuse. 
 
 Negative Reuse 
 
 In this connection should be mentioned what may be termed 
 negative reuse. An instance of this is learning from the results of a 
 mistake not to repeat the error. Another form of negative reuse is 
 that in which, having learned an exclusive property of an object or 
 group of objects, we infer the opposite or negative of this property 
 for other objects. This form of reuse is useful in some varieties 
 of proof, in detective work, and in certain kinds of scientific in- 
 vestigation. 
 
22 SOURCES OF EFFICIENCY 
 
 Scales of Reuse 
 
 It is also important to observe that species of reuse may be 
 arranged according to a certain scale of value. Thus the reuse of 
 one's powers of invention and discovery is a higher kind of effi- 
 ciency than copying or imitating the work of another person directly. 
 When fire was first discovered, it was an economy for man to reuse 
 it by keeping it from going out and by transferring it from place to 
 place. But later, noticeably after the invention of the lucifer match, 
 man substituted for the reuse of fire once made, the higher reuse of 
 work done by the inventor of the match and by other scientific work- 
 ers. A still more general case of highly important repeated use is 
 reuse of reuse. Thus when a farmer after reusing the methods of a 
 government expert in raising corn and finding them profitable, 
 later reuses the methods of other experts in raising cotton, wheat, 
 clover, etc., he practises reuse of reuse, or reuse of the second order. 
 In general, from our point of view, repeated use of the primal agen- 
 cies of efficiency now under investigation is reuse of the highest 
 order. 
 
 Obscure Cases 
 
 Certain cases of more or less obscure reuse should be mentioned. 
 These are illustrated by the action of enzymes and catalysts in 
 chemistry. For example the presence of a plate of platinum greatly 
 accelerates the combination of oxygen and hydrogen to form water. 
 This action takes place without any noticeable change in the plat- 
 inum plate. Hence the plate can be reused indefinitely for the pur- 
 pose mentioned. The fact is plain but the nature of the process 
 involved is obscure. Other cases of like nature are regarded as less 
 obscure only because they are more familiar. In this connection may 
 be mentioned the repetition in nature of like forms such as atoms, 
 molecules, cells, crystals, and organisms, and of the qualities of 
 parents in their offspring, often after a number of generations in 
 which the given qualities have not been present. 
 
 Another case of partially obscure reuse is that which is often 
 called influence. Examples of this are the effect of a large and 
 efficient army in preserving peace, of a reserve of capital in pre- 
 venting a panic, or many of the changes wrought in a community 
 by the mere presence in it of a strong personality. 
 
REUSE 
 
 23 
 
 Complex and other Forms of Reuse 
 
 Other species of reuse might be characterized as conscious or 
 unconscious, swift or slow, feeble, automatic, or irresistible, but it 
 does not seem necessary to examine these and like cases in detail. 
 In concluding the topic of classification of cases of reuse, special 
 mention should be made of compound and complex forms. An 
 illustration is the case of a soldier discharging his gun. In doing 
 so he reuses the metal in the gun, the wisdom of his general, the 
 work of scouts and officers, the work of drill, and the labor of 
 men who invented the use of metals and gunpowder, and much 
 more implied by these items and also outside of them. An even 
 more complex case is the reuse of western civilization, for instance,, 
 by the Japanese. Looked at from another point of view, a single 
 act of reuse may involve not only the repeated use of many differ- 
 ent objects and kinds of work, but also a variety of forms of reuse,, 
 as those which have been named plural, prophetic, fanshaped, 
 heterogeneous, and unconscious. 
 
 ADVANTAGES IN REUSE 
 
 Economics due to Reuse 
 
 We shall next consider the advantages in reuse as a source of 
 efficiency. Some of these benefits are so obvious as to need no ex- 
 tended discussion. Among these are economy of material, and 
 hence of money and other resources. Thus if a manufacturer 
 instead of building an additional factory uses his old factory by 
 night as well as by day, he saves the cost of the new building, of 
 ground on which to place it, of taxes, repairs, watchmen, and 
 insurance. 
 
 In like manner repeated use means a saving of time and strength, 
 and thus, in effect, gives new strength, and lengthens and enlarges, 
 life. 
 
 Added Power 
 
 Other advantages, not always so obvious as the above, often ap- 
 pear in connection with reuse. Thus economy of resources sets 
 free certain powers, often higher powers, in the reuser, to be em- 
 ployed in more efficient ways than reuse itself. These methods wilt 
 be indicated more definitely in later chapters. 
 
2 4 SOURCES OF EFFICIENCY 
 
 Infinite Value in Reuse 
 
 Special mention should be made of the absolute, or relatively 
 infinite gain which sometimes results from reuse, as when it enables 
 a person to overcome an otherwise insuperable difficulty. Thus if a 
 man wishes to carry to the top of a hill a rock which is too large for 
 him to manage as a whole, he may often accomplish his purpose by 
 breaking the rock to pieces and carrying it up the hill piecemeal by 
 reuse of his powers. Similarly, the lever, pulley, inclined plane, 
 and like mechanical devices often enable us to achieve otherwise 
 impossible results. A realization of the general value of this princi- 
 ple of efficiency is expressed in the proverb "Divide and conquer". 
 
 Other Values 
 
 In some cases reuse gives beneficial results which are obvious but 
 which are difficult fully to analyze, either on account of their com- 
 plexity or for other reasons. Thus reuse of a scaffolding in a 
 sense produces the building. The inertia or persistence reuse of 
 each of a set of pictures on the retina or in the brain gives the 
 result called the moving picture. 
 
 As a more abstract illustration of the species of efficiency function 
 under consideration we have the method of proof called mathemat- 
 ical induction. In this form of proof, a unit step of reasoning is 
 first demonstrated, and then reused an unlimited number of times, 
 and a final result thus obtained, often apparently not demonstrable 
 in any other way. 
 
 Reuse Greater in Higher Organisms 
 
 It may be well also to look at the advantages of reuse in a 
 collective, historical, and, in a sense, pictorial way. 
 
 If we examine the forms of animal life, as we proceed from lower 
 to higher forms, we find a progressive increase in the amount of 
 reuse and in the elevation of the character of reuse. In fact the 
 extent and quality of repeated use practised by an organism may be 
 said to form a measure or test of the place of the organism in the 
 scale of life. 
 
 Thus if we first consider subjective reuse, that is, the reuse of 
 parts or members of itself by an object, we find that a lower 
 organism such as the amoeba, while it of course reuses its own 
 substance, often does not reuse forms or structures of this substance. 
 
REUSE 25 
 
 On the contrary, as has been already pointed out, it improvises a 
 new arm or mouth whenever the need for such arises. On the 
 other hand, it is the rule for a higher organism to reuse its limbs 
 and organs. In man this reuse of the physique or body is sur- 
 rounded by and included in a still higher class of reuse, viz. : that 
 of certain mental powers. 
 
 If we next consider objective reuse, that is, the reuse by an 
 organism of objects outside of itself, we find that the same law 
 holds ; that is, the higher the organism in the scale of life, the more 
 extended in both time and space is the reuse practised by it, and the 
 higher is the order of this reuse. Thus the spider reuses its web 
 for but a few days. Man reuses his houses and railroads for many 
 years; and he reuses systems and theories which are entirely above 
 and beyond the world of the spider and of lower organisms in 
 general. 
 
 High Degree of Reuse in Great Men 
 
 We find also that the greatest men and the greatest nations have 
 been the greatest reusers. Newton said he had been able to accom- 
 plish what he did because he stood on the shoulders of giants. 
 Shakespeare freely reused the forms of ancient art, plots and 
 stories, preceding philosophies as summed up by Montaigne, Chris- 
 tianity, and all the current thought and discoveries of his own age. 
 In fact it has been laid down as a law that "men of the largest 
 original power make the most use of the results obtained by other 
 men". 
 
 What we regard as the sudden and miraculous manifestations 
 of genius are often, and perhaps always in some respect, the unob- 
 served accumulations of acts of reuse. Thus the marvellous pro- 
 ducts of Greek sculpture were in large part due to many generations 
 of Greek workmen and artists, each generation using what the pre- 
 ceding ones had learned, and each adding its own contribution to 
 artistic tradition. 
 
 Departments of Knowledge Based on Reuse 
 
 If we look at the matter from another point of view, each depart- 
 ment of human activity or thought is found to have at its foun- 
 dation certain elements or units which are reused in certain 
 characteristic and systematic ways. The fruitage of the entire body 
 of reuse in each case is so great as to make it an advantage to mark 
 
26 SOURCES OF EFFICIENCY 
 
 off each aggregate and its possible future developments, as a 
 separate domain of knowledge or life. 
 
 For instance, the existence of trigonometry as a distinct branch 
 of mathematics is due to the fact that certain men once calculated 
 certain numerical tables, and that other men in using these tables 
 have reused and got for nothing the work done by these computers. 
 Also the tables having been computed, men using them found it an 
 advantage to give characteristic names to the functions represented 
 in the tables, later to denote these functions by specific symbols, and 
 by the aid of these symbols to build up an extensive system of rela- 
 tions among the concepts thus treated. In a word, a simple system 
 of reuse developed into an extensive yet definite domain of economic 
 and efficient relations. 
 
 In this connection it should be noted that every great invention 
 or idea, almost without exception, at first occurred to its originator 
 in some special or individual form, and was afterward developed by 
 various kinds of reuse into a more general form. 
 
 Functional Foremen 
 
 At present in many lines of business the realization of the value of 
 reuse is increasing. Thus in F. W. Taylor's system of conducting 
 business, called scientific management, it is proposed to observe or 
 work out the best method of performing every item of work, and to 
 have so-called functional foremen appointed so that by them each 
 workman can be thoroughly instructed in the methods thus worked 
 out. 
 
 Loss due to Absence of Reuse 
 
 Another method by which to grasp the importance of the princi- 
 ple of reuse in human life is to try to realize what existence would 
 become if this method of obtaining results were eliminated. Thus, 
 in the individual life, actions like walking, breathing, and the use 
 of memory would cease. In the relations of individuals, a large part 
 of what goes by the name of co-operation, as well as all use of the 
 work done by one's predecessors, expanding as it does into a remote 
 past, would be cancelled. 
 
 As we study other primal efficiency principles in succeeding chap- 
 ters, we shall find that reuse has additional important uses in con- 
 nection with these principles. 
 
REUSE 27 
 
 Definition of Reuse 
 
 It may be well at this point to define the term reuse as clearly as 
 possible. 
 
 To use an object means to combine the given object with other 
 objects so as to produce results of value (a surplusage or positive 
 non-equivalence: see Chapter IX, p. 152). 
 
 To reuse an object means to repeat the process of use in whole 
 or part. 
 
 METHODS OF APPLICATION 
 
 We shall now consider the most efficient methods of applying the 
 principle of reuse. 
 
 Vast Number of Species of Reuse 
 
 In order to reap the largest possible benefit from the employment 
 of this principle of efficiency it is important to consider it first with 
 reference to the category of number; that is, to realize 
 
 ( 1 ) The vast number of objects and entities which may be reused ; 
 
 (2) The vast variety of forms which each species of reuse may 
 
 assume; 
 
 (3) The great number of elements which may enter into a seem- 
 
 ingly simple act of reuse. 
 
 A mastery of the category of space also aids in the extended and 
 improved use of the principle of efficiency under consideration. 
 For instance such mastery aids in learning to reuse data in widely 
 separated domains ; in realizing the various spatial ways in which 
 reuse may spread; and in determining which of these forms will 
 be most effective in a given case. 
 
 Possible Extent of Reuse 
 
 It is also important in this connection to realize the extent to 
 which reuse may be carried. Thus, in the department of scientific 
 work alone, it is estimated that 10,000 men of substantial ability are 
 at work making original researches, and that each volume of a 
 scientific journal contains the results of 100,000 brain-power hours 
 of work. All of these results are available for each and every 
 worker as material of reuse. 
 
28 SOURCES OF EFFICIENCY 
 
 Reuse increased by Auxiliary Objects 
 
 Of high importance also is the study of the use of auxiliary ob- 
 jects in connection with reuse (see Chapter VII, p. in). Thus 
 paper, ink, and language, as used in making permanent records of 
 otherwise transitory material, are important aids in the reuse of 
 ideas and experience. Buildings in which books can be stored are 
 a farther aid to the extended reuse of the facts and ideas recorded 
 in books. If the books are occasionally sent out in travelling libra- 
 ries, railroads and the forces which operate railroads may also be 
 regarded as agencies auxiliary to repeated use. Paint on a house 
 preserves the house and thus leads to the continued use of the house 
 long after it would otherwise have perished. A servant by means of 
 a letter is enabled to reuse or get advantage from work done in a 
 previous situation. Photographs are aids to reuse in many evident 
 ways. 
 
 A more abstract form of auxiliary entity is an extended view of 
 things as an aid in selecting the best material or devising the most 
 efficient units and methods of reuse in a given case. A wide outlook 
 gives a greater variety of material to select from, and thus opens 
 the way to the utilization of more efficient data and methods of 
 reuse. 
 
 By the use of auxiliaries certain limitations in reuse may often 
 be overcome. Thus a ton of coal cannot be burned a second time, 
 but the heat generated in burning the coal may be used to make 
 a machine which may be reused many times, or to sustain a think- 
 ing person whose thought product may be reused and expanded 
 indefinitely. 
 
 Reuse of the Best Materials 
 
 This leads us to the question as to what are the most efficient 
 kinds of reuse. Many elements enter into a solution of this problem. 
 We can here mention only a few of the more important. Among 
 the best data for reuse purposes are those which are most accurate, 
 have been most thoroughly tested, or are most finished or perfected 
 in any way. In other words, whatever we do or make it pays to do 
 in such a way that the results obtained shall be reusable. Hence the 
 proverb that whatever is worth doing at all is worth doing well, here 
 receives a new illumination. Thus the best plays, like Shakespeare's, 
 are reused most extensively, especially if we consider the higher 
 quality of the hearers of such plays and the large amount of indirect 
 
REUSE 29 
 
 reuse that follows from this fact. The best books live and continue 
 to be reused ; so of the best scientific work, political work, and work 
 of any kind. 
 
 If a work of art be of a high order, it will be reused not only 
 frequently but in a great variety of ways as by copies, photographs, 
 and variations. The same law holds for any unusually meritorious 
 product. Such work will also be reused with great speed and ease. 
 The Arabic system of Arithmetic was introduced into Europe about 
 the year 1200 A.D. It was so superior to the Roman system that, 
 notwithstanding the primitive state of culture of that time, it spread 
 rapidly and practically without opposition from land to land. So 
 smooth and rapid was the transition that it is almost impossible to 
 trace its stages. 
 
 To give a negative illustration of the principle under discussion, 
 the Chinese alphabet is so crude and the characters composing it 
 capable of so little reuse and therefore so numerous that it is esti- 
 mated that a Chinese compositor walks 20 miles a day in setting up 
 type, while a compositor in the English language may remain in a 
 practically stationary position. 
 
 Highest Forms of Reuse 
 
 The most efficient cases of reuse imply not only material but also 
 forms of a high order. Thus imitation is usually a low form of re- 
 peated use and often detrimental in many of its results, while 
 prophetic reuse is almost invariably highly valuable. Reuse of reuse 
 is also one of the highest forms of this source of efficiency. For 
 example, if a particular instance of reuse of any kind has been 
 observed, it is frequently a highly efficient process to reuse this 
 reuse in other domains. Thus after it had been observed that 
 germs of certain diseases travelled by the reuse of the motion of one 
 insect, as the mosquito, it might at once have been inferred that other 
 germs travel by other insects as ticks, fleas, and flies, and investi- 
 gations made accordingly. 
 
 Often it is profitable to start with a low order of reuse and de- 
 velop it step by step into a higher order. Thus in teaching geogra- 
 phy it is usually best to have the pupil begin with the study of his 
 local surroundings and to reuse these till he forms general concep- 
 tions of the earth as a whole which he can then reuse deductively. 
 So in general it is often well to begin with psychological or inductive 
 reuse and develop it into the more rapid and powerful logical and 
 deductive reuse. 
 
30 
 
 SOURCES OF EFFICIENCY 
 
 Limitations in Reuse 
 
 Of highest importance in the practical application of reuse is the 
 study of the limitations connected with it. Every source of effi- 
 ciency is hedged in by characteristic restrictions. Thus in the case 
 in hand the materials capable of reuse are limited in certain ways 
 some of which have been indicated on a previous page. Similarly 
 the forms of reuse are limited. More specifically, a given material 
 is capable of only certain special forms of reuse. Also each form or 
 kind of reuse brings its own limitations. Repeated use is also 
 hedged in by certain deficiencies in the persons or agencies which 
 attempt to carry out the process involved. 
 
 Adaptation in the Application of Reuse 
 
 Hence in many cases much study is necessary in order to deter- 
 mine that particular species of reuse which it is most advantageous 
 to employ in a given case, or whether indeed it may not be better 
 to employ some other prime agent of efficiency. Thus imitation is 
 one of the simplest and easiest forms of reuse, but it often tends to 
 an atrophy of reuse processes of a higher kind, as of powers of 
 invention and discovery. Just as the tape worm, living directly on 
 another organism, has neither mouth nor digestive tract so the mere 
 imitator loses the powers of invention and initiative. 
 
 Herbert Spencer reused the principles of biology in the field 
 of psychology with good results, but when he applied the same 
 principles in sociology, the results were misleading rather than 
 illuminating. 
 
 Similarly different kinds of reuse wax in value or lapse into 
 danger with changing circumstances. Marginal reuse is particularly 
 variable in this respect. In a multitude of cases where its applica- 
 tion is possible, it is necessary to determine whether it will pay best 
 to repair an object or to procure a new one; that is, whether to 
 mend or end the object. 
 
 One of the best ways in which to avoid the limitations and evils 
 of reuse of a low order is to use such forms of reuse in combination 
 with reuse processes of higher order, or indeed with other of the 
 primal sources of efficiency. For example in undertaking any spe- 
 cific investigation it is of the utmost importance to learn at the 
 outset what other workers in the same line have accomplished. 
 These results can be reused with the utmost freedom and without 
 
REUSE 31 
 
 any ill effect (rather with multiplied benefit) if at the same time 
 we reuse our higher powers of invention and adaptation. 
 
 If we surround direct concrete reuse with other reuse of higher 
 orders, the more of the former the better. As a result of this free 
 combination of different orders of the principle in hand, many of 
 the processes involved will in time become automatic and instinctive 
 (and at the same time in a sense hyper-rational). 
 
 Ideal Species of Reuse 
 
 In conclusion it may be well to state that the final and inclusive 
 method of applying this principle is to reuse the most efficient mater- 
 ials in the most efficient way for the most efficient ends. In order 
 to reduce this ideal to definite form under any given circumstances 
 a knowledge of other primal principles as given in the chapters 
 which follow will be useful and, indeed, necessary. 
 
 Summary of Chapter 
 
 The substance of the preceding chapter may be summed up as 
 follows : The most primitive and, in a sense, fundamental source 
 of efficiency is the act of reuse or repetition. Reuse takes many 
 special forms, each of which has a wide variety of applications, both 
 in the daily detailed life of the individual, and in elaborate systems. 
 Among the most important individual forms of reuse are those 
 which have been termed marginal, prophetic, and reciprocal. 
 
 Reuse means not only economy of material and effort, but also 
 new and aggressive power. Often this new power is infinite or un- 
 limited in nature, in that it produces an advantageous result not 
 otherwise obtainable. The value of reuse is also shown by the fact 
 that the higher the organism, or the greater the man, the greater 
 is the power of reuse. So human progress in general is marked by 
 an increasing amount and by higher forms of reuse. 
 
 In order to obtain the utmost results in the application of reuse, 
 it is important to realize the vast number of possible species of 
 reuse, to select or devise the best adapted form in each application, 
 and to perfect every product of one's work so that it shall be 
 capable of the utmost reuse. The highest form of reuse is reuse 
 of the fundamental agencies of efficiency. 
 
32 SOURCES OF EFFICIENCY 
 
 EXERCISE 2 
 
 Give an example* of reuse of 
 
 I. An inorganic object 2. An idea 3. An act of volition 
 
 4. Name an object which cannot be reused in a specified way. 
 
 5. Give an example of dual reuse. 
 
 6. Of reuse indefinite with respect to the number of repetitions. 
 
 Give an illustration of each of the following species of reuse: 
 
 7. One dimensional 10. Reciprocal 13. Negative 
 
 8. Two dimensional 11. Prophetic 14. Obtained by motion 
 
 9. Marginal 12. Growth 
 
 15. Give two related cases of reuse one of which is of low and the other of 
 higher order. 
 
 Name the form of reuse in each of the following: 
 
 16. Killing weeds before they come up. 
 
 17. Use of a portable garage. 
 
 18. Of a bedroom bureau convertible into a writing desk. 
 
 19. Of the word apples as the plural of apple. 
 
 20. Of the results obtained at a government agriculture experiment station. 
 
 21. Symbiosis (or commensalism) in biology. 
 
 22. The law observed in old China that "if any official thinks that a custom 
 generally observed in his province might with advantage be used in the 
 while country" he is to send an account of it to the central government so 
 that it can be utilized by other provinces. 
 
 22>. A given Morris chair is adjustable at four different angles. Hence it 
 will take the place of how many different chairs so far as the resting of a 
 single person is concerned? 
 
 What is its degree of efficiency in this respect? 
 
 What form of reuse is involved in 'this instance? 
 
 24. A given pair of gloves when mended at a cost of 10 cents will last half 
 as long as a new pair which will cost $1.10. Determine the degree of efficiency 
 in mending and using the old pair. What form of reuse is here involved? 
 
 Give an illustration where reuse results in 
 
 25. Economy of material. 
 
 26. A saving of time and strength. 
 
 27- Attainment of a result otherwise impossible. 
 
 28. How is an envelope with a transparent front a means of reuse to a 
 business man? 
 
 29. State some of the advantages in a son's learning and following his 
 father's business. Some of the disadvantages. 
 
 30. Specify the different items and species of reuse involved in the use of 
 the graphophone. 
 
 * By "example", as thus called for, is meant one that is different from those 
 already cited in the text. 
 
REUSE 
 
 33 
 
 31. State the advantages in the use of a universal machine. The disad- 
 vantages. 
 
 32. Name the different kinds of reuse possible in a large corporation. How 
 do these differ from the forms of reuse possible in a private firm? 
 
 33. Give an example where reuse otherwise impossible is obtained by 
 means of an auxiliary object. 
 
 34. Give an instance where reuse produces loss of some kind. 
 
 35. A universal machine which occupies 40 square feet of floor space takes 
 the place of five other machines which would occupy 25, 30, 20, 18, and 32 
 square feet respectively. Compute the degree of space efficiency in using the 
 universal machine. 
 
 36. How many items of reuse occur in one application of the principle 
 "things equal to the same thing are equal to each other"? 
 
 37. Show in what way logical deduction from general facts is marginal 
 reuse. Illustrate. 
 
 38. Define imitation as a special form of reuse. 
 
 39. The solar calendar originated in Egypt. Trace the reuse of this 
 calendar. 
 
 40. Discuss the meaning and functions of analogy as a kind of reuse. 
 
CHAPTER III 
 
 THE UNIT AND ITS MULTIPLIER 
 
 Illustrations of Manifold Use 
 
 Efficiency is sometimes obtained by using an object many times 
 simultaneously instead of many times in succession. This process 
 differs from reuse in being manifold in space instead of manifold in 
 time. Thus if a book is taken from a library by several persons in 
 succession and read by each of them, the book is said to be reused. 
 But if the book is taken out but once and read aloud to a company 
 of people, we have a case of simultaneous manifold use, or, more 
 briefly, of manifold use. Other illustrations of simultaneous mani- 
 fold use are the publication of an article in several newspapers at 
 the same time by a press syndicate; the cutting of several coats or 
 other garments simultaneously by the use of a machine; duplex, or 
 sextuple telegraphy whereby a number of messages are sent over a 
 wire at the same time; the substitution of "James and John swam" 
 for "James swam and John swam", the word swam in the former, 
 expression being put to a double use. 
 
 Illustrations of Multuse 
 
 By combining the principle of successive use in time with that of 
 manifold use in space we arrive at a principle more general than 
 either of these efficiency processes, and including each of them as a 
 special case. Thus if a book is taken from a library repeatedly and 
 each time is read to a different audience, the use of the book is 
 manifold in both time and space, and we shall have what may be 
 termed multuse. Other illustrations of multuse are a speech re- 
 peated to several successive audiences ; a painting exhibited several 
 times and on each occasion viewed by a different and often changing 
 group of people; a school building used not merely for the instruc- 
 tion of children but for various social and cultural purposes on 
 successive occasions by the community as a whole ; the imitation of a 
 model farm or of a piece of model road by different sets of men; 
 the various uses of the alphabet after it had once been invented. 
 Evidently the list of such illustrations may be enlarged without 
 limit. 
 
 34 
 
UNIT AND MULTIPLIER 
 
 35 
 
 Manifold use and multuse are so similar to reuse that they do 
 not seem to need any special treatment apart from that given inci- 
 dentally in the remainder of this chapter. 
 
 Illustration of a Unit and its Multiplier 
 
 A still more comprehensive principle of efficiency than any that 
 has yet been mentioned is that of the unit and its multiplier. This 
 source of efficiency includes reuse, manifold use, and multuse, as 
 special cases, and also has characteristic efficiencies of its own. For 
 instance if the book mentioned above as taken from the library, 
 contains a certain important idea this idea may be regarded as a 
 unit. Then the number of uses of this idea by the reader of 
 the book, or which follow directly or indirectly from such reading, 
 may be regarded as the multiplier of the specified unit. This mode 
 of viewing the matter has the advantage of enabling us to drop for 
 the time being all the processes of transmission between the datum 
 and the result and freely to use the datum and its result in ways to 
 be pointed out later. 
 
 Other Advantages in the Unit and Multiplier 
 
 The unit used with a multiplier as a source of efficiency also has 
 certain other characteristic advantages. Thus both reuse and mult- 
 use include or imply the element of personality in two ways, (i) 
 They imply a user or actor. (2) They imply an aim or end, and a 
 person enjoying this aim or end when attained. In the idea of the 
 unit and multiplier we set aside, in a measure, this idea of person- 
 ality, and thus free ourselves from the caprices, limitations, and 
 various entanglements inherent in it. We are thus enabled, for 
 instance, to put in the forefront objective and quantitative elements, 
 and to shape and adjust these to meet given aims and needs. Also 
 we are set free to expand the application of a given case without 
 limit in many respects. In a word in the unit and multiplier we have 
 the category of multuse in a more general, objective, and manifold 
 form. 
 
 Looked at from another standpoint, in reuse the normal method 
 is to take the data material of reuse as we find them and to let the 
 methods and results of the process depend upon or follow from the 
 natural qualities of the material. But in the use of the unit and 
 multiplier we have much greater freedom. Because of the some- 
 what abstract nature of both the unit and multiplier we may often 
 
36 SOURCES OF EFFICIENCY 
 
 create more or less artificial units which will meet given ends or 
 needs in a more effective way than will natural data. Thus in a 
 primitive stage of human development, the length of the human 
 foot, or some other part of the human body as the arm or a finger, 
 was utilized in measurement reuse. In later and better systems 
 units such as the meter have been devised. These units are more 
 uniform than the former anatomical ones, and are better adapted in 
 many other ways to meet fundamental and far-reaching conditions 
 of life. Similarly the atom has been devised to give a certain kind 
 of control of the material universe, and electrical units to perfect 
 the use of electricity. In a word, in the processes of reuse, the 
 unit creates the multiplier and result. On the other hand, in the 
 unit and multiplier, the multiplier and result may create the unit. 
 
 Other advantages in the use of the unit and multiplier will be 
 evident after we have catalogued and illustrated the different princi- 
 pal forms which these instruments of efficiency may assume. 
 
 CLASSIFICATION OF UNITS 
 
 Units Classified According to their Materials 
 
 Units, like the data of reuse, may be classified either according to 
 the character of the materials of which they are composed, or ac- 
 cording to the forms which they assume. 
 
 With reference to the materials composing them, units are 
 classified in much the same way as are the data of reuse (see pp. 
 15-18). Thus we may have an' inorganic unit such as an atom, 
 molecule, or crystal, or any object composed of these. Similarly 
 we may have as a unit of work the horse-power, or the energy re- 
 quired to lift 33,000 pounds one foot in one minute. So also we 
 may have biologic units of various kinds, as cells, tissues, organs, or 
 entire organisms such as different plants or animals. Similarly we 
 have psychic units, examples being perceptions, feelings, ideas, or 
 acts. Social and political units are also in use, as cities, counties, 
 and states. So each department of thought and action contains its 
 own characteristic units. Various examples of these departmental 
 units will be given in the course of the discussions which follow. 
 
 It may be well to state at this place that, owing to the more 
 abstract nature of units, many of the limitations mentioned on 
 p. 18 with respect to materials proposed for reuse do not apply 
 to the same extent to objects treated as units in a multiplicative 
 process. 
 
UNIT AND MULTIPLIER 37 
 
 Units Classified According to Form 
 
 We next consider the classification of units according to their 
 forms or certain other abstract characteristics. 
 
 Considered with reference to the categories of space and quantity, 
 units may be grouped according to their size, shape, or position. 
 
 With respect to number, units may be single, dual, triadic, or 
 n-fold, according to the number of elements composing them. Thus 
 the ton-mile and acre- foot are each dual in nature. The unit of 
 work mentioned above (the horse-power) is triadic. The numerical 
 characteristic of units is frequently expressed as the number of 
 dimensions in the unit. 
 
 As to time units may be temporary or lasting. 
 
 As to force they may be active or passive. 
 
 Natural and Artificial Units 
 
 Since more or less artificial units are the source of special superior 
 results which are characteristic of the unit and multiplier principle, 
 the distinction between natural and artificial units is of the first 
 importance for our purpose. 
 
 A natural unit is any individual object as we find it in the world 
 about us, as a man, tree, grain of wheat, or a day. 
 
 A semi-artificial unit is a natural object which has been partially 
 modified so as to facilitate its use as a unit. An example is the 
 mean or average of a number of objects, as the mean solar day, 
 or the fractional part of a physically undivided object, as l /\. of the 
 area of the United States. Another instance is a room in a house 
 taken as a measure of the size of the house, as when we speak of a 
 six-room., or an eight-room house. A like case is the description of 
 a cotton farm in the South as a one-mule or a two-mule farm. 
 
 The value of slightly artificial units is illustrated by the operation 
 of that form of universal suffrage where one man has one vote, 
 regardless of differences among men, and questions are decided by 
 the principle of majorities. Among the advantages which arise 
 from this somewhat artificial idea of uniformity among voters are 
 the ease and speed with which decisions are thus obtained as com- 
 pared with decisions left to popular plaudits, riots, or revolutions, 
 and often to a series of violent actions and reactions. It is to be 
 noted that in this use of the average voter, the inequalities among 
 men are not wholly ignored but are left to adjust themselves by 
 
38 SOURCES OF EFFICIENCY 
 
 indirect methods as by the various influences which more able men 
 exert upon those less able. 
 
 An artificial unit is a unit devised by man. Instances of such 
 units are an hour, dollar, or pound ; a lesson, dose, or experiment, a 
 letter, word, sentence, paragraph, page. Other more extreme illus- 
 trations are the various legal fictions, such as the one which regards 
 a corporation as a person, or the hypothetic units employed in 
 science and in philosophy. 
 
 A set of units often forms a series increasing regularly in size 
 or in importance in some other way. The inch, foot, yard, and mile 
 form an example of such a scale of units. Similar instances are 
 furnished by the different tables of compound numbers given in 
 Arithmetic. Each developed field of work is usually supplied with 
 such a set of units in some shape. Such scales of units will be 
 treated more fully in Chapter VI (p. 95). 
 
 Many other special forms of units, each of more or less value, will 
 appear as we proceed. 
 
 It is also to be observed that units of the various kinds mentioned 
 above may be combined to form a vast variety of complex units. An 
 instance of a complex unit is a library, or a civilization. 
 
 CLASSIFICATION OF MULTIPLIERS 
 
 A multiplier is primarily a number but this numerical essence in 
 many cases is embodied in certain materials or entities, which, 
 while disguising the nature of the multipliers in some ways, in 
 others furnish the immediate instrumentalism by which the multi- 
 plier is handled or applied (see pp. 49-50 for analysis and definition 
 of multiplier). 
 
 Classification of Multipliers According to Materials 
 
 It is convenient to classify many multipliers according to the 
 materials in which they are thus more or less embodied. 
 
 Many kinds of what may be regarded as material or concrete 
 multipliers are in use. For instance, from one point of view, the 
 lever is a multiplier of man's available energy. In like manner 
 every mechanical appliance which is a modification of the lever, as 
 the wheel, pulley, inclined plane, screw, and every machine composed 
 of these, is a multiplier belonging to' the same general class. 
 
 Many other instruments used by man are multiplicative agencies. 
 Thus the lens manifolds man's power to see both small objects and 
 
UNIT AND MULTIPLIER 39 
 
 distant objects. In the same class of multipliers may be mentioned 
 the sounding board of a piano, the needle and mirror of a galvano- 
 meter, the relay circuit of a telegraph instrument, and the vibrating 
 membrane of a telephone receiver. In fact, from one point of 
 view, all the machinery which man uses, taken as a whole, may be 
 regarded as a gigantic multiplier of his power. 
 
 An instance of a different kind of material multiplier is the use 
 of capital to enlarge the application of the business power in a man. 
 
 Similarly various forces in nature, when properly applied, become 
 in effect multipliers of man's power to achieve results. The hole 
 drilled in a rock (the unit) is vastly increased by the explosion of a 
 charge of dynamite (the multiplier). In a much larger sense, coal 
 and water-power are mani folders of man's power. Acting in con- 
 junction with mechanical multipliers these forces produce note- 
 worthy results. Thus it is estimated that the steam and gas engines 
 in use in the world do the physical work of 2,000,000,000 of men 
 and thus increase the manual power of the human race at least 
 sevenfold. 
 
 It is to be noted in this connection that motion from certain points 
 of view may be regarded as a multiplier. Thus it is possible for a 
 man of small resources to manifold them by keeping them in rapid 
 action. Also we have the case of a point generating a line by 
 motion, and similar geometric illustrations. The physical and chemi- 
 cal properties of matter under certain circumstances are important 
 multipliers of man's powers. Thus a granite monument, or the 
 chemical and physical properties of granite which make such a 
 monument lasting, multiply an inscription carved on the monument 
 by means of the duration imparted to the inscription. So ink and 
 paper impart a certain permanence to a fact or idea recorded by 
 their use and give a manifold extension to such records. 
 
 The biological field is full of illustrations of the principle in hand. 
 The oolites and certain bones in the ear are magnifiers of the vibra- 
 tions in the membrane of the ear made by sound waves. Other 
 nerves of sensation have multipliers of different kinds, as hairs, 
 papillae, etc. Many of the bones of the body act as levers in other 
 ways. Reproduction itself is a process of multiplication. 
 
 More Abstract Multipliers 
 
 In the realm of mind, psychic units have different multipliers as 
 memory, imagination, reason, fear, surprise, joy, interest, faith, and 
 
40 
 
 SOURCES OF EFFICIENCY 
 
 courage. In connection with an act of wrong doing, deliberate in- 
 tention accompanying an act gives it a peculiar gravity. So in 
 ethics, the spirit in which a gift or sacrifice is made is a multiplier 
 of its value. 
 
 Special mention should be made of certain imperfectly under- 
 stood subjective multipliers, such as that psychic action which 
 enlarges perceptions of discrete phenomena into a continuity; or 
 that complex of different multiplicative powers which expands a 
 hint or suggestion into a complete whole; or causes that which is 
 partly hidden to be most fully expressed. 
 
 Many social agencies are multipliers of a high order of power. 
 Among these are language, the printing press, railroads, the post- 
 office, publicity, political systems, and civilization as a whole. 
 
 In a certain sense the quality of a unit is its multiplier. Thus the 
 power of an act is multiplied if this act be applied to the apexal (or 
 strategic) point in a domain of material. Thus the dog jumps for 
 the throat of its victim; and the bee when attacking a person tries 
 to sting the eye. Hence comes the importance of acting at a 
 psychological moment, or of seizing a strategic point, or of con- 
 trolling routes of transportation in business and in war. Hence 
 also the value of being able to influence processes of education, and 
 of being able to control the fountain sources or underlying causes 
 of any movement. Reform a man, it has been said, and you reform 
 one man ; reform a boy and you reform a whole multiplication table 
 of men. 
 
 Multipliers Classified by Forms 
 
 Multipliers may also be characterized and classified according to 
 certain formal elements prominent in them. Since material often 
 in a measure determines form, in many of the species to be men- 
 tioned in this relation form and material are closely connected. 
 
 A multiplier, like a unit, may be characterized numerically. For 
 instance, when we kill two birds with one stone, the multiplier is 
 dual in power and effect. In like manner it is evident that it may be 
 any other number large or small. Also a multiplier may be dual (or 
 larger) numerically in that it is a combination of two (or more) 
 multiplicative agencies. Thus a dual multiplier may be formed 
 by the combination of a subjective and objective multiplier, as 
 when conscience and public opinion unite in the condemnation of a 
 given act. 
 
UNIT AND MULTIPLIER 41 
 
 A multiplier may also be characterized by some spatial principle 
 prominent in it. For instance a multiplier may be linear in form. 
 Thus when a cannon ball is fired not across but down a line of 
 soldiers its effect is multiplied in a linear way. Similarly we have 
 manifolders that are fan-shaped, conically expanding, radiating from: 
 the center of a circle or sphere, spreading like the trunk and 
 branches of a tree, or of other geometric forms. Similarly a multi- 
 plier may be one, two, three, or w-dimensiona! in character. 
 
 An important spatial case, though one often difficult to analyze 
 completely, is that where the multiplying power is due to relative 
 position. Thus in the number 876508 the left hand 8, as compared 
 with the right hand 8, is multiplied one hundred thousand times in 
 value by its relative position. Similarly position is a multiplier of 
 one's power in many social and other relations. 
 
 A margin of empty space also, by virtue of its power to give 
 freedom and room for expansion, often constitutes an important, 
 though sometimes subtle enlarger of utilities. 
 
 With respect to time a multiplier may be temporary or permanent. 
 Often also time itself is spoken of as a multiplier though time in this 
 case is of course but a symbol for the causes or multipliers acting 
 in time. With respect to time we also' have predictive multiplication 
 as when a gardener multiplies the efficiency of his work by killing 
 young weeds before they have broken the surface of the ground. 
 In fact many of our mental powers such as fear, conscience, inter- 
 est, or even reason, have predictive multiplication as one of their 
 chief functions. 
 
 By reciprocal multiplication is meant the action of two objects 
 each of which acts as both unit and multiplier with respect to the 
 other. Illustrations are the hunter and his dog, the general and his 
 army, theory and practice, matter and form, labor and capital, the 
 plan and elevation of a building, humor and pathos, two friends, 
 two elements in a good dish, as pork and beans, two flowers which 
 fertilize each other. Also any number of elements may enter into 
 a reciprocal multiplicative relation. Thus when a number of friends 
 or business men cooperate, the ideas of one member of the circle are 
 multiplied (often many times) by the use made of them by other 
 members of the circle. 
 
 Multipliers may be of different orders of power. This matter also 
 will be discussed more fully later (pp. 51-52). 
 
42 
 
 SOURCES OF EFFICIENCY 
 
 Indirect and Obscure Multipliers 
 
 Some multipliers are negative in character. An instance is the 
 removal of an obstacle in order that a direct multiplier may act. 
 Thus, instead of fanning oneself on a hot day, one may often get the 
 same result with far less labor by opening a window and letting a 
 breeze blow through the room. In a vastly higher field results of 
 the first importance are often achieved by merely setting free intel- 
 lectual or social forces. Most important for our purpose is the 
 disentanglement of the prime efficiency agents or principles in a 
 given domain and allowing them to act without hindrance. 
 
 Another important kind of negative multiplication is that of 
 division of error or loss. Thus if we assay a specimen of the ore 
 in a poor mine before working the mine extensively, we may divide 
 by thousands the loss which would have resulted from attempting to 
 operate the mine on a large scale. In general, every experiment or 
 testing on a small scale of a proposed plan or method, constitutes a 
 unit which, if successful, will later have a positive multiplier, but 
 which if it fails to give good results has a negative multiplier in that 
 it prevents extensive loss. 
 
 Multipliers are often vague or obscure in whole or part. In- 
 stances are that action in an organism by which small doses of a 
 vaccine or serum lead to immunity from a specified disease. Other 
 instances are various kinds of influence, growth, and propagation. 
 
 Complex Multipliers 
 
 The different species of multipliers enumerated above may be 
 compounded and complexed together in various ways. Thus, to 
 consider an extreme case, various objective multipliers compounded 
 together give us our whole system of civilization as a multiplier of 
 any good (or evil) unit. Similarly subjective multipliers when com- 
 bined give us the entire mind and its experiences as an enlarger of 
 any impression. 
 
 Subjective and objective multiplicative agencies give us, for 
 example, the system of credit and banking which multiplies the 
 usefulness of the small stock of gold possessed by the world; or 
 the process which has expanded the observation of the attractive 
 power of a piece of rubbed amber into the science and art of elec- 
 tricity; or that which has enlarged the observation of the smudge 
 made by sunlight on a piece of silver into the science and art of 
 photography. 
 
 
UNIT AND MULTIPLIER 
 
 43 
 
 An important special case of the complex multiplier is that which 
 often creates enormously large rewards for the winner of a race by a 
 margin however small. Similar are the multipliers which act in the 
 process of evolution and cause those organisms to prevail and sur- 
 vive Which excel by however small a margin of fitness. 
 
 An important special case of abstract and complex multiplier is 
 the process called generalization. 
 
 For our purpose the most comprehensive and powerful multi- 
 pliers will be found to be the principles of efficiency which are being 
 investigated in this book. 
 
 ADVANTAGES IN THE USE OF UNITS AND MULTIPLIERS 
 
 Many of the statements that were made in Chapter II (pp. 23-26) 
 concerning the efficiency functions of reuse apply also to the unit and 
 multiplier. But the fact that the unit and multiplier principle is more 
 abstract and general (less restricted as to the categories of person- 
 ality and time) gives it in some respects a deeper and broader mean- 
 ing and usefulness. Just as the unit and multiplier process is more 
 thoroughgoing and manageable so also are its fruits. 
 
 Other Superiorities to Reuse 
 
 For instance, the application of a pulley to lift a weight may be 
 viewed either as a case of reuse or as a case of the multiplication of 
 one's powers. The advantage of expressing the process in the 
 unit and multiplier form is that it enables us to adapt our pulley 
 machinery accurately to the size of the weight to be lifted, and thus 
 at times to avoid costly experiments and much waste of energy. 
 Similarly in many other cases by putting a given efficiency principle 
 in the unit and multiplier form, we obtain increased economy or 
 efficiency in its application. 
 
 The superior efficiency of highly developed forms of the unit and 
 multiplier principle over more or less haphazard reuse is illustrated 
 by a comparison of the English language with the Chinese. The 
 printing of English has been reduced to the use of a few well 
 selected units with large multipliers, while the Chinese characters 
 still consist of a multitude of ancient ideographs. As a result a 
 font of English type weighs 50 pounds and costs $5 while a font of 
 Chinese type weighs 1000 pounds and costs $100. Furthermore 
 the typewriter and linotype greatly facilitate the use of the English 
 language, but cannot be employed in the use of Chinese because of 
 
44 SOURCES OF EFFICIENCY 
 
 the multitude of its primary symbols. The comparative inefficiency 
 of the Chinese language is also illustrated by the fact mentioned on 
 a previous page that the Chinese compositor walks 20 miles a day 
 while the compositor of English type stands still. 
 
 Increase of Power obtained by Multiplication of Units 
 
 Machines also, by the reuse of which they are capable, increase 
 human power. But this increase is greatly magnified by standard- 
 izing machines, that is, by reducing machines as far as possible to 
 the unit and multiplier form. 
 
 Similarly the reciprocal reuse of their work by scientific men is 
 much enlarged by putting the results of their work in a manifold 
 unit and multiplier form as in journals and periodicals, and by ex- 
 pressing these results as far as possible as principles, laws, and 
 formulas stated in terms of more or less conventional units. 
 
 Systems due to Units and their Multipliers 
 
 This suggests a still more general and far-reaching advantage 
 which characterizes the use of the unit and multiplier methods viz. : 
 the fact that the development of adapted species of unit and multi- 
 plier often leads to the combination of these into extended systems 
 with a corresponding development of efficiency results. 
 
 Duality of Unit and Multiplier a Source of Power 
 
 Another specific and prime source of efficiency in the use of the 
 unit and multiplier is found in the duality which characterizes the 
 unit and multiplier when considered in comparison with the single 
 concept prominent in the principle of reuse. As a result each of the 
 two instruments involved, the unit and the multiplier, can be devel- 
 oped in independent aggressive fashion. Thus the unit can be 
 adapted to any given purpose and the multiplier, owing to its 
 explicit numerical form and abstract nature, can in like manner be 
 freely extended. Also the limitations of the dual concepts may be 
 more readily studied and remedied, and auxiliary objects, such as 
 symbolisms, may be more readily applied to them. 
 
 Transcendent Results 
 
 The result of a multiplication often transcends in some special 
 way the data employed. Thus a drop of water when multiplied be- 
 
UNIT AND MULTIPLIER 45 
 
 comes the ocean. But the ocean is much more than a drop of water 
 with a numerical multiplier. So rock is more than a grain of sand 
 or an atom manifolded. 
 
 Taking up a different form of transcendence, the microphone by 
 multiplying the force of a vibration makes the vibration audible and 
 the microscope by multiplying the, JQp^it which falls on the retina 
 of the eye causes the invisible to be seen. A disease germ when 
 multiplied may produce first sickness and then death. A variation 
 in the anatomy of a reptile when given a large multiplier has pro- 
 duced the bird. A point when multiplied by motion produces a 
 line. Trifles when multiplied together in a work of art beget what 
 is called perfection. According to the law of evolution a multiplica- 
 tive increase in the number of individuals belonging to a species, 
 leads on the one hand to the death of many individuals in the species, 
 and on the other hand to the development of other individuals into 
 a higher kind of organism. In many different domains a multiplica- 
 tive accumulation of minute changes often produces a conversion or 
 a revolution. These transformational fruits may all be hastened and 
 increased by the choice or creation of adapted units and multipliers, 
 as contrasted with more accidental reuse. 
 
 Progress obtained in Various Departments 
 
 We may realize the importance of the unit and multiplier princi- 
 ple in a more pictorial way by noting that the history of human 
 progress, in one aspect, has been largely a history of improving 
 units and multipliers. Thus in the field of inorganic science, pro- 
 gress has been made by the use of the atoms devised by the ancient 
 world, and still further progress by replacing atoms in part by ions 
 and electrons. So immense advances have been made in biology by 
 recognizing the cell as the fundamental unit, and in political life by 
 regarding the individual citizen, not the tribe or the city, as the 
 primal unit. The same source of increasing efficiency is prominent 
 in other departments of life or thought. 
 
 Historical Illustrations of Advantages 
 
 In like manner human progress has been marked by increasing and 
 improving multipliers, and every period of unusual achievement has 
 been one where large intense multipliers have been at work. Thus 
 the epochs of Greek and Italian art, the cathedral building age, the 
 
46 SOURCES OF EFFICIENCY 
 
 various religious eras, each came and flourished when they did, 
 from one point of view, because of the large popular multipliers of 
 the new item of efficiency or value connected with each of these 
 periods. More recently the printing press, the railroad, steamboat, 
 telegraph, and similar agencies have produced new multipliers 
 which have given new values to every unit of progress and greatly 
 accelerated many forward movements. 
 
 Also in the history of progress new units and new multipliers 
 have acted and reacted on each other in various ways. This is 
 illustrated by the fact that the new social and political units in the 
 United States have given rise to vast multipliers of every new in- 
 vention and improvement. The new multipliers in turn have led to 
 the development of new units, particularly of small units which 
 could not have established themselves but for the large multipliers 
 ready to be applied to them. These new units are illustrated in 
 the numerous small improvements made in various machines and 
 tools. 
 
 Advantages Illustrated by Great Men 
 
 Similarly every great man as a part of his work has created at 
 least one new efficiency unit, or given some old unit a new and nota- 
 ble multiplier. Thus Christ brought into the world in a vitally new 
 form the principles of the fatherhood of God and the brotherhood 
 of man. Paul by his knowledge of the Greek philosophy and the 
 Roman political system gave a large multiplier to the units which 
 Christ supplied. 
 
 Departments Determined by Units and Multipliers 
 
 In a fuller sense also we see that every department of knowledge 
 or activity is based on (or means) a few fundamental units reused 
 and multiplied. This principle holds true even in apparently in- 
 formal and unsystematic fields of activity. Thus we have the ele- 
 mentary units of dancing, a few fundamental strokes in penmanship, 
 and similar primary units in boxing and music. Likewise, though 
 often in a far higher sense, each branch of science has its alphabet, 
 grammar, and logic, and because of the great and distinct body of 
 economy and efficiency thus generated its existence as a distinct de- 
 partment is justified. 
 
UNIT AND MULTIPLIER 
 
 47 
 
 Absence of Units and Multipliers Means Loss 
 
 Another collective way in which to realize the value and impor- 
 tance of the unit and multiplier principle is to try to picture what 
 life would be without this instrument of efficiency. In this case 
 mankind would need to dispense with the dollar, mile, inch, quart, 
 day, year; with the science of number and measurement; and with 
 the more informal sets and systems of units and multipliers which 
 pervade all life. 
 
 Limitations in the Utility of Units and Multipliers 
 
 Before closing this presentation of the efficiency functions of the 
 unit and multiplier, some statement should be made of the limita- 
 tions connected with this source of efficiency. Prominent among 
 these are certain limitations in the nature of things (to be studied 
 more fully later, see p. 265) which on the one hand often prevent 
 the formation of units and on the other check the action of 
 multipliers. 
 
 Also a unit may be evil or destructive in its nature; hence its 
 multiplier may operate to produce injurious results. Illustrations 
 are the Colorado potato beetle, the gypsy moth, and mistakes and 
 sins of all kinds. 
 
 Also the unit and multiplier principle has certain drawbacks due 
 to the abstract and impersonal nature of units and of number. 
 Hence arises the need of other efficiency principles to be used in 
 connection with the one under consideration. 
 
 Complex Fruits 
 
 It is evident that the various fruitages of the unit and multiplier 
 may be compounded and complexed in many ways. In this connec- 
 tion the operation of the principle of dialectic (see Chapter XIV, p. 
 249) is important. Thus a single observation made by Prof. Roent- 
 gen has developed into the whole science of X-rays with its world 
 of surgical and other more general applications. 
 
 The most important use of the unit and multiplier principle, as 
 will later be made more evident, is the power of this agent to set 
 free and develop other efficiency principles both objectively and 
 subjectively. 
 
48 SOURCES OF EFFICIENCY 
 
 ANALYSIS OF THE UNIT AND MULTIPLIER 
 
 A general statement of the improved sources of efficiency in the 
 unit and multiplier principle was made on pp. 35-36. In making 
 a closer examination of this matter it will be an advantage to make 
 use of the principle of marginal reuse as presented in Chapter II 
 (p. 19). Thus by showing in what respects the unit and multiplier 
 principle differs from reuse, we utilize the work which has already 
 been done in analyzing and defining reuse. 
 
 Tabular Comparison 
 
 The corresponding qualities and elements which enter into the 
 two principles under discussion are shown in the following table : 
 
 Reuse Unit and Multiplier 
 
 Personal Impersonal 
 
 Time is essential Time is secondary and quantity is 
 
 primary 
 
 Emphasis on datum and result Emphasis on process 
 
 Concrete Abstract 
 
 Fruitage usually direct and im- Fruitage often indirect and re- 
 mediate mote 
 
 Qualitative Quantitative 
 
 Voluntary and intentional Multipliers often act independ- 
 
 ently of or even contrary to 
 human will 
 
 Synthetic Analytic 
 
 Summing up the matter in a single sentence, reuse is concrete, in- 
 dividual, subjective, empirical, opportunistic, geometric, often ir- 
 regular and haphazard; the unit and multiplier principle is abstract, 
 social, objective, systematic, analytical, logical, artificial, algebraic. 
 
 We may also proceed in our analysis of the principles in hand 
 by anticipating to some extent certain principles of efficiency to be 
 treated later and by showing the relation of the unit and multiplier 
 principle to certain other primal sources of efficiency. 
 
 Relation to Other Efficients 
 
 Thus with respect to the diversity or separation principle (see 
 Chapter VIII) the unit and multiplier method is based externally 
 on a certain freedom from the entanglements of space, time, and 
 personality, and internally consists essentially in a specific distinc- 
 tion between the unit and the multiplier. The treatment given 
 
 
UNIT AND MULTIPLIER 49 
 
 later of diversity as a source of efficiency will show how each of 
 these separations opens the way to a group of advantages, some 
 abstract, and some concrete. 
 
 Similarly with respect to the principle of uniformity the unit and 
 multiplier data and processes may often be standardized and thereby 
 largely increased in power. With respect to orders of material 
 (see Chapter VI) the unit and multiplier agency is as a rule of 
 higher order than reuse. With respect to the categories of mo- 
 tion and force, it is more active and rapid. It also has a larger 
 dialectic power. With respect to directive use it is more 
 manageable. 
 
 It should also be noted that the principle of limitation acts in 
 important ways in the formation of the reuse and unit and multi- 
 plier agencies. For instance there would be no need for the em- 
 ployment of either of these principles of efficiency if certain limita- 
 tions did not exist and compel the use of such methods. Hence 
 the study of the meaning and forms of limitation should aid us in 
 the development and application of each of the two principles 
 under discussion. 
 
 Analysis of Special Case 
 
 A word should also be said about the nature and classification 
 of certain special cases of efficiency which are at least closely con- 
 nected with the idea of the unit and multiplier. For instance if 
 we bait a hook with a piece of meat and catch a fish, the question 
 may be raised as to whether the bait may be regarded as a unit 
 and the fish caught as the product. A similar question may be 
 asked as to a seed which is planted and the yield which results. In 
 the one case the bait is lost as food. In the other the seed is partly 
 lost and partly transformed into the resulting crop ; certain elements 
 of soil and atmosphere also enter into the matter. Hence we may 
 say that in the direct aspect the question is a complicated one, but 
 that if we reduce the matter in each case to an amount of energy 
 expended, and a return of energy, we find that both cases are es- 
 sentially instances of unit and multiplier. The same analysis applies 
 to a variety of like cases. 
 
 Definitions 
 
 Before closing this part of the discussion it may be well to formu- 
 late, as best we can, definitions of the unit and multiplier. 
 
50 SOURCES OF EFFICIENCY 
 
 A unit is any entity used manifoldly in space or time or in any 
 relation. 
 
 The multiplier expresses the number of manifold uses made of 
 a unit. 
 
 The various elements which our analysis has made clear as en- 
 tering into the unit and multiplier principle may all be made the 
 means of a more effective application of the principle. Some of the 
 improved methods thus suggested we now proceed to point out. 
 
 METHODS OF APPLICATION 
 
 Repetition of Advantages in Reuse 
 
 Many of the remarks made in Chapter II in connection with the 
 best methods of utilizing the principle of reuse apply also to the 
 unit and multiplier. However the fact that the unit and multiplier 
 concept is more abstract and general than reuse gives rise to im- 
 portant additional considerations. 
 
 Adaptation of Unit and Multiplier to Each Situation 
 
 Owing to the fact that both unit and multiplier may take many 
 diverse forms, also that these forms are adaptable and largely un- 
 der control, it is important to study each special case where a unit 
 and multiplier are to be employed and to select the most efficient 
 species of each for the work in hand. 
 
 As an aid for this adaptive work it is important to realize and 
 keep in mind in some systematic 'way the large number of possible 
 forms of units, including particularly the various forms of natural, 
 artificial, and semi-artificial units ; and to treat multipliers in like 
 manner. 
 
 Frequent Value of even Imperfect Units 
 
 Where effective units are difficult to obtain, it is important to 
 realize the value of even imperfect ones in connection with more 
 or less efficient multipliers. Thus, in a situation of great difficulty, 
 rather than do nothing it is often well to make a start or beginning, 
 however crude, and to trust that if no others are at hand, natural 
 multipliers will act on the unit thus made, that the crude initial 
 units will improve, and that new units and multipliers will appear. 
 
 This procedure often takes a complex form. For instance when 
 plunged into a complex and difficult situation where comprehensive 
 systematic methods of action are impossible, it is well to give each 
 
UNIT AND MULTIPLIER 51 
 
 available scrap of efficiency its largest possible multiplier, and to 
 trust that later developments and coordinations will appear. 
 
 In particular in cases of difficulty it is important to realize the 
 value of such somewhat crude multipliers as patience and persistence. 
 
 Sometimes special methods must be employed to get any unit 
 whatever. Thus in breeding new kinds of plants, often the great 
 difficulty is that of getting a plant to vary at all. After a variation 
 of any kind has been obtained, means exist of developing it in 
 a desired channel and often to high degree. In other cases the 
 difficulty consists in getting any practical multiplier whatever. Thus 
 a man with a new and useful idea or invention may for a long 
 time find it impossible to obtain the means of making a wide use 
 of his conception. 
 
 It is well to fix in mind the rule that the principle of the unit and 
 multiplier is an important aid in all cases where it is important to 
 make a little go a long way. Thus it applies to the problem of 
 utilizing the power, without impairing the scenic grandeur, of 
 Niagara Falls. For if the full volume of water were sent over the 
 Falls during a specified hour during each day and sightseers should 
 collect to see it at that time, all the energy of the Falls might be 
 utilized in a mechanical way during the other twenty-three hours 
 of the day. 
 
 Art of Adapting Units 
 
 Methods of devising units to meet the conditions in a given field 
 may be developed into an art. Thus instead of saying that the 
 British Empire increased 4,000,000,000 acres between the years 
 1800 and 1900, we may express the matter much more effectively for 
 many purposes by saying that the British Empire during the nine- 
 teenth century increased at the rate of 2 acres per second. So 
 instead of saying that a certain star is 20,000,000,000,000 of miles 
 distant, we may say that it is at a distance of three light years. It is 
 often a profitable exercise to spend one's leisure in devising units 
 and conceiving of their multipliers, and thus acquiring the art of 
 rapidly discovering, forming, or improving these instruments of 
 efficiency. 
 
 A Scale of Relative Value 
 
 As an important aid in this process, it is desirable to obtain a 
 thorough appreciation of the fact that both units and multipliers 
 
52 SOURCES OF EFFICIENCY 
 
 may be of different orders of perfection or efficiency, and that it 
 is highly useful to be able quickly to recognize and utilize those 
 highest in power under any given circumstances. For instance the 
 most serviceable units for general use are those which are definite, 
 permanent, and readily reproducible. 
 
 As a special case of permanency it is to be noted that, other 
 things being equal, old and established units are preferable, since 
 they have been frequently tested, already have large multipliers, and 
 any mastery which we already have of them may be reused. 
 
 Particular mention should be made at this point of the efficiency 
 significance of the Arabic number system. When frequently used 
 this system comes to act almost automatically in a number of ways 
 in the extension of results. A special use of it is as an aid in the 
 multiplicative process called generalization. In generalizing a fact 
 we infer that what is true of one, two, or some objects in a class, 
 is true of all. In generalizing a process we extend the process 
 from two or three steps to an unlimited number of steps. 
 
 Devising more Fundamental Units 
 
 The power which we have of changing and adapting units often 
 enables us to reduce a given set of them to the same common de- 
 nominator, so to speak; that is, to more fundamental and inclusive 
 units. In certain processes of mathematics, science, and philos- 
 ophy, this process has been carried to an extreme degree, the 
 result being units of great abstractness and hence of inclusiveness 
 and power, when rightly used. For the process of progressive 
 inclusiveness gives also an increasing systematization and inter- 
 relation of units and other sources of power. 
 
 Best Standard Method 
 
 Before closing this part of the discussion it may be well to make 
 a statement of the best standard method for the combined use 
 of units and multipliers in the so-called practical world. As a 
 preliminary fact we observe that, owing to the highly organized 
 state of society, large multipliers for any new unit of advantage are 
 omnipresent, while only rarely does a large new unit of efficiency 
 appear. Hence the best standard method of employing units and 
 multipliers in combination, is to rely mainly on small units and 
 large multipliers, but to have an eye open for large units as ex- 
 
UNIT AND MULTIPLIER 53 
 
 ceptional possibilities. Thus a machine which saved two or three 
 drops of solder in putting a lid on a tin can, produced a fortune 
 for its inventor because this saving had a multiplier of 700,000,000 
 each year. Similarly a fortune was obtained from the invention 
 of the hook eyelet used on shoes, and another from the addition 
 of the gimlet point to the old fashioned blunt screw. For a like 
 reason a steel manufacturer is ready to send his machinery to the 
 scrap heap and replace it by new, if by so doing he can save 10 cents 
 a ton in making steel ; and a cotton manufacturer will do likewise 
 if he can save 1/16 cent per yard in making muslin. 
 
 In like manner the greatest masters of chess strive primarily not 
 for brilliant strokes, but to make the most of each minute advantage 
 which appears, or which they can devise. So in the highest forms 
 of art the multipliers dominate the units. 
 
 Ideal Species of Unit and Multiplier 
 
 It is well to remember that, for general purposes of thought and 
 life, the best units and multipliers alike, from our standpoint, are 
 the primal efficiency principles which we are studying in this book. 
 The specific meaning of this statement will be developed later. 
 
 Summary of Chapter 
 
 At this point it will be well to recapitulate the substance of the 
 present chapter. 
 
 The principle of the unit and multiplier includes reuse as a 
 special case, and hence is a more comprehensive agency of efficiency. 
 The unit and its multiplier are often superior to reuse in efficiency 
 because of the fact that in reuse we must take the data of life as 
 we find them, while units and multipliers may often be created and 
 shaped according to our needs and wishes. Innumerable varieties of 
 both units and multipliers exist, or may be created, each endowed 
 with its own special efficiency powers. Special mention should be 
 made of natural and artificial units, and of predictive, reciprocal, 
 and indirect multipliers. 
 
 The use of units and multipliers means economy and new 
 powers of various kinds. In some cases the results take the form 
 of elaborate systems. In other cases they are transcendent in the 
 sense that they could not otherwise have been obtained. The study 
 of great men and the history of human progress furnish a multitude 
 of illustrations of these values. 
 
54 SOURCES OF EFFICIENCY 
 
 In order to reap the largest possible fruit from the use of the 
 units and their multipliers, it is necessary to follow many of the 
 methods indicated for reuse in the last chapter. Thus it is im- 
 portant to realize the great variety of possible units and multipliers, 
 and to adapt different forms of these to different situations. It is 
 an advantage at times to arrange units in a scale according to their 
 relative values, and to realize the great utility of even an imperfect 
 unit or multiplier in a difficult situation. The ideal species of units 
 and multipliers alike are the fundamental principles of efficiency 
 which we are studying. 
 
 EXERCISE 3 
 
 1. Give an example of manifold simultaneous use. 
 
 2. Also of use that is manifold both in a simultaneous and a successive 
 way. 
 
 Point out the unit and the multiplier in each of the following cases : 
 
 3. The use of the carpenter's level 5. Of lieutenants by an able man 
 
 4. Of a parliamentary motion 6. Of the rudder of a ship 
 
 7. The use of yeast in making bread. 
 
 8. Newton's reputed use of the falling apple in discovering the law of 
 gravitation. 
 
 9. State which of the units employed in Exs. 3-8 are natural and which 
 artificial. 
 
 10. Name some of the units employed in political and governmental organ- 
 izations. 
 
 11. In engineering 12. In agriculture 13. In education 
 Name three units which are 
 
 14. Artificial 15. Natural 16. Semi-artificial 
 
 Give two illustrations of multipliers which are 
 
 17. Mechanical 18. Biological 19. Abstract 20. Predictive 
 
 21. Reciprocal 22. Negative 23. Branching or radiating 
 
 State the meaning of each of the following units and give some of the 
 advantages resulting from its use. 
 24. A horse-power 25. A watt 26. A candle-power 
 
 27. What species of multiplier is implied in the statement "a thing well 
 begun is half done"? 
 
 28. The driver of a load drawn by six horses is how many times as 
 efficient as the driver of a one horse load? 
 
 What primary principle of efficiency enters here? 
 
 29. If a microphone makes audible an otherwise inaudible sound, state the 
 degree of efficiency obtained by its use. 
 
 30. The process of reducing two or more fractions to a common denomina- 
 tor means what with reference to the use of units? 
 
 
UNIT AND MULTIPLIER 
 
 55 
 
 What advantages result from his process? 
 
 31. Explain as a case of unit and multiplier, the use of a bolt on a door. 
 
 32. All the various colors may be built up by combining three primary 
 colors, viz. : blue, green, and red. How is the principle of unit and multiplier 
 here involved? What advantages result? 
 
 33. Give an example of the multiplication of a loss. 
 
 34. Give two illustrations of publicity as a multiplier, and state the useful 
 results which have followed in each case. 
 
 35. Give an instance where the use of a small unit and large multiplier i& 
 more advantageous than the use of a large unit and a small multiplier. 
 
 36. In what respect is a change of the direction of one's motion a unit?' 
 What is the multiplier in this case? 
 
 37. Why is knowledge gained early in life often worth many times as; 
 much as knowledge gained later? 
 
 38. State the corresponding principle with reference to mistakes. 
 
 39. All units used in physics may be built up out of what three fundamental 
 units ? Illustrate. 
 
 40. What is meant by the dimensions of a derived unit in physics? 
 Illustrate. 
 
 41. Chemically all material objects are composed of what units? 
 
 42. In fighting battles the method used by Napoleon on land and that used 
 by Nelson on sea were essentially the same. Explain the method and show 
 that in effect it constituted an application of the unit and multiplier principle. 
 
 43. Explain the sense of proportion in an observer as a case of manifold 
 unit and multiplier and give two examples. 
 
CHAPTER IV 
 
 THE GROUP 
 
 Illustration 
 
 Just as the principle of reuse was enlarged into the broader and 
 deeper principle of the unit and multiplier, so the latter principle 
 may be extended so as to form a still more general agent of effi- 
 ciency, viz. : that of the group or assemblage. To indicate in a 
 brief way what is meant by this, we may continue an illustration 
 already used in connection with reuse and the unit and multiplier. 
 If an orator preserves a speech and uses it repeatedly, we have a 
 case of reuse. If this speech is published simultaneously in several 
 newspapers, the method of the unit and multiplier is employed. 
 If a number of the orator's speeches are collected and published 
 together in a volume, we have an example of the use of the group 
 method as a means of obtaining efficiency. 
 
 The Group broader than the Unit and its Multiplier 
 
 The process of reuse implies a certain likeness in the steps in- 
 volved. The use of the unit and multiplier is also a more or less 
 homogeneous process. But in the group various unlike elements 
 may be combined and treated efficiently. Thus the combination of 
 various speeches in a book facilitates their study and analysis as 
 a whole, as well as their preservation and manipulation in libraries. 
 
 Special Advantages in the Use of Groups 
 
 Many groups occur in a state of nature, or appear, as it were, 
 of themselves in the world about us, and become immediate sources 
 of efficiency. Thus the sight of a school of fisbes suggests the 
 unit and multiplier method of catching them by a net ; a collection 
 of workmen in a factory opens the way to address them all at 
 the same time on any given subject; the fact that goods are packed 
 in barrels may enable some one by quick handling to save them 
 from being consumed in a fire. 
 
 A low order of force may often be utilized in manipulating 
 groups. At the same time the idea of the one and many owing to 
 
 56 
 
THE GROUP 57 
 
 its great generality frequently operates in two opposite directions 
 (see direct and inverse groups on p. 59). Even more important 
 is the fact that the character of the ties which combine objects in 
 groups facilitates the building of groups into extended systems. 
 The group method is so flexible that it may be used in a crude in- 
 cipient way and also as a highly finished and final instrument of 
 efficiency. 
 
 CLASSIFICATION 
 Classification of Groups according to Materials 
 
 Groups may be classified according to the materials of which 
 they are formed. Thus, inorganic groups are groups of objects 
 like atoms, bricks, dollars, acres. 
 
 Biologic groups are illustrated by a group of cells, a field of 
 wheat, or a herd of cattle. 
 
 Examples of social groups are the family, a convention, or a 
 nation. 
 
 Combinations of perceptions, or ideas, are instances of more 
 ideal groups. 
 
 It is to be noted carefully in this connection that a group of 
 objects is often closely connected with a group of forces or of 
 uses. Thus in a gang plow we have a group of like objects (the 
 plow shares), and with each use of the plow the work of the plow- 
 man receives a multiplier, that is, is converted into a group. 
 
 Classification of the Ties of Groups 
 
 It is also often advantageous to characterize and classify groups 
 according to the ties which bind or connect the elements compris- 
 ing a group. 
 
 Thus a tie may be a material thing like a pin, piece of wire or 
 twine, an elastic band, a basket, box, barrel, or dish. 
 
 Also a tie may be a physical force of some sort as cohesion, gravi- 
 tation, or magnetism. 
 
 Likewise it may be a biologic, psychic, social, ethical, or religious 
 force. 
 
 Ties may also consist of some more abstract relation, as of any 
 likeness as of color, size, weight, shape, temperature, value, age, 
 origin, development, feeling, or belief, or uniformity in any func- 
 tion or relation. 
 
58 SOURCES OF EFFICIENCY 
 
 Special mention should be made of spatial likeness, that is, of 
 concentration in space and consequent likeness of position. Some 
 of the many advantages which often follow from this species of 
 groupism will be pointed out later. 
 
 Of equal importance is simultaneity, or likeness in time. 
 
 Concentration in both space and time is illustrated by the force- 
 acting in the head of an arrow, and in the mode of action of many 
 weapons and tools, or the force exerted by an army. 
 
 Special mention may also be made of the combinations of ob- 
 jects in a field of vision or in a state of consciousness. 
 
 Relation of Ties to the Elements of Groups 
 
 It should be noted also that in some cases the tie is something 
 external to the elements of a group as when objects are held to- 
 gether by a piece of string. In other cases the tie is in itself an 
 element or in some way embodied in an element as when a herd of 
 animals is held together by one of the number, or a solar system 
 by its sun. From some points of view however an external tie 
 may often be regarded as a heterogeneous element in a group. 
 
 Complex Ties 
 
 The tie which holds a group together is often manifold or com- 
 plex in nature. Thus when pupils are grouped in rooms in a graded 
 school, the groups of pupils are determined not only by the 
 walls and floors of the building but also by the likeness of pupils in 
 age and development, and by the leadership and control of teachers. 
 Similarly a family is bound together by biologic, psychic, social, 
 ethical, and many different efficiency ties. 
 
 It is to be noticed also that one tie may be an aspect of, or may 
 lead to, another principle of combination. Thus cohesion leads to 
 spatial concentration; and nearness of men in space may lead to 
 likeness of dress or opinions. 
 
 When the tie which holds a group together is strong or feeble„ 
 temporary or permanent, static, vibrant, or changing, the group 
 may be characterized accordingly. 
 
 Classification of Groups according to their Forms 
 
 Hence the nature of the tie which holds a group together to 
 some extent determines the form of the group. But groups may 
 
THE GROUP 59 
 
 take individual forms for other reasons, and should often be char- 
 acterized and classified according to these forms. 
 
 Thus a group which contains two, three, or n elements may be 
 termed a dual, triple, or w-fold group (or a duad, triad, or 7i-ad). 
 Similarly a group may be large or small, finite or infinite. It may 
 be one, two, or three dimensional, and may assume any geometric 
 shape whatever. 
 
 An important distinction for our purpose is that between homo- 
 geneous and heterogeneous groups, that is, groups composed of 
 like or unlike elements, respectively. 
 
 It is to be noted that in determining the character of a group in 
 this respect much depends on the point of view. Thus an orchard 
 viewed as containing apple, pear, and cherry trees constitutes a 
 heterogeneous group, but viewed as containing trees merely (as 
 contrasted with corn stalks, for instance) it is a homogeneous 
 group. In other words by the use of more general ideas, a hete- 
 rogeneous group may often be converted into a homogeneous one. 
 
 Natural groups are those which exist independently of any change 
 in unit or tie wrought by human agency. Examples are the solar 
 system, a cluster of wild flowers, the petals in one of the flowers, a 
 herd of wild animals, or a school of fishes. 
 
 Artificial groups are those which in some respect have been 
 formed by man, as a bundle of toothpicks, or a class of scholars. 
 
 With respect to order it is useful to make a distinction between 
 direct and inverse groups. 
 
 A direct group is one formed by the inclusion of two or more 
 objects or elements into one whole or aggregate, as when a number 
 of objects are tied together to make one package. 
 
 An inverse group is one formed by the expansion of a single 
 object into many forms or elements, as when a grain of wheat 
 produces a number of other grains, or a piece of rock is separated 
 into its constituent elements. 
 
 A combination of the direct and inverse relations gives rise to 
 the dual-reciprocal group. This consists of two groups of elements, 
 each element in a group being connected with several or all of the 
 elements in the other group. An illustration is a set of workmen 
 and a set of tools so related that any workman may use any one of 
 the tools. 
 
 This dual reciprocal relation may be represented diagrammatically 
 
6o SOURCES OF EFFICIENCY 
 
 by a group of points A, B, C, D, E (indicating 
 
 E 
 
 «•■ 
 
 3 
 
 "J workmen), and another group i, 2, 3, 4, 5 
 \x\ v ">- > (standing for tools) and a series of dotted 
 
 \\\ ^»^ nnes connecting each point in the first group 
 \\ \ with each in the second. In the diagram as 
 
 given in the text only a few specimen connect- 
 ing lines are drawn. 
 v \ In this way qualities (or properties) may 
 
 \ #I X be regarded as forming objects and objects 
 \ may be analyzed into qualities. This enables 
 
 • n| us to handle a group of qualities as a single 
 object, or a group of objects by means of a 
 common quality. Similar efficient group relations connect forms 
 and materials ; symbols and things ; objects and places ; generals 
 and particulars ; principles and details ; causes and consequences. 
 For one piece of material may take many different forms, and one 
 form or mold may be filled with many different substances; one 
 symbol may represent many different objects ; and one object may 
 be represented by many different symbols. 
 
 By an extension of the above process, a number of groups (as n 
 groups) may be combined to form an w-reciprocal group. The 
 simplest form in which this species of group can occur is that in 
 which in a group of n elements each element in turn may assume 
 the leadership of the remaining elements. 
 
 Manifold Groups 
 
 A group may be manifold in the sense that it may be character- 
 ized in many different ways. Thus a family is determined as a 
 group primarily by certain biologic considerations, but it may also 
 be determined by the common physiological and mental peculiari- 
 ties of its members, by the fact that these members occupy the 
 same home, and it is also often an w-reciprocal group because of 
 the services which each member renders to the other members. 
 
 In concluding this portion of the discussion attention should be 
 called to the fact that reuse is a temporal group homogeneous as 
 to the quality of its elements ; and that the unit and multiplier form 
 a group homogeneous with respect to both the size and quality of 
 its elements. 
 
 EFFICIENCY FUNCTIONS OF THE GROUP 
 
 To help make clear that the group should be regarded as an in- 
 dependent primary agent in obtaining useful results, a number of 
 
THE GROUP 6l 
 
 the efficiency properties of the group were pointed out and illus- 
 trated in the opening paragraphs of this chapter. Beside these 
 properties the group principle has other uses which invite special 
 attention. 
 
 The Group a Source of Economy and Reuse 
 
 A group means a special field of application for the reuse and 
 unit and multiplier principles. Hence almost all that has been 
 said concerning the efficiency functions of these agents applies to 
 the group also. Grouping objects is also a means of storing them 
 in a small space and finding them readily. Hence it means an 
 economy of space as well as of time. It may mean an economy of 
 time in other ways. When goods are combined in packages they 
 can be transferred much more rapidly from one place to another 
 than if handled one by one. This leads to many other obvious 
 advantages. 
 
 Other Direct Uses of Groups 
 
 When objects are collected in groups they may the more readily 
 be protected from harm and loss. In this connection also we have 
 the proverb that in union there is strength. The acquisition of 
 knowledge is often facilitated also, since what is true of one member 
 of a group is likely to be true in a measure also of the other mem- 
 bers of the group. 
 
 Transcendent Uses 
 
 It is important to note that certain of the fruits of the group 
 method are what may be termed transcendental, that is, they are 
 qualitative and infinite, and often, apparently, could not be obtained 
 in any other way than by the use of the assemblage principle. Thus 
 a number of men by combining are often able to achieve an object, 
 such as building a railroad, which no one of them singly would be 
 able to accomplish. Other transcendent results which may follow 
 (often in an unexpected and dialectic way) are confidence and 
 stimulus to the builders and certain benefits to the public which 
 result from the operation of the road. 
 
 A mere improvement in a group may lead to a like series of 
 results, as when an increase in the number of vibrations in a wire 
 creates an audible sound, or a concentration of the essential parts 
 of a gas engine makes the aeroplane possible. 
 
62 SOURCES OF EFFICIENCY 
 
 Complex Fruits 
 
 Owing to the general nature of the group the various classes of 
 advantages connected with its use often occur together in a highly 
 complex and self -developing way. Thus the combination of many 
 small and scattered telegraph and telephone systems into one large 
 organization brings many advantages, as increased range and fre- 
 quency of use for each instrument, hence economy of service, hence 
 improved service, and therefore a better development in many ways 
 of the country served. 
 
 Many similar but larger benefits have resulted from the union of 
 the various states composing the United States, with further ad- 
 vantages such as security from enemies and oppression. 
 
 When a number of small rural schools are combined to form one 
 large central school, the pupils may be distributed in grades, fewer 
 and better teachers employed, each teacher's work will receive a 
 larger multiplier, reciprocal reuse of the combined libraries will 
 result, outside lecturers may be employed, with a dialectic of other 
 advantages to the various local communities concerned. 
 
 When a railroad is electrified, a large number of locomotives are 
 replaced by one central power house. This has the advantage of 
 replacing many engineers by one; that is, of multiplying the work 
 of the engineer employed. The firemen on the locomotives are re- 
 placed largely by mechanical methods of handling fuel. The con- 
 centration involved also makes it possible to protect the engine from 
 cold and loss of heat by the use' of surrounding walls and other 
 devices. It also prevents loss in the form of steam blown off when 
 a locomotive is standing still. Many other direct and indirect ad- 
 vantages might be mentioned. 
 
 As a still more general illustration we may consider the relation 
 of different forms of energy. Franklin identified lightning and elec- 
 tricity with manifest fruitful results. Oersted went a step further 
 and showed the common nature of magnetism and electricity with 
 still further advantages. Joule and Mayer advanced still further 
 and revealed the essential identity of all physical forces as light, 
 heat, kinetic energy, and electricity. It would take a volume to 
 enumerate the beneficial results which have followed from this close 
 grouping of the forces of nature. For the more vital and compre- 
 hensive the elements comprising a group, the greater, as a rule, 
 are the advantages following from the use of the group. 
 
THE GROUP 63 
 
 Uses from other Points of View 
 
 The value of the group principle might be made evident from 
 many other points of view as by trying to realize what life would 
 become without the use of groups, or by noting that the history of 
 human progress has been, in one respect, a history of improving 
 groupages. It is also a help in realizing the importance of the 
 group as a source of efficiency to observe the useful powers of 
 certain special forms of the group principle as of unity, union, 
 concentration, combination, cooperation, etc. Stating the matter 
 in a more general form we note that every word beginning with a 
 syllable like con-, com-, col-, syn-, syl-, or sys-, stands for a 
 specifically realized group. Concepts, for instance, are group ideas, 
 which, to use the comparison of William James, are a kind of seven 
 league boots carrying us forward in our thinking with magical 
 rapidity and ease. So groups in general give wings to the various 
 processes of life. 
 
 "The man who will show me the one in the many", says Plato, 
 "I will follow about like a God." All that mankind has learned 
 since Plato's time has but added to the force of his words. 
 
 Limitations in Utilities of Groups 
 
 Certain limitations in the advantages connected with the use of 
 groups, or of one-in-manynesses, should be mentioned before closing 
 this part of the discussion. Thus a very extensive unification fre- 
 quently brings the drawback of stifling competition and often of 
 checking invention and initiative. A high degree of concentration 
 may also increase the evil results of error or abuse; that is, be a 
 source of loss instead of gain. For instance, when all the lights 
 of a city are combined in one electrical system, an explosion at 
 the central power house may plunge the whole city into darkness. 
 Direct theft of a large bulk of wheat or corn is almost impossible, 
 but if the value of the grain be condensed into a diamond or rep- 
 resented by a signature written on a piece of paper, such theft be- 
 comes relatively easy. 
 
 Hence the general statement may be made that groups owing 
 to their more comprehensive nature often lead to greater dangers 
 and losses than occur in the application of the reuse and unit and 
 multiplier principles. 
 
64 SOURCES OF EFFICIENCY 
 
 ANALYSIS AND DEFINITION 
 
 Comparison with Reuse and Unit and Multiplier 
 
 The more or less ultimate sources of efficiency in the group and 
 its principal components and characteristics in other respects have 
 already been stated in the preceding part of the chapter. Thus, as 
 compared with reuse and the unit and multiplier, the group idea is 
 less personal, implies in less degree the idea of time and succession,, 
 is more static and more remote from the idea of immediate gain. 
 The unit elements composing it may be less uniform, definite, and 
 homogeneous. In a word in its widest sense, the group concept is 
 less concrete and hedged in by categories ; that is, is more abstract 
 and general. 
 
 Uniqueness in the Group 
 
 It is also to be remembered that the group, like other primal 
 instruments of efficiency, contains a certain unique and character- 
 istic essence which perhaps is largely beyond analysis, and which 
 to a certain degree is the source of its efficiency. 
 
 Definitions 
 
 A definition, even though it be imperfect, is often an aid in 
 using a concept. We may define a group as a manyness which can 
 be treated in some respect as one. 
 
 The elements of a group are .the individual objects which are 
 combined to constitute the group. 
 
 Fundamental Nature of the Group 
 
 In the concept of the group, or of the one as related to the many, 
 we have what is perhaps the most fundamental source of efficiency 
 at our disposal. We obtain other approximately primary sources of 
 efficiency by combining groups in certain special ways or by giving 
 the parts of a group certain special forms. These additional primary 
 agents of efficiency will be treated in the chapters which follow. 
 
 METHODS OF APPLICATION 
 
 Much that was said in previous chapters concerning the best 
 methods of utilizing reuse and the unit and multiplier principle as 
 sources of efficiency applies to the general group or assemblage 
 principle. But in connection with the group as such these methods 
 
THE GROUP 65 
 
 are often to be modified, and in some cases new principles of 
 method developed owing to the peculiar characteristics of the 
 group. 
 
 Vast Number of Groups 
 
 For instance, in order to make the most efficient use of the 
 group, it is important to realize the vast number of groups which 
 exist or may be devised. It facilitates this conception to realize the 
 immense variety of elements which may be combined in assemblages, 
 the great diversity of means by which these elements may be bound 
 together, and the many different forms which groups as a whole 
 may assume. In developing these conceptions we are aided by the 
 comparative freedom of the group idea from limiting categories, 
 and also by the possibility of beginning with very abstract and gen- 
 eral elements and forms, and annexing different categories, or con- 
 crete considerations, singly or in combination, in systematic ways. 
 
 Adaptation of Groups 
 
 It is also important to study the application of groups with refer- 
 ence to the different practical limitations which arise in different 
 cases. The very great variety of possible groups makes such study 
 necessary in order to select the best form of group for any given 
 purpose. Thus it is desirable to know the peculiar advantages and 
 disadvantages in each form of concentration or unity. For ex- 
 ample if the extent to which magnetic energy can be concentrated 
 in a bar of soft iron had been realized earlier, the invention of the 
 dynamo would have been accelerated a number of years. In like 
 manner the knowledge that the energy contained in a ton of radium 
 equals that contained in 1,500,000 tons of coal may some day be of 
 immense direct practical importance. 
 
 Symbolism an Aid to Groups 
 
 In cases where the unit objects under treatment must remain 
 scattered it should be noted that the formation of more or less 
 permanent groups is often facilitated by affixing some common 
 mark or sign to elements belonging to a required group. Even 
 when it is not necessary to do so, it often adds to efficiency results 
 to follow this method, as when the soldiers belonging to a given 
 regiment wear some distinguishing symbol. 
 
66 SOURCES OF EFFICIENCY 
 
 Practice in Making Groups 
 
 Owing to the fundamental efficiency importance of the group it 
 is highly advantageous to practice forming groups on all possible 
 occasions till the group habit is formed. In this connection it is 
 important to realize the many ways in which the formation of 
 groups can be aided by the use of such simple concrete objects as 
 pins, elastic bands, mucilage, pigeonholes, chests of drawers, or by 
 the use of mere relative position. Similarly it is important to form 
 the habit of making mental groups, as by cultivating the perception 
 of similarities and differences. 
 
 It may be well to mention a few of the advantages which result 
 from the formation of the group habit. We have (i) the direct 
 economies of space used in storing objects; (2) the utilization of 
 groups by the unit and multiplier and like methods; (3) the subse- 
 quent more or less spontaneous development of individual groups 
 into systems; (4) the development of the power quickly and easily 
 to improvise groups in any given situation. 
 
 Standard Groups 
 
 Mention should be made of the importance of the thorough 
 mastery and preferential use of certain standard forms of groups. 
 It is often useful for society in general to employ such groups. 
 At the same time each individual may make special use of certain 
 standard groups adapted to his personality and surroundings. 
 
 Other things being equal it is important to use groups in which 
 the elements, ties, and forms are as vital and comprehensive as pos- 
 sible. Thus mastery of a group of the primary efficiency princi- 
 ples which are under investigation will be found to include a host 
 of more detailed efficiency methods. In this connection it should not 
 be forgotten that while a group may on the one hand be a crude incip- 
 ient implement, on the other it may be a final polished instrument 
 giving unusual speed and power to an efficiency process. 
 
 Manifold Groupings 
 
 The use of groups combined in systems will be considered in the 
 next chapter. At the present point, however, mention should be 
 made of the advantage of using, more or less simultaneously, several 
 group methods in a given domain of material. Thus the process of 
 
THE GROUP 67 
 
 extracting the meaning from a book may often be facilitated by 
 reading the book backward or beginning at the middle, or in va- 
 rious scattered places, and employing special methods of grouping 
 the facts and ideas contained. This procedure not only often brings 
 important economies but also leads to many higher results. It is 
 often useful to use this method in connection with a more system- 
 atic use of groups, as in social or political work, or in the co- 
 operation of the parts of a large corporation. 
 
 Definition of Efficients 
 
 In referring to the primary efficiency principles which we are 
 studying, it will often be convenient to denote them as a class by 
 the term Efficients. For example, the primary agents of efficiency, 
 or the Efficients studied thus far, are reuse, the unit and multiplier, 
 and the group. The adjective, efficiental, means pertaining to the 
 Efficients. 
 
 Summary of Chapter 
 
 A brief statement of the ground covered in the present chapter 
 will now be of use. A still broader and more fundamental principle 
 of efficiency than either reuse or the unit and its multiplier is the 
 group. Groups may be classified according to objects composing 
 them, or according to the ties which hold these objects together, or 
 according to the forms of the groups themselves. Special mention 
 may be made of groups which are homogeneous or heterogeneous, 
 natural or artificial, direct, inverse, reciprocal, or manifold. 
 
 Groups are sources of economy and new power in ways additional 
 to those characteristic of reuse and of units. Hence the values of 
 groups are correspondingly more transcendent and complex. The 
 group is so fundamental in its nature that the other primal sources 
 of efficiency may be regarded as various methods of using the 
 group. 
 
 Here also it is important to realize the great number of possible 
 groups and to adapt different species of groups to different uses. 
 Especial attention is also to be paid to the use of symbolism in con- 
 nection with groups, to constant practice in their formation, to the 
 use of standard groups, and, in some cases, to the use of manifold 
 groupings. 
 
68 SOURCES OF EFFICIENCY 
 
 
 
 EXERCISE 4 
 
 
 
 Give an example 
 
 of each 
 
 of the following species 
 
 of 
 
 groups : 
 
 I. Inorganic 
 
 
 6. Logical (or ideal) 
 
 11. 
 
 Complex 
 
 2. Biologic 
 
 
 7. Homogeneous 
 
 12. 
 
 One dimensional 
 
 3. Social 
 
 
 8. Heterogeneous 
 
 13. 
 
 Two dimensional 
 
 4. Mental 
 
 
 9. Natural 
 
 14. 
 
 Three dimensional 
 
 5. Religious 
 
 
 10. Artificial 
 
 
 
 Give an example of each of the following kinds of group-making ties: 
 
 15. Inorganic material 18. Chemical force 21. Social force 
 
 16. A living object 19. Biologic force 22. Religious force 
 
 17. Physical force 20. Mental force 23. Ideal force 
 
 24. Give an example of a tie that is external to the elements constituting a 
 group. Also to a tie it hat is embodied in one of the elements. 
 
 25. Give an example of a direct group. Of one that is inverse. Of dual 
 reciprocal groups. Of an w-reciprocal group. 
 
 26. Find the degree of time efficiency in teaching a classi of 48 persons 
 for an hour, as compared with teaching each of the 48 persons individually 
 for an hour. As compared with teaching them in groups of 16. Of 8. 
 
 27. Also state the time efficiency of each of the other processes in Ex. 
 26 as a per cent of the first process. 
 
 28. Give an example where a person's work is multiplied in value by the 
 use of a natural group of some kind. By the use of an artificial group. 
 
 29. Give an instance where the use of groups gives speed in handling 
 objects. 
 
 30. Where it saves property from destruction. 
 
 31. Where it results in economy of the attention or of other mental forces. 
 
 32. Where complex advantages result. 
 
 33. Where a transcendent result is obtained. 
 
 34. Give an example of the use of the group method as a crude initial 
 instrument of efficiency. 
 
 35. Also where it is a finished, final instrument. 
 
 36. Show how the spinning jenny illustrates the group principle as a means 
 of obtaining efficiency. 
 
 37. In one day one man by using a common plow turned over ij^ acres of 
 land. Another man using a gang plow turned over 40 acres in two days. 
 State the degree of wage efficiency in the second process as compared with 
 the first. Also express the efficiency of the first process as a per cent of 
 the second. 
 
 38. Why should goods when bought on a large scale cost less? 
 
 39. Combine 8 roses + S lilies -f- 6 pinks into a single group by the use 
 of some more general word than those used in the given expression. 
 
 40. Give two examples of the advantages of concentration (or of the dis- 
 advantages of separation). 
 
THE GROUP 69 
 
 41. State the efficiencies connected with the use of one comprehensive elec- 
 tric light system for a city, instead of several thousand oil lamps. 
 
 42. Give an example where a number of scattered and moving objects 
 are combined into a group by means of symbols or marks of some kind. 
 
 43. State the advantages! of the concentration of electricity in the form of 
 high voltage on a transmission wire. 
 
 44. Also those in the close alliance for a century and a half of the different 
 members of the Rothschild family. 
 
 45. Ascertain the etymological meaning of the words logic, category, con- 
 sciousness, and law, and show that in the meaning of each the group idea is 
 prominent. 
 
 46. State some of the advantages of having those cells in an organism 
 which perform the same function collected in one or two organs, as in the 
 biain, liver, lungs, etc. 
 
CHAPTER V 
 
 MULTIPLICATIVE GROUPS 
 
 Groups may be used not only singly, but also in combination in 
 the form of extended systems, with a corresponding increase of 
 efficiency results. 
 
 Illustration of Multiplicative Groups 
 
 For example, if the commanding general wishes a secret order to 
 be conveyed verbally to each soldier in his army, he does not at- 
 tempt to speak personally to each individual in the army, or even 
 to have a messenger do so. The general communicates the 
 order to his corps commanders, each of whom conveys it to his 
 division commanders, each of whom transfers it to his immediate 
 subordinates, and so on till the private soldiers are reached. In this 
 way the order is conveyed with repeated use of the advantages 
 which characterize the group method, viz. : less labor, greater speed, 
 practical simultaneity of knowledge, quickness and unity of action, 
 less time for betrayal, ancl freedom for the commanding general to 
 devote most of his time and energies to more important work than 
 the communication of orders. In this case the system of groups 
 involved consists of the group of corps commanders, the various 
 groups of division generals, and so on. 
 
 Diagram of Essence of a Multiplicative Group System 
 
 To put the matter in an abstract and comprehensive form, if we 
 have a group of n elements (as A, B, C, etc.), each of which is 
 connected with a set of other elements (as A with a, b, c) forming a 
 secondary group; each element in a secondary group being con- 
 nected in like manner with elements in a tertiary group, and so on ; 
 we have a series of groups so related that the aggregate may be 
 termed a system of multiplicative groups. This is the instrument of 
 efficiency to be studied in the present chapter. 
 
 In the diagram the group composed of the elements, A, B, C, etc., 
 
 70 
 
MULTIPLICATIVE GROUPS 
 
 71 
 
 is termed the prime group, or the group of the first order; the 
 
 groups represented by a, b, c, and d, e, 
 X i f etc., are termed the secondary groups, 
 £1 ^Z— ? or groups of the second order ; the set 
 of groups which include x, y, z, etc., are 
 — pfr °^ ^ e tn ^ r< ^ order, and so on. 
 
 CLASSIFICATION 
 
 The various elements and ties which 
 enter into the formation of multiplicative 
 groups are, in general, the same as those 
 mentioned in connection with single 
 groups (see pp. 57-58). Hence the clas- 
 sification of multiplicative group systems 
 with reference to elements and ties, is 
 approximately identical with that given 
 in the preceding chapter for groups. 
 
 It is different however with the classi- 
 fication of multiplicative group systems 
 /> rt= ^^ _ pf p with respect to the forms which they may 
 
 assume. Owing to the more elaborate 
 nature of systems of groups, these sys- 
 tems appear in certain important forms 
 which are peculiar to the category of efficiency under investigation. 
 
 Numerical Species of Multiplicative Groups 
 
 A multiplicative group system may be characterized by some 
 number prominent in its structure, as by the number of orders of 
 groups which it contains. Thus we may have a dual system, as a 
 group of teachers and their groups of pupils ; or a 3-order system, 
 as superintendents, teachers, and pupils. An important special case 
 is that of the infinite system, or one which contains an unlimited 
 number of orders. 
 
 A multiplicative group system may also be characterized by some 
 standard number of elements used in each of the constituent groups 
 of the system. Thus the system as pictured in the above dia- 
 gram is a grouping by threes. An important special number form 
 is a dual system in which each group consists of only two elements, 
 a positive and a negative one. Such a system is used in the so- 
 
72 SOURCES OF EFFICIENCY 
 
 called game of Twenty Questions, where the aim is to identify a 
 particular object by twenty successive questions each of which is 
 answered yes or no. What is essentially this method is also em- 
 ployed in much detective work and scientific investigation. 
 
 Spatial Forms of Group Systems 
 
 Spatially, multiplicative systems may be characterized by the 
 number of their dimensions. Thus we may have a one-dimensional 
 or linear system. This consists of a number of elements arranged 
 in a line and treated by some multiplicative method. This form is 
 so important that it will receive special treatment later (see p. j6). 
 
 Evidently also a group system may be two-dimensional or areal 
 in arrangement. By way of illustration we have the diagram given 
 on p. 71, or a river and its branches, or a family tree as ordinarily 
 diagrammed. An important case of somewhat different nature is 
 that of an area divided and subdivided into parts, an example being 
 a country divided into states, counties, and townships. 
 
 Similarly a group system may have three dimensions. An ex- 
 ample is a tree and its branches. An illustration of a three-dimen- 
 sional multiplicative group system of somewhat different kind is a 
 house divided and subdivided into parts as rooms, closets, shelves, 
 drawers, etc. Three-dimensional systems of many special geometric 
 shapes are possible as cone-shaped, pyramidal, spherically radial, 
 and other forms. 
 
 It is important to discriminate between group systems whose 
 parts are continuous or connected throughout, and those which are 
 discontinuous or made up of parts more or less separated in space. 
 An example of the former is a river system, or a tree and its 
 branches. An example of the discontinuous form is an army as 
 organized into regiments, brigades, and divisions. 
 
 Other Important Forms of Multiplicative Groups 
 
 With reference to the category of time, multiplicative group 
 systems may be temporary and provisional, or permanent. It is 
 often convenient to describe genetic or causal systems as temporal, 
 since they are determined by factors acting in time. An instance 
 is a family tree or the consequences resulting from an event like 
 the explosion of the battleship Maine in the Havana Harbor in the 
 year 1897. 
 
MULTIPLICATIVE GROUPS 73 
 
 As to order we have species which act forward or backward, di- 
 rectly or inversely, by expansion or contraction, by synthesis or 
 analysis. 
 
 Systems of multiplicative groups may differ qualitatively in in- 
 numerable ways. The most important distinction in this respect for 
 our purpose is that denoted by the terms homogeneous and hete- 
 rogeneous. A group system may be homogeneous (or heterogen- 
 eous) in several different ways, as with respect to the number of 
 elements constituting its individual groups ; or as to the size or other 
 characteristics of the individual elements, or of the ties binding 
 them ; or with respect to the forms of the component groups. Thus 
 a telephone system is heterogeneous for the reason that part of it 
 (the system of connected wires) is continuous and part (the system 
 of keyboards) is discontinuous. 
 
 Other cases of heterogeneous multiplicative group systems are a 
 house and its parts ; or the classification of sensations according to 
 their quality, intensity, and duration ; or a system of transportation 
 consisting of ocean steamships, railroads, trolley lines, automobiles 
 or carriages, and human locomotion. 
 
 Federal Species of Multiplicative Groups 
 
 Special attention should be paid to certain important individual 
 forms of multiplicative group systems. We consider first what 
 may be regarded as the normal or standard form; that is, the best 
 form for general purposes. The illustration given in the opening 
 paragraph of this chapter (p. 70) is of this type. It may be de- 
 scribed as the federal or hierarchical species. It may have one, 
 two, three, or n dimensions, and may often be transformed from one 
 of these dimensional states into another. Other illustrations of it 
 are the organization of the Roman Catholic Church, or any similar 
 ecclesiastical, or any political system of government. Many busi- 
 ness organizations are of the same general type. For instance in 
 the building trade we find a combination of architects, contractors, 
 foremen, mechanics, laborers, and apprentices. 
 
 It is to be noted that the normal or federal type may be either 
 continuous or discontinuous. Examples of the latter are those 
 given in the preceding paragraph. Illustrations of the continuous 
 or branching federal type are a tree and its branches, the gas or 
 water pipes of a city, the nerves, or blood vessels of the human body. 
 
74 SOURCES OF EFFICIENCY 
 
 The use of latitude and longitude as a means of locating all 
 places on the earth's surface may also be regarded as the use of 
 a branching group system. The same statement applies to a sys- 
 tem of coordinates of any sort as used in mathematics or science. 
 
 A federal system may also be continuous in certain parts or re- 
 spects, and discontinuous in others. An instance is that cited above 
 of a telephone system of wires and keyboards. An important case 
 of somewhat different nature is that which may be termed articu- 
 late, as the system of bones in the human skeleton ; or, more broadly, 
 the system of bones, muscles, and organs in the human body; or, 
 more broadly still, the essential parts of every biological and social 
 organism. Articulate language, both oral and written, is largely 
 of the same nature. 
 
 Constitutive Group Systems 
 
 The normal or standard federal system may take two other 
 contrasted but closely related forms. The first of these is what 
 may be termed the constitutive multiplicative group form. This 
 consists of a domain divided into certain major parts, each of these 
 parts being divided into smaller parts and so on. An example is 
 that already given of a country divided and subdivided into states, 
 counties, and townships. Other illustrations of constitutive multi- 
 plicative group systems are a city marked off into wards, blocks, and 
 houses; a library separated into alcoves and shelves; a book re- 
 garded as consisting of chapters, paragraphs, sentences, and words ; 
 or a drama as formed of acts, scenes, lines, and words. 
 
 Marginal Group Systems 
 
 The other of the two species named above may be termed the 
 marginal form. In this type each subgroup is something apart from 
 and attached to an element in the group above. Thus in the organiza- 
 tion of the Roman Catholic Church the cardinals are apart from 
 and attached to the Pope. So in a river system, or the branches of 
 a tree, the smaller branches are apart from and attached to the 
 larger branches. Hence in a marginal multiplicative group system, 
 the tie which holds the elements of a subgroup together is con- 
 tained in an element of. the next higher group ; while in a con- 
 stitutive group the tie is in some outside object or some abstract 
 consideration. 
 
MULTIPLICATIVE GROUPS 75 
 
 A multiplicative group system may be part marginal and part 
 constitutive. Thus a railroad system (marginal) may have at- 
 tached to it certain cities (constitutive). So an organization may 
 have the two forms as parallel aspects or elements. Thus we may 
 have a continent subdivided into certain realms of ecclesiastical 
 jurisdiction (constitutive) and these districts governed by a system 
 of church officials (marginal). Similarly the area drained by a 
 river system may be regarded as divided constitutively while the 
 river system itself is marginal in structure. 
 
 Strandal Multiplicative Groups 
 
 A strandal multiplicative group system is one formed of linear 
 elements each of which is subdivided into parts of different orders. 
 A system of this kind may be regarded as constitutive from one 
 point of view and marginal from another, and hence is useful in 
 connecting one of these two types with the other. An example of 
 the strandal type is a river and its branches. For in a river system, 
 if the water which enters each small tributary be followed in its 
 course through the larger branches and main stream to the ocean it 
 may be regarded as a continuous strand in the system, and the 
 whole river system may be regarded as a systematized bundle of 
 strands, and hence as constitutive in its nature. 
 
 In like manner if we regard the trunk parts of a railroad system 
 or a tree as manifolded by reuse or by swifter use, each of these 
 systems as a whole may be regarded as strandal. Almost all mar- 
 ginal systems may be analyzed in a similar way and thus reduced 
 to the strandal of constitutive form. 
 
 An important case to be considered in 
 ,,. ,. . ,1 , r ,, , 1st Form 2d Form 
 
 this connection is that of the permuta- 
 tions or combinations of a set of ele- /- 
 ments, as of letters (or sounds) which r^1 
 are combined to form words. Thus an ( 
 array of letters as first written in the i , 
 accompanying tabulation at the right is A-l B ■) 
 marginal in structure. But if the let- ( 
 ters in the higher groups be regarded as 
 reused the array may be rewritten in the ^ 
 second form, which is essentially consti- 
 tutive in nature. 
 
 A 
 
 AAA 
 
 B 
 
 AAB 
 
 C 
 
 AAC 
 
 
 ABA 
 
 A 
 
 ABB 
 
 B 
 
 ABC 
 
 C 
 
 ACA 
 
 
 ACB 
 
 A 
 
 ACC 
 
 B 
 
 
 C 
 
 
76 SOURCES OF EFFICIENCY 
 
 The advantages connected with the first method of arrangement 
 are certain economies as of material, the more evident indication of 
 groupages to the eye, and reuse in certain kinds of mastery. The 
 advantages in the second form are that each completed strandal 
 element, as ABA, can readily be identified wherever placed; that 
 consequently selections from such a system may be arranged in 
 linear order with any desired gaps, as in the cards in a card cata- 
 logue, or with the words in a dictionary; or that they may be ar- 
 ranged in various useful orders such as are employed for instance 
 with the words of a sentence. This brings us to a fuller consider- 
 ation of the linear type of group systems. 
 
 Linear Group Systems 
 
 A linear multiplicative group system has already been defined as 
 one whose elements are arranged in a line. A straight line itself 
 when divided and subdivided into feet, inches, and fractions of an 
 inch is an example of a constitutive linear system. The division of 
 time into centuries, years, months, days, etc., is a similar instance; 
 a series of dots (or any separate objects) when arranged in a 
 line and combined variously may form a linear constitutive or a 
 linear marginal group system, according to circumstances. Im- 
 portant somewhat general instances of this class are the number 
 signs i, 2, 3, 4, 5, etc., written in order, or the alphabet A, B, C, D, 
 etc. It is often an advantage to. treat by the linear multiplicative 
 group method any temporal succession of events, as thoughts in 
 one's consciousness, or acts to be performed during a given period 
 of time as a day or year. Similarly, as was illustrated with refer- 
 ence to the above diagram, it is frequently a source of efficiency to 
 convert a domain of material into this form, as when we arrange 
 words alphabetically in a dictionary and are thus enabled to reuse 
 our knowledge of the order groupings in the alphabet in looking up 
 the meaning of a word. 
 
 Quite as important as the linear is what may be termed the semi- 
 linear, or approximately linear system of multiplicative groups. 
 This is a linear succession of elements each of which is somewhat 
 areal in its nature. 
 
 Illustrations of the semi-linear species are a line of print, or more 
 noticeably the pages in a book, a card catalogue, a succession of 
 
MULTIPLICATIVE GROUPS yy 
 
 states of consciousness, the notation of a piece of music, or the 
 keys constituting the keyboard of a piano. 
 
 A group system may be areal in some parts and linear in others. 
 
 Two Principal Types of Group Systems 
 
 Hence, in general we find two principal types of multiplicative 
 group systems : 
 
 The first is, in the main, spatial, logical, deductive, full of uni- 
 formities, abstract, a priori, and largely constitutive. 
 
 The second is dominantly temporal, genetic, branching, strandal, 
 full of diversity, concrete, a posteriori, inductive, and largely 
 marginal. 
 
 The federal system includes the essence of both of these types. 
 
 Complex Group Systems 
 
 Multiplicative group systems may be combined and complexed in 
 various ways. A simple instance is the combination of the root 
 system and the branch system of a tree by means of a common 
 trunk. Of like nature are any group systems of intake with the 
 corresponding system of output, or related systems of induction and 
 deduction. Also two or more systems may be combined and used 
 in more or less parallel fashion as an aid to each other. Thus we 
 have the multiplicative mechanism of a clock, corresponding to 
 the multiplicative division of time into parts. Another illustration 
 is the combination of an alphabetical name list and a number list 
 to denote the employees of some large organization. 
 
 Manifold Mutiplicative Grouping 
 
 An important source of efficiency in manipulating a domain of 
 material is a manifold multiplicative grouping of the given domain. 
 A .simple example of this is the multiplicative grouping in one way 
 of the parts of machine for shipment; and of the same parts in 
 another way, when the machine is erected for use. So the contents 
 of a book may be grouped multiplicatively in different ways, as by 
 chapters and also by an index. The words of a language may be 
 grouped multiplicatively either as parts of speech, or etymologically, 
 or alphabetically, or with respect to likeness of meaning as in a 
 thesaurus. 
 
 Similarly the parts of a country are often grouped in various 
 
78 SOURCES OF EFFICIENCY 
 
 multiplicative ways, as by political divisions, by the use of latitude 
 and longitude, according to elevation and drainage, with reference to 
 railroad or other transportation lines ; by rainfall, climate, resources, 
 population, culture, and other categories. So plants may be classi- 
 fied according to their uses, by lines of descent, or by the technical 
 methods used by botanists, or according to the color, size, and season 
 of appearance of their flowers. 
 
 A combination in any given business of what are called line or- 
 ganization and staff organization is an important example of 
 manifold multiplicative grouping. 
 
 Similar illustrations might be cited without limit. For so simple 
 an object as a straight line may be divided multiplicatively in an 
 endless number of different ways. 
 
 Manifold Reciprocal Group Systems 
 
 Manifold multiplicative grouping sometimes takes a form which 
 may be termed reciprocal. For example we may form a family tree 
 by taking an ancestor and tracing his descendants ; or we may form 
 a family tree which spreads in the opposite direction by beginning 
 with a descendant and tracing his ancestors back through preceding 
 generations. When the same material is treated thus in two opposite 
 directions, the result may be termed a dual reciprocal system. Such 
 systems may exist with respect to a set of objects and their qualities, 
 between forms and substances, generals and particulars, structures 
 and functions, and other similarly related pairs of categories. 
 
 An n-reciprocal group system is also possible. Thus in a domain 
 of n elements each element may be made the starting point or apex 
 of a multiplicative group system which includes most or all of the 
 given n elements. This n-iold reciprocal multiplicative relation 
 prevails more or less among all the individuals in a civilized com- 
 munity ; among a number of cities connected by a network of rail- 
 roads, telegraph, or telephone wires. It exists among the nerve 
 centers or even the cells of the human body ; and indeed, in certain 
 ways, among all the atoms, ideas, and entities of the universe. 
 
 An important instance of the species under consideration is that 
 of scientific formulas, or formula-equations, such as s = ^ gt 2 , 
 each letter of which may be given the lead in turn. The result is 
 
 other formulas, as g = -H an ^ t _ J—, each of which represents 
 a useful aspect of the matter in hand. 
 
MULTIPLICATIVE GROUPS 
 
 79 
 
 Rectangular Arrays 
 
 Another important case of the w-reciprocal class of multiplicative 
 group systems is that of a rectangular net work or array of any kind, 
 as the rows of corn in a field, the trees in an orchard, a set of pigeon- 
 holes, the streets in certain cities, the fibres of woven cloth, or the 
 strands in a piece of wire netting. The manifold multiplicative nature 
 of such arrays is illustrated by the fact that when pressure is brought 
 to bear on any point in a piece of woven cloth or netting, such 
 pressure is met by a special multiplicative system of cohesion radia- 
 ting from the point of stress. 
 
 Some combinations of group systems are so complex that their 
 complete analysis into component systems is difficult if not impossi- 
 ble. As an example of this we have rays of light radiating from a 
 center, reflected or refracted by different objects, and variously used 
 or transferred by them. Still more complex is the organization of 
 the human body and mind, or the development of events in human 
 history. It is to be noted however that in all such complex systems 
 there appear spots and aspects of more or less explicit multiplicative 
 structure which are sources of important efficiencies in many ways. 
 
 EFFICIENCY PROPERTIES OF MULTIPLICATIVE GROUPS 
 
 Since the multiplicative group principle is an extension of the 
 group idea and hence of the reuse and unit and multiplier principles, 
 it has the useful properties of these preceding instruments of effi- 
 ciency in an extended and pronounced form. A system of multi- 
 plicative groups also has certain efficiency functions peculiar to 
 itself and characteristic of its own more developed nature. 
 
 Economics due to Multiplicative Groups 
 
 An application of the multiplicative group principle naturally 
 carries with it a greater economy of material than a single act of 
 reuse or the employment of one group. For instance reusing a 
 word by means of a prefix saves the invention of one new word; 
 but the use of prefixes and suffixes in a multiplicative group way in 
 connection with a word stem takes the place of the formation of a 
 multitude of entirely new words. In the machinery used in trans- 
 fering power in a factory, one large wheel may be replaced by a 
 number of small wheels, geared tandem and having an aggregate 
 
80 SOURCES OF EFFICIENCY 
 
 weight which is only a fraction of that of the large wheel. This 
 economy of material in the wheels leads to an economy of space also 
 and hence of material and grounds for buildings. A railroad system 
 which connects a number of cities and smaller places is usually con- 
 structed as a trunk line with a number of branches and subbranches. 
 It is easy to see that such a system requires less roadway and material 
 of practically all kinds than would be required if each station on 
 the whole road system were connected directly with every other 
 station. The same principle of economy of material is found in a 
 system of telegraph or telephone lines, and in the blood vessels and 
 nerves of any organism. In fact this economy appears in charac- 
 teristic ways in each of the species of group systems which have 
 been discussed. 
 
 The use of a multiplicative group method and system may also be 
 accompanied by a notable economy of energy. There is a saving 
 of strength in speaking to a number of persons assembled as a 
 group; much greater then is the economy which results when a 
 message is conveyed through a large system of groups as in the 
 opening illustration of the chapter. 
 
 If the words in a dictionary were not arranged in alphabetic and 
 therefore linear multiplicative group order or in some other system- 
 atic way, in looking up a given word we should need to look at 
 every word in succession till we came to the desired word. Hence 
 on the average, we should need to examine one half the words in 
 the dictionary, and therefore go through, say, 150,000 items of work 
 instead of 5 or 6. 
 
 Similarly if the population of the world were not grouped multi- 
 plicatively in some way as in that indicated by the address on a 
 letter, a messenger sent with a letter to any particular individual 
 would need to interview, on the average, one half of the people in 
 the world before finding the desired person. 
 
 By like methods it may be shown that the use of multiplicative 
 groups often leads to economics of time, space, money, and re- 
 sources of all kinds. 
 
 Increased Power due to Multiplicative Groups 
 
 The use of systems of groups leads not only to diminished ex- 
 penditures but also to an increase of results. For instance by the 
 
MULTIPLICATIVE GROUPS 8l 
 
 use of organized methods the products of a farm may often be 
 greatly increased. By facilitating the consultation of encyclopedias 
 and journals, the multiplicative group principle leads to an en- 
 larged reuse of the work of others by any one investigator and 
 hence to an augmentation of results. So in general by making 
 communication and transportation of all kinds easy, the systematic 
 application of the group principle increases the volume and elevates 
 the character of reuse and multuse. 
 
 A system of multiplicative groups, for many purposes, may be 
 regarded as a single group of a high order with the efficiency 
 properties as already stated for the single group correspondingly 
 increased. Examples are the electric lights in a city, the soldiers in 
 an army, or the citizens of a country. 
 
 Group Systems Produce other Efficients 
 
 Multiplicative group systems are also sources of efficiency in 
 more indirect ways. These may be better realized if we anticipate 
 to a slight degree some of the principles of efficiency to be investi- 
 gated more fully later. Thus multiplicative groups often produce 
 the uniformities or equivalences (see Chapter VIII, p. 130) which 
 are the basis of many new single groups or organized groupages. 
 This may happen in different ways as 
 
 ( 1 ) By the extended propagation of original data ; 
 
 (2) By discovery of the fact that different domains contain or 
 
 are governed by the same group systems ; 
 
 (3) By virtue of the power possessed by an infinite series of 
 
 filling in a gap between two widely separated or contra- 
 dictory objects. 
 
 These uniformities not only give rise to new groupages but to 
 other results which will be presented in Chapter VIII (p. 130). An 
 illustration of these is the fact that the recognition of a common 
 multiplicative group essence in a tragedy, a symphony, and a system 
 of government may lead to much marginal reuse in acquainting 
 oneself with these, and obtaining pleasure and profit from them. 
 
 Multiplicative groupages are also sources of diversity in its 
 various forms and hence lead to the fruits of diversity, such as 
 delicacy of motion, tact, new units, etc. For instance all machinery 
 
82 SOURCES OF EFFICIENCY 
 
 which acts with fine gradation of power will be found to be charac- 
 terized by a well developed multiplicative structure. 
 
 Other similar illustrations are the deliberation and relative wisdom 
 with which a federal government acts as compared with the sudden- 
 ness and passion of a mob or even, in many cases, of a pure demo- 
 cracy. Likewise a multiplicative grouping of religious beliefs makes 
 possible a unity of view in certain prime or first group matters while 
 leaving freedom as to details, and in this way produces efficiency 
 results of a high order. An illustration of a different kind is the 
 diversity of function produced by the multiplicative group structure 
 of a wire netting. In such a structure the economy of material is so 
 great that space is left through which the air may freely pass, while 
 flies and mosquitoes are excluded. 
 
 A multiplicative group system also often opens the way for cer- 
 tain advantageous directive processes (see Chapter XI, p. 192), 
 as for substitutions and exchanges. Thus if the process of making 
 a chair or any other article be grouped multiplicatively, certain 
 parts of the process may be performed by machinery instead of by 
 hand, with a great saving of time and labor. 
 
 So certain primal parts of a physiological or mental process may 
 become automatic or instinctive; that is, be performed by force of 
 a low order or even automatically. 
 
 Results Not Otherwise Attainable 
 
 The systematic use of the multiplicative principle frequently 
 brings certain remote and unanticipated results. Some of these 
 are often unique and apparently otherwise unattainable. Thus in 
 the solution of a mathematical problem of a certain kind the 100,000 
 or more guesses and tests which would be necessary if no systematic 
 method were followed may be reduced, for example, to 30 used in 
 successive groups of say 5 each. Since a solution by the former 
 method is practically impossible such solutions as have been obtained 
 in the way indicated may be said to be due entirely to the multi- 
 plicative group principle. Similarly air thus far has been liquefied 
 only by a stepping down of temperatures. So on a vastly larger 
 scale, if human activity had not been highly organized the existing 
 triumphs of art, engineering, and science would never have come into 
 being. 
 
MULTIPLICATIVE GROUPS 83 
 
 Complex Results 
 
 Evidently the above benefits of group organization may be com- 
 plexed in many ways. As an illustration we have the varied and 
 manifold fruits of good government. 
 
 Values in Terms of Human Progress 
 
 The efficiency value of the multiplicative group principle, like 
 that of the other Efficients may be presented in certain general and 
 more or less pictorial ways. For example we have the fact that 
 human progress has been characterized and largely determined by 
 improving multiplicative group systems. This is true not only of 
 civilization as a whole but also of each department of life and 
 knowledge. Thus for example mathematics consists mainly of a 
 multiplicative grouping of space and quantity ; psychology of a simi- 
 lar grouping of mind ; physical science of a like grouping of matter 
 and force; history of the multiplicative grouping of various data 
 with respect to time ; logic and philosophy of a treatment of multipli- 
 cative groups as independent of and underlying other categories as 
 far as possible. An improvement in each of these domains has meant 
 an improvement in its multiplicative group essence. The human eye 
 and ear are superior to the other sense organs because the former 
 contain superior multiplicative group systems. Electricity became a 
 distinct science as soon as it was developed into a multiplicative 
 group set of relations among certain primal units and elements. 
 
 In human progress the multiplicative principle has also acted 
 in certain comprehensive and sweeping ways. Thus each new 
 discovery has not simply added to, it has multiplied all preceding 
 achievements. 
 
 Lack of Group Systems Means Loss 
 
 The negative method may also be utilized in realizing the effi- 
 ciency values of the principle of multiplicative groups. The African 
 negro is not lacking in many unit elements of efficiency, but his 
 life as a whole in his native land is barbarous because he lacks the 
 power of forming any extended group system. Similarly if the 
 principle of multiplicative organization were eliminated from human 
 life in general, the world's affairs would drop back many steps 
 toward chaos. 
 
84 SOURCES OF EFFICIENCY 
 
 Familiar Words Showing Value of Group Systems 
 
 Another method of glimpsing the world of efficiencies of which 
 the multiplicative group method is the source is that of recalling 
 the benefits connected with particular but familiar forms of multi- 
 plicative groups such as organization, system, classification, co- 
 ordination, correlation, method, and order. Every progressive or 
 step by step process is essentially an application of the multiplicative 
 group principle. 
 
 Limitations in Utilities of Group Systems 
 
 Before concluding this statement of the uses of systematic group- 
 ism, attention should be called to certain disadvantages which often 
 accompany the application of this principle. Naturally the draw- 
 backs connected with reuse or any single group will often appear in 
 an enlarged way when many groups are used. But multiplicative 
 group systems also have peculiar limitations of their own. In the 
 first place a multiplicative group system often means a certain 
 amount of added machinery which, unless it is carefully used, be- 
 comes an encumbrance or even a positive evil. Expressing the 
 matter in another way we may say that under certain circumstances 
 it is more efficient to use a single large group than a system of 
 smaller groups. 
 
 Also a multiplicative group system may be a highly efficient agent 
 in the propagation of an evil act or unit of any sort. Thus the 
 value of the printing press has been largely negatived by the de- 
 grading purposes for which it has sometimes been employed. 
 
 An extended articulate machinery is exposed to other evils often 
 highly insidious. For instance in a federal government where the 
 citizens choose certain representatives, and these select other repre- 
 sentatives of a higher order, and so on, at each step of the process 
 danger exists of forgetfulness, selfishness, or corruption. So in 
 every multiplicatively organized structure, weakness and danger are 
 connected with every stage and method of articulation. It is the 
 highly organized wheat plant not the simpler grass which is subject 
 to blights and diseases. 
 
 Self-protective Power in Group Systems 
 
 It is to be noted however that a multiplicative group system con- 
 tains within itself certain means of correcting or even preventing 
 
MULTIPLICATIVE GROUPS 85 
 
 its own defects. Thus the expansiveness inherent in a multiplicative 
 system gives a largeness of view and grasp which tends to check 
 the evils specified above. Also the multiplicative propagation of an 
 error by increasing the results of the error quickly calls attention 
 to the error and the need of its correction. Again, in almost every 
 domain of material cross multiplicative group systems are possible 
 which tend to the prevention of error and loss. Thus in forms of 
 highly developed representative government, not only are certain 
 cross-groupings such as the legislative, executive, and judicial sys- 
 tems already in use, but others such as the initiative, referendum, 
 and recall are being adopted. 
 
 ANALYSIS AND DEFINITION 
 
 We wish now to investigate the ultimate sources of efficiency in 
 the multiplicative group principle in so far as these differ from, or 
 are an advance upon those already found in the single group. The 
 way may thus perhaps be opened for increased efficiencies in the 
 use of multiplicative groupages. 
 
 Number, Space, and Like Elements 
 
 Owing to the presence of different orders of groups it is evident 
 that in multiplicative group systems the element of number is more 
 prominent than in groups singly treated. 
 
 The category of space is also more evident owing to the stress 
 laid on the relative position of the parts of a system and the result- 
 ing shapes. 
 
 The element of order is here also almost entirely new and with 
 it some prominence is given to the category of time. 
 
 More emphasis is likewise laid on the category of force for not 
 only are elements bound together in groups, but groups are held 
 together to form higher groups. 
 
 Efficiental Elements 
 
 A group system implies a certain uniformity in several ways as 
 among the elements of a group in relation to each other, among 
 the groups which are placed together in a given order, and in the 
 ties which bind elements or groups together. In like manner differ- 
 
86 SOURCES OF EFFICIENCY 
 
 ences are supposed in, and are a necessary part of a system of 
 multiplicative groups. 
 
 Such a system also implies something outside of itself both in 
 general, and also from the particular fact that an element may be 
 shown to be a node or point in which several categories of utility 
 intersect. 
 
 A certain limitation in the nature of things is also implied in a 
 multiplicative group system, for otherwise progress would be by a 
 single instantaneous step, and not by progressive stages. In fact 
 we may regard each multiplicative group system as cut or carved out 
 by an including matrix of limitations. 
 
 A system of groups also differs from a single group and from a 
 mere unorganized aggregate of groups by a certain inherent dynamic 
 or dialectic property, which causes it to act both externally by expan- 
 sion and internally by reorganization as in the formation of im- 
 proved units, ties and subgroups, or manifold cross multiplicative 
 groupings. 
 
 Unique Element 
 
 A multiplicative group system like each of the other Efficients 
 contains something which is unique and characteristic; which is 
 perhaps beyond analysis and may be termed transcendental. 
 
 Later we shall find that most of the constituents specified above 
 are themselves capable of a similar analysis into components. Our 
 analysis will then become a multiplicative expansion of constituents 
 revealing a systematic array of ways in which the efficiency princi- 
 ple under consideration may be improved. 
 
 Definitions 
 
 At this point it may be well to make a brief statement of the 
 efficiency characteristics of certain special well known forms of 
 multiplicative group systems. 
 
 Classification and coordination differ from multiplicative groups 
 in general in that they are relatively passive and inert. 
 
 Organization as such lacks the progressive orderly relation of 
 parts which is prominent in the multiplicative concept. 
 
 The same is true, to a certain extent, of the idea of system. 
 
 For some purposes, a summary of the results of the above analysis 
 
MULTIPLICATIVE GROUPS 87 
 
 in the form of a definition is useful. A multiplicative group system 
 may be defined as a succession of groups, all the elements in each 
 group (except the highest) being closely connected with some one 
 element in another group (called a group of higher order). 
 
 From another point of view, multiplicative groups form the com- 
 mon essence of organization and system, developed with a view to 
 increased efficiency. 
 
 METHODS OF APPLICATION 
 
 We shall next consider the best methods of utilizing the principle 
 of multiplicative groups as a source of efficiency. 
 
 Vast Number of Group Systems 
 
 In the first place, as with the other Efficients, it is important to 
 realize the great number of forms which the instrument in hand may 
 assume. The number of different group systems is evidently greater 
 than the number of different individual groups. For not only may 
 the component groups of a system take various forms, but their 
 modes of combination may also differ. It is to be noted in this 
 connection that one of the best ways of realizing and carrying in 
 mind the great diversity of forms which the multiplicative group 
 principle may assume is to arrange these forms in a multiplicative 
 way; that is to apply the multiplicative group principle to itself. 
 
 Adaptation in Application of Systems of Groups 
 
 Owing to the comparatively elaborate nature of a multiplicative 
 group system, the selection of the best form of instrument of this 
 kind to meet any given set of circumstances is of even greater 
 importance than when dealing with single groups. Thus for in- 
 stance the invention or selection of the best possible elements out of 
 which to form a group system often requires close study to the end 
 that the resulting instrument may be as comprehensive and mani- 
 fold as possible in its action. In general small elements or elemental 
 groups are best adapted for this purpose. For example it has been 
 found that the individual rather than the tribe or the family is the 
 best unit for an elaborate social organization. Similarly we have 
 the atom or ion in physical science, and the cell in biology. How- 
 ever, immediate practical limitations and relations are often of such 
 
88 SOURCES OF EFFICIENCY 
 
 a nature as to call for the use of much larger units than at first 
 would seem desirable. Thus the fact that most men read on the 
 average but a small part of each page of a newspaper leads to the 
 use of a large page in order that a reader may rapidly extract from 
 the paper what he needs. 
 
 As a rule it is best if possible to have the component groups of a 
 system contain as nearly as possible the same number of elements ; 
 that is, to have a multiplicative group system governed by a certain 
 dominant number. This is illustrated in the decimal system of nota- 
 tion in arithmetic, in the metric system, and in the use of 12 as a base 
 in certain relations of denominate numbers. In some cases a dual 
 system, especially one consisting of positive and negative elements 
 is highly efficient (see p. 71). A system of triads is often used in 
 composing speeches or works of art, use being made of certain 
 standard triadic groups such as the past, present, future; or data, 
 means, end; or theme, antitheme, combination. 
 
 The largest number of objects which a person can grasp simul- 
 taneously in his field of vision is said to be 7. Hence perhaps we 
 have 7 colors in the spectrum as it is usually divided, 7 days in the 
 week, and 7 intervals in the octave. These facts illustrate the im- 
 portance of group systems governed by the number 7. It is to be 
 noted also that the printed page is made up of approximately 40 
 symbols, and spoken language of 40 sounds. The more the matter 
 is studied the greater is seen to be the desirability of systems based 
 on or utilizing certain standard number groups. 
 
 Relative Advantages in Different Species 
 
 It is also important to investigate the advantages and disadvan- 
 tages of each special form of group in other respects, and often to 
 devise special forms adapted to peculiar sets of circumstances. 
 
 Thus the federal form (described on p. 73) has certain character- 
 istic useful properties such as the ease with which it may be grasped 
 visually and changed in case of need into other forms. 
 
 In like manner the linear species has certain efficiency functions 
 peculiar to itself. In general it corresponds to the linear habit of 
 consciousness and our method of dealing with objects in time, 
 and its use leads to reuse of those habits. Properly conceived such 
 a system may be readily expanded or contracted and modified in 
 
MULTIPLICATIVE GROUPS 89 
 
 other useful ways. These advantages are illustrated for instance 
 in a card index. 
 
 The infinite series is useful in bridging gaps, in correcting or 
 preventing errors, and in other more technical ways. 
 
 Evidently also manifold multiplicative group systems, including 
 parallel and reciprocal forms, have many special uses. These func- 
 tions may be negative, as in preventing misuse or overuse of any one 
 form, or positive as in supplementing each other's defects or in- 
 creasing each other's efficiency. Thus when the chemical elements 
 are systematically grouped not only according to their atomic 
 weights, but also with respect to their spectra, and with regard to 
 their useful properties, many checks on error and many aids to 
 increased efficiency result. 
 
 Frequent Value of Even Crude Systems 
 
 In a difficult situation the value of even a crude multiplicative 
 group method should not be overlooked. It is also important to 
 remember in such connections that in view of the large number 
 of ways in which groups may be formed, some sort of organized 
 group instrumentalism is always possible. Thus in scientific inves- 
 tigation a working hypothesis, however temporary and provisional, 
 prevents much aimless groping and frequently, indeed, seems nec- 
 essary to the attainment of definite results. So in another field, the 
 Puritan theology, however crude and imperfect it may have been, 
 at least furnished a comprehensive and vigorous system, and hence 
 perhaps gave the New England character its sturdy and aggressive 
 qualities. 
 
 One is aided in using relatively imperfect systems with some 
 boldness because of the fact that the multiplying principle is not only 
 self-corrective, but also self-developing. 
 
 Transformations of Multiplicative Group Systems 
 
 The power to transform one species of multiplicative group system 
 into another is often an important source of efficiency. Frequently 
 several successive transformations of this kind must be made to meet 
 successive changes in a situation. The different evolutions of an 
 army during a battle or a campaign are an example of this process. 
 
 Standard units or types of transformation of multiplicative group 
 
go SOURCES OF EFFICIENCY 
 
 systems may often be employed to advantage. An instance is the 
 conversion of a fan-shaped into a linear system. Another case is 
 the transformation of a linear system into a rectangular array (as 
 of pigeonholes) for the sake of economy of space and as a means to 
 useful cross multiplicative group processes. 
 
 Similar conversions are that of a three dimensional system into a 
 two dimensional one ; a continuous into a discrete form ; constitutive 
 into marginal ; heterogeneous into homogeneous ; and the reverse 
 of each of these. Perhaps also it may be said that any one kind 
 of multiplicative group system may be converted into any other. 
 
 Important special cases are the various methods of classifying 
 persons by means of their finger tips, with a final reduction of a 
 branching system of classified persons into a linear card catalogue 
 form. A process like this is sometimes termed a lexiconizing of 
 data. 
 
 Symbolisms for Group Systems 
 
 By the principle of neighborhood or positional symbolism to be 
 developed later (see p. 167) important special abbreviations are 
 often obtainable in representing a multiplicative group system of 
 some particular kind. Thus in such representations the symbols for 
 the higher groups in a system may frequently be omitted. For 
 example in the address on a letter, the name of the country is often 
 not expressed, and that of the continent almost always omitted. The 
 great power of the Linnean system of classifying biological species 
 is due not only to the fact that it is a multiplicative group system, 
 but also to the property that, owing to its multiplicative nature, all 
 the names involved except two, viz. : those for genus and species, 
 can usually be omitted. Similarly the name for each human being 
 usually consists of only two or three words, and often only the 
 initial letters of one or more of these words are used. 
 
 The judicious use of symbolisms not only brings negative ad- 
 vantages in the shape of economies of various kinds but also a 
 dialectic of positive advantages to be presented more fully in the 
 chapter on Symbolism (p. 164). 
 
 Calculus Methods 
 
 The simultaneous use of successive transformations and of adapted 
 symbolisms together suggest the idea of creating certain group sys- 
 
MULTIPLICATIVE GROUPS 
 
 91 
 
 terns by calculus methods. Such methods consist essentially in 
 obtaining results in a more or less mechanical way by the aid of 
 adapted symbolisms. Thus a problem in grouping like the follow- 
 ing may be proposed and solved. If 250,000 species of plants are 
 classified as a multiplicative group system of 9 orders, on the average 
 how many elements will each group in the system contain? The 
 solution of the problem reduces to the solution of the equation 
 .r 9 — 250,000 and the result obtained is x = 4. 
 
 Every slide rule represents what is in essence a multiplicative 
 group system, and the use of the slide rule is largely a mechanical 
 method of manipulation a multiplicative group system. 
 
 A study of the efficiency nature of logic and mathematics will 
 show that these subjects constitute particular forms or applications 
 of multiplicative group principles, and that the calculuses in them are 
 therefore illustrations of the calculuses possible in dealing with 
 group systems in general. 
 
 Ideal Species in Multiplicative Groups 
 
 Finally in this connection attention should be called to the impor- 
 tance of keeping in mind at all times the ideal system of multiplica- 
 tive groups and of realizing this ideal as nearly as possible in all 
 cases. From our point of view this ideal species is a multiplicative 
 grouping of the Efficients, by means of the Efficients, and for effi- 
 ciental ends. 
 
 At the same time it is not to be forgotten that for immediate 
 practical purposes the best general form is the two-dimensional 
 federal system, accompanied by some linear species as an auxiliary. 
 
 From many parts of the preceding discussion it is evident that the 
 application of the principle of multiplicative groups will be aided in 
 various ways by a study of other primal efficiency agents in the 
 chapters which follow. 
 
 Summary of Chapter 
 
 It will be an advantage at this point briefly to state results arrived 
 at in the present chapter. Simple groups may be combined to form 
 groups which are multiplicatively related in various ways. The 
 different species of group systems are characterized mainly by their 
 forms. Among the most important of the individual forms are those 
 termed linear, federal, constitutive, marginal, and manifold. 
 
92 SOURCES OF EFFICIENCY 
 
 The efficiency functions of group systems are those of single 
 groups in a more extended form, with other useful functions added. 
 Among these uses are economy and delicacy of action, and great 
 intensity of force. Group systems also give rise to or aid the other 
 Efficients in peculiar ways. Multiplicative groups also form the 
 underlying essence common to all kinds of system, organization, and 
 coordination. Hence a study of multiplicative groups should give a 
 thorough mastery of various forms of system and organization. 
 
 In making use of group systems, besides realizing their great num- 
 ber, and methods of adapting them to special situations, it is im- 
 portant to understand how to use several species of systems in 
 combination, and how to transform one species into another. Of 
 like importance is the use of group systems in connection with other 
 Efficients. The ideal group system is that one in which the com- 
 ponent elements are the other Efficients. 
 
 EXERCISE 5 
 
 Give an example of each of the following species of multiplicative group 
 systems : 
 
 i. Of three orders 12. Constitutive 
 
 2. Of more than three orders 13. Marginal 
 
 3. Linear 14. Continuous marginal 
 
 4. Areal IS- Discontinuous marginal 
 
 5. Three dimensional 16. Rectangular 
 
 6. Provisional • 17- Dual reciprocal 
 
 7. Permanent 18. N-reciprocal 
 
 8. Direct IQ- Semi-linear 
 
 9. Inverse 20. Conically expanding 
 
 10. Heterogeneous 21. Parallel 
 
 11. Homogeneous 22. Manifold 
 
 23. Complex 
 
 24. Name three natural multiplicative group systems. 
 
 25. Also three artificial ones. 
 
 26. Also three which are part natural and part artificial. 
 
 27. Describe some system of filing documents and explain this as a form 
 of multiplicative groups. 
 
 28. State the different multiplicative group organizations found in a large 
 hotel. 
 
 29. Also in a large department store. 
 
 30. On a large well managed farm. 
 
 31. Explain the multiplicative group system used in dividing the Bible into 
 parts so as to make them readily accessible. 
 
MULTIPLICATIVE GROUPS 
 
 93 
 
 32. State the advantages in having the human arm jointed; that is, formed 
 of articulate parts. 
 
 33. How is the slowness with which a clock runs down obtained and what 
 are the advantages in this slowness? 
 
 34. Why is it that a number containing only six figures is able to express 
 the result of the most accurate measurement that man can make by the aid 
 of appliances, thus far invented? 
 
 Give an example of a multiplicative group system which is a means to: 
 
 35. Economy of material 39. Uniformity of action 
 
 36. Economy of space 40. Delicacy of action 
 
 37. Economy of energy or force 41. Substitution of a cheap force 
 
 38. Reuse for a costly one 
 
 42. A transcendent result 
 
 43. Give an illustration of the drawbacks which sometimes accompany the 
 use of multiplicative groups. 
 
 44. Napoleon compared his mind to a chest of drawers. State some of 
 the advantages in a mind disciplined so as to be usable in this way. 
 
 45. Is it correct to state that an organism is high in the scale of being in 
 proportion to the degree of its multiplicative group organization? Illustrate. 
 
 46. It is said that the commanding general of an army sometimes carries 
 in mind and is able to recognize individually 100,000 soldiers. Show how sys- 
 tems of multiplicative grouping may aid in this process. 
 
 47. What are the advantages in influencing a community by influencing its 
 leaders? In correcting the evils in a community by correctig the causes which 
 underlie these evils. 
 
 48. State some of the various cross multiplicative groupings used in keeping 
 a set of business accounts. What are the advantages in this manifold group- 
 ing of accounts? 
 
 Give two instances where a multiplicative group mechanism gives 
 
 49. Concentration of force 51. In space 
 
 50. Concentration in time 52. A high velocity 
 
 53. Slowness of motion 
 
 54. Why does it pay a railroad system to develop its trunk lines more 
 thoroughly than the branch lines? 
 
 55- Show that the efficiency of the insurance methods used in business 
 arises essentially from a multiplicative grouping of values and a surrender of 
 certain of those of low order that those of high order may be made certain. 
 
 56. To which species of multiplicative groups does that belong which is 
 formed by the banks outside of New York City, their correspondents in New 
 York City, and the New York City clearing house? Explain the efficiency 
 functions of such a system. 
 
 57- The so-called golden section has been suggested as a fundamental 
 principle in esthetics. Show that this principle is essentially a special applica- 
 tion of the multiplicative principle. 
 
 58. State some of the advantages which result when the materials in the 
 
94 SOURCES OF EFFICIENCY 
 
 store room of a factory are arranged according to a multiplicative group 
 system. 
 
 59. State some of the advantages which have resulted from the demonstra- 
 tion that all material objects may be regarded as composed of a few chemical 
 elements grouped together multiplicatively in various ways. 
 
 60. A classification of the compounds of the elements of carbon, by the gaps 
 which it revealed led to the prediction and discovery of certain hitherto un- 
 known compounds. What species of efficiency result was this? 
 
 61. Show how the multiplicative grouping of knowledge is an aid to a per- 
 son both in learning something about everything and everything about some- 
 thing. 
 
 62. State the symbolism for the different orders in a multiplicative group 
 system used in the following : 3° 7' 5". 
 
 63. Give an example of the transformation of a linear multiplicative 
 group system into an areal or solid one, for the sake of economy of space. 
 What other advantages result? 
 
 64. Give an example of the transformation of a marginal multiplicative group 
 system into the strandal form, and point out the advantages which result. 
 
 65. If 500,000 species of plants are classified as a multiplicative group 
 system of 8 orders, how many elements, on the average, will each of the 
 component groups of the system contain? 
 
 Trace the historic development of multiplicative groups in the field of 
 
 66. Education 67. Politics 68. Business 
 
CHAPTER VI 
 
 ORDERS OF MATERIAL 
 
 Illustration 
 
 It is often a source of efficiency to substitute for a given multi- 
 plicative group system a series of objects each of which represents 
 an entire order of the given group system. For example it is 
 frequently convenient to represent an ecclesiastical hierachy by the 
 series, layman, priest, bishop, archbishop, cardinal, pope, or by part 
 of this series. 
 
 Uses of a Multiplicative Series of Objects 
 
 Such a representative set of terms is particularly useful in cases 
 
 ( i ) Where it is difficult to form or discover an explicit and well 
 
 developed multiplicative group system ; 
 (2) Where a group system has been so highly developed that it 
 may be made to assume a more special and peculiarly efficient form. 
 
 In these latter cases successive multiplicative degrees of groupism 
 have become so familiar as to have acquired the aggregate of useful 
 qualities which we often denote by the term materiality or substance. 
 Hence a single object may be used for each order of groups, the 
 result being a certain mechanical ease and simplicity in dealing with 
 organizations and systems, though the process is often accompanied 
 by compensating limitations and drawbacks. 
 
 In this way we arrive at a new principle of efficiency, broader in 
 some ways than that of the multiplicative group instrument and 
 narrower in others. This new instrument of efficiency we term 
 multiplicative orders of material, or more simply orders of material. 
 
 CLASSIFICATION 
 Classification According to Materials 
 
 Multiplicative orders of material will be first classified according 
 to the material in which they occur or of which they are composed. 
 The first to be considered are those multiplicative series found in 
 
 95 
 
96 SOURCES OF EFFICIENCY 
 
 the physical inorganic world. An example of such a succession is 
 that formed by the ion (or electron), atom, molecule, crystal, and a 
 body in mass. It is important to observe that in this case as in many 
 others, the progressive many-to-oneness may be regarded in several 
 aspects or as the resultant of several elements, as those of size, 
 number, force, and various functions. Another important general 
 multiplicative order in the inorganic world is that of solid, liquid, gas, 
 ether. This also is the resultant of several elements of successive 
 groupism. 
 
 The above orders of material are found, in whole or part, in 
 practically every domain of inorganic material. Each field of work 
 in the physical universe also usually furnishes one or more multi- 
 plicative series peculiar to itself. Thus in the domain of astronomy 
 are found satellite, planet, sun, constellation. 
 
 Those multiplicative series which occur in different specific fields 
 of toolage are particularly important for our purpose. Thus in 
 water transportation we have the raft, rowboat, sailboat, steamboat, 
 with subordinate multiplicative progressions connected with each of 
 the given terms. The resultant series involved may here be regarded 
 as one of general efficiency. 
 
 Of implements used in breaking up the ground in agriculture, 
 we have the hand, hoe, spade, plow, gangplow. Of instruments 
 used in reaping grain the multiplicative succession is the hand, knife, 
 cycle, scythe, cradle, mowing machine, reaper, reaper and binder. 
 Other fields of work furnish like instances. 
 
 In the domain of living organisms various important series of 
 objects multiplicatively connected are also found or have been con- 
 structed by man. Among the instances which might be cited are 
 cell, organ, individual, society; bone, flesh, blood; annual, . biennial, 
 perennial plants ; individual, species, genus, family, order, class, 
 kingdom. 
 
 More Abstract Series 
 
 In the region of mind, as to cognition the succession is perception, 
 memory, reason; as to emotion, the list is happiness, joy, blessedness, 
 In the field of will we find impulse, volition, determination; in that 
 of moral character occur physical courage and moral courage; or 
 act, habit, character, destiny. 
 
ORDERS OF MATERIAL gy 
 
 The many multiplicative group systems in the social and political 
 world give rise to corresponding multiplicative series of objects. 
 Thus in connection with the feudal system are found serf, burgher, 
 knight, duke, earl, prince, king. A system of law courts at the 
 present time is presided over and to a certain extent represented by 
 the police justice (or justice of the peace), and by circuit, superior, 
 and supreme judges. Many other social and political multiplicative 
 gradations will suggest themselves to the reader. 
 
 Similarly multiplicative series are in use in various more or less- 
 abstract worlds. Hence we have for instance such a series with 
 respect to position, or culture, or usefulness. In this general class 
 the most important series for our purpose in many respects is one 
 of degrees of efficiency. For instance a political worker at first 
 must usually expend a large amount of effort and be satisfied with 
 small returns. Later, after he has acquired position, he may obtain 
 much larger results by the mere utterance of a word ; and later he 
 may produce still larger results by mere unconscious influence. 
 
 The most comprehensive and in many respects most useful multi- 
 plicative series in the world of objects is the complex resultant one 
 denoted by the terms mineral, vegetable, animal, spiritual. 
 
 Classification According to Form 
 
 Often also it is an aid to efficiency to classify orders of material 
 according to categories of form. 
 
 Thus some principle of space, as that of magnitude for example, 
 may be so prominent as to give the series a certain characteristic 
 individuality. For example we may have a multiplicative series 
 determined mainly by the element of size, an example being bay, 
 gulf, sea, ocean. The principle of relative magnitude fixes the 
 different grades of anthracite coal, viz., rice, pea, chestnut, stove, 
 furnace. 
 
 Similarly we have the different standard sizes of various articles 
 of merchandise and the materials used in processes of manufacture. 
 These gradations are sometimes due to natural causes but more often 
 to the commercial process called standardization. 
 
 Important special cases of quantitative series are the tables of 
 compound numbers as taught in arithmetics. For example in money 
 we have the mill, cent, dime, dollar, eagle. Other like series are 
 used in the measures of weight, length, area, volume, etc. 
 
98 SOURCES OF EFFICIENCY 
 
 As to geometric form a multiplicative succession of objects is 
 essentially a linear succession of points. Owing to the occurrence of 
 secondary, or auxiliary, or parallel series the geometric form of the 
 series as a whole may be slightly branching (or semi-filiar). An 
 example is the series, 
 
 horse, trolley, railroad, steamboat, 
 
 creeping, walking, riding by , 
 
 ( bicycle, motor-car, aeroplane. 
 
 We here approach compound and complex orders of material. 
 
 Multiplicative series of objects may also be characterized by the 
 element of number. Thus a dual series, that is one composed of 
 only two objects is often comprehensive and important. Examples 
 are the pairs of terms, appearance and reality, reputation and char- 
 acter, mind and matter, form and substance, relative and absolute. 
 
 Important triadic forms also occur. Instances are past, present, 
 future ; data, means, end ; historical, psychological, logical. 
 
 The series, simple, compound, complex, is an important one, 
 determined both by principles of number and by spatial arrangement. 
 
 A time element, as that of relative permanence, may also form 
 the most essential characteristic of a multiplicative gradation of ob- 
 jects. For instance in law a written document is on a higher plane 
 of importance than verbal statement, because written words are 
 more lasting than mere verbal speech. So degrees of precedence in 
 time may, in effect, constitute a multiplicative series. Thus we 
 have the legal maxim that possession is nine points of law. Simi- 
 larly preventive work is of a higher order than that which is merely 
 remedial. 
 
 A segregative series is one which has arisen by the gradual 
 elimination of sizes of forms of objects lying between the objects 
 constituting the series. An example of this is the scale of sizes 
 of type now used in printing. 
 
 Many other terms of quality may be applied to various orders of 
 material. Among these are the words homogeneous, heterogeneous ; 
 natural, artificial, semi-artificial; positive, negative; increasing, di- 
 minishing ; direct, inverse ; contingent, absolute. 
 
 Some special explanation should be made of the last pair of terms 
 in the above list. Owing to the shortness of human life and other 
 species of limitation, the gap between two successive terms in a 
 progressive series may be absolute or infinite from the efficiency 
 
ORDERS OF MATERIAL 99 
 
 point of view. Thus in grading various specimens of a given kind 
 of fruit, as of apples, all above a certain size may have a market 
 value while all below have no market value. So in a scale of 
 temperatures, all within a certain range may mean life, and all 
 above the limit of this range may mean death. All the events in a 
 certain future may be accessible and under control, while all in the 
 past are beyond control. 
 
 Complex Cases 
 
 Complex orders of material of many different kinds occur. Some 
 resultant species have already been mentioned and illustrated. 
 Another instance is that composed of the materials used in making 
 a fire, as match, paper, kindling wood, and coal, the component fac- 
 tors being size, inflammability, duration and others less conspicuous. 
 
 Similarly the stages of formal education denoted by the terms 
 primary, secondary, collegiate, university, constitute a multiplicative 
 series which is a resultant of such factors as the age, growth, and 
 maturity of the pupil, and the difficulty and comprehensiveness of 
 subjects of study. 
 
 Probably every multiplicative series is in some respects a resultant 
 of a number of such series. 
 
 Often one multiplicative series give rise to another. Hence 
 parallel series may occur. Thus side by side with the arrangement 
 of bodies as solids, liquids, gases, and the ether, we have the senses 
 of touch, taste (and smell), hearing, and vision. 
 
 Groups of Orders of Materials 
 
 Various orders of material may constitute the elements in a multi- 
 plicative group system. Thus the different series in the domain of 
 psychology may be arranged as a multiplicative system. 
 
 In like manner it is often a source of efficiency to develop in a 
 given domain of material a manifold multiplicative cross structure 
 of objects. For example the different kinds of money in use may 
 be viewed in various serial ways. Thus with respect to relative 
 bulk we have copper, silver, gold, paper. According to security the 
 order is gold, silver, copper, paper. Another arrangement 
 could be formed according to steadiness of value during a given 
 period of time. Similarly the different ways in which the facts in 
 
IOO 
 
 SOURCES OF EFFICIENCY 
 
 a department of knowledge may be presented are denoted by the 
 terms genetic (or historical), psychological (or inductive), and logi- 
 cal (or deductive), and a multiplicative series may be developed cor- 
 responding to each of these terms. 
 
 Different species of multiplicative gradations may also be com- 
 bined and complexed in various more or less irregular ways. An 
 illustration is the aggregate of such series utilized in an entire 
 process of education. 
 
 General Multiplicative Series 
 
 The following tabular combination of multiplicative series is of 
 far-reaching importance because of the comprehensiveness of its 
 terms and also because of its specific applicability to many special 
 cases by aid of slight variations. 
 
 General Multiplicative 
 
 Objective 
 
 Subjective 
 
 Series 
 
 Side 
 
 Side 
 
 Material 
 
 Iron, wood, etc. 
 
 Muscular sense 
 
 Concrete 
 
 Sound, color, ether, 
 mechanical and bio- 
 logical force 
 
 Vision 
 
 Semi-concrete 
 
 Mind as object 
 
 Mind as subject 
 
 Abstract 
 
 Civilization, religion, 
 etc. . 
 
 Reason 
 
 Efficiency-abstract 
 
 Categories., Efficients 
 
 Efficiency powers 
 
 N 
 
 N' 
 
 N" 
 
 The first column of the above table contains a general succession 
 which is the resultant of a large number of efficiency factors to be 
 considered in some detail later (see p. 105). Besides the efficiencies 
 which spring from the direct use of the first column, other useful 
 results are obtained by noting that the actual use of this column in- 
 volves the use of two sets of factors, usually termed the objective 
 and subjective respectively. Hence it is useful to develop these 
 into two other parallel sets as given in the second and third columns. 
 
 It should be observed that the series mineral, vegetable, animal, 
 spiritual, also corresponds in a general way to that given in column 
 •one. 
 
ORDERS OF MATERIAL IOI 
 
 EFFICIENCY FUNCTIONS OF ORDERS OF MATERIAL 
 Uses Compared with Those of Multiplicative Groups 
 
 Since orders of material are a modified form of multiplicative 
 group systems, it follows that the uses of orders of material are 
 closely related to those of multiplicative groups. In general the 
 efficiency functions of orders of material are in some cases those of 
 incipient and imperfectly formed multiplicative group systems, and 
 in others .those of final or highly finished systems. 
 
 Thus it has already been pointed out that in a field of great 
 difficulty, where an explicit group system cannot be found or devel- 
 oped, it is possible to form an order of materials which will perform 
 many of the efficiency functions of a group system. For instance 
 in the series denoted as solids, liquids, gases, and the ether, complete 
 grasp of the precise and fundamental group inclusions involved is 
 lacking, yet the multiplicative relation approximated in the series 
 is the source of a vast number of utilities and efficiencies. Prob- 
 ably if the multiplicative principles contained should be discovered 
 and fully explained, the series as stated above would still continue 
 to be a convenient instrument by which to handle the complex of 
 group inclusions involved. 
 
 Economics due to Orders of Materials 
 
 The economy of material which characterizes multiplicative group 
 systems is even more noticeable in orders of material. For in the 
 latter that large fraction of a group system which is covered by an 
 entire order of groups is represented by a single object. Thus in 
 the series, individual person, man, mammal, etc., the word man not 
 only includes the 1,600,000,000 human beings now in the world but 
 all past and future generations of men. 
 
 Also the use of a multiplicative series of objects means an in- 
 creased economy and efficiency of energy as compared with the use 
 of a corresponding multiplicative group system. For owing to the 
 concretish nature of the terms of a series of objects, such a series 
 may frequently be operated by a lower and cheaper order and a 
 smaller amount of force. In other words orders of material are 
 characterized by their extreme triggerishness. The terms of such a 
 series constitute handles or palpable means by which to manipulate a 
 group system to advantage. In other words, in this respect, an order 
 
102 SOURCES OF EFFICIENCY 
 
 of objects is a simple mechanical tool by which to handle a complete 
 far extended group system. 
 
 Other Characteristic Efficiencies 
 
 Orders of material often lead to efficiency in ways perculiar to 
 themselves. The properties of a series of objects formed by stand- 
 ardization are an example in point. For example the formation of 
 certain standard parts in the manufacture of automobiles has led to 
 large economies in the manufacture of each of those parts, and often 
 to important improvements in the quality of the parts. Similarly 
 the separation of freights into different groups of materials to be 
 carried by fast and slow freight trains and by water produces im- 
 portant economies and efficiencies in the carriage of each of these 
 classes of material. 
 
 Orders of material also often possess in distinctive form and in 
 larger measure certain other efficiency properties of multiplicative 
 group systems such as the power of self-development, of utilizing 
 auxiliary quantities, and of opening the way to directive work of a 
 higher order. 
 
 Fruits stated Collectively 
 
 The efficiency value of orders of material may also be presented in 
 other more concrete and pictorial ways. For instance it may be 
 shown that such series are at work 'in every highly developed depart' 
 ment of life or action. The building material called concrete con- 
 sists of the triadic series, gravel, sand, and cement. A well balanced 
 system of diet consists essentially of starches, fats, and protein. 
 Every great work of art contains the principle of multiplicative 
 gradations in one or more forms. Poor writing, as Shakespeare 
 says, is "words, words, words", that is, a mere additive aggregate; 
 while good literature consists of words and ideas in multiplicative 
 relations. For example the following couplet from Browning 
 largely gets its power from the two multiplicative series of two 
 terms each which it contains : 
 
 "Be a god and hold me with a charm ; 
 Be a man and fold me with thine arm." 
 
 The efficiency in life insurance comes from the fact that it trans- 
 
ORDERS OF MATERIAL 
 
 103 
 
 fers money (or resources) from a lower to a higher stage of utility; 
 that is, from the field of luxury to the field of necessity. 
 
 Values in Terms of Human Progress 
 
 Hence also it will be found that great men are men who have 
 known how to work with or in material of a high order. In war 
 the superior general by a simple stroke of strategy overwhelms the 
 mere tactician however clever. So the statesman dominates the 
 politician. 
 
 In fact we may say that the whole of human progress has been 
 an advance from stage to stage in multiplicative series fashion. 
 Some of the more important of these stages are indicated in the 
 following table : 
 
 Stages in 
 General 
 
 Characteristic 
 Industry- 
 
 Material for 
 Tools 
 
 Savage 
 Barbarous 
 Semi-civilized 
 Civilized 
 
 Hunting 
 Grazing 
 
 Agriculture 
 Manufacture 
 
 Wood, bone, stone 
 Copper, bronze 
 Iron, steel 
 Electrical machinery 
 
 Human progress has also been marked by the use of an increas- 
 ing number of multiplicative series and by series of a progressively 
 
 high order. 
 
 Limitations in Utilities 
 
 Along with the advantages which come from the appeal to our 
 sense of materiality or thinghood in orders of material, come also 
 certain disadvantages which must be reckoned with. 
 
 Thus orders of material are apt to harden or fossilize into tyran- 
 nical forms which limit the user of them by their premature finality. 
 An extreme instance is the caste system of India. A more subtle and 
 pervasive case is the use of the distinctions between solids, liquids, 
 and gases as ultimate and complete. A milder form of this disad- 
 vantage is merely a vague lack of flexibility. 
 
 Also the brevity and extreme inclusiveness in the terms of a 
 multiplicative series of objects often leads to certain oversights or 
 distortions in the application of such a series. 
 
104 SOURCES OF EFFICIENCY 
 
 In other words the multiplicative series as a source of efficiency 
 is vivid and triggerish, but often crude and narrow. It has the de- 
 fects of its qualities. 
 
 The orders of material which characterize our system of juris- 
 prudence furnish illustrations of what has just been said. The 
 careful gradation of crimes and the formulation of a certain succes- 
 sion of definitions, precepts, maxims, and laws, are most useful 
 where so many varied, conflicting, and often selfish interests con- 
 verge as in the realm treated by jurisprudence. On the other hand 
 many of the distinctions and standards involved are more or less 
 artificial and leave the way open to numerous errors and abuses. 
 
 ANALYSIS AND DEFINITION 
 
 Comparison with Multiplicative Groups 
 
 In orders of material as compared with multiplicative group sys- 
 tems, ties and forms recede into the background while unit elements 
 become prominent. 
 
 Also the concept of number is more specific and distinct, as is also 
 that of order. 
 
 With respect to force or energy, we may say that the multiplica- 
 tive series is more static and passive ; that is, it constitutes a near and 
 familiar but not always aggressive toolage. 
 
 Appearances often Deceptive 
 
 It is also to be carefully noted in this connection that an order of 
 objects, while it is essentially multiplicative in nature and action, is 
 often additive in appearance. Thus when we climb a mountain our 
 steps are additive in that each step increases our elevation above 
 the sea level by the same amount; but at the same time each new 
 step increases the area of vision in a multiplicative way. Similarly 
 equal increments in temperature may produce multiplicative changes 
 in any given material. If the radius of a circle be divided into 
 equal parts the areas of the corresponding circles form a multiplica- 
 tive succession, and a like property holds for the sphere and other 
 solids. Hence it is important to remember that vital efficiency 
 properties, not mere outward appearances, determine whether a 
 given set of objects form a multiplicative succession. We here 
 glimpse from another point of view the fact that the multiplicative 
 
ORDERS OF MATERIAL 105 
 
 series contains its own characteristic sources of efficiency and 
 hence possesses a characteristic uniqueness and individuality. 
 
 Each particular form of multiplicative series is capable of its own 
 special analysis. The dual series denoted by the terms concrete and 
 abstract is so important and frequently used that it seems desirable 
 to try to determine its efficiency meaning as exactly as possible. 
 This is best done by considering the relation of the terms concrete 
 and abstract to certain other more or less elemental categories of 
 efficiency. 
 
 Meaning of Concrete and Abstract 
 
 With respect to mind, the concrete relates primarily to the senses, 
 the abstract to the reason. 
 
 In relation to force or energy, the concrete is that which has been 
 thoroughly assimilated and reduced to the mechanical trigger state. 
 Thus we cannot help seeing a red color, or feeling a pain when 
 touched by a piece of very hot iron; the color red and hot iron are 
 accordingly termed concrete. 
 
 With regard to space. the efficiencies embodied in the concrete are 
 more special, local, and individual. 
 
 With respect to uniformity, the abstract possesses in higher degree 
 special properties of continuity, uniformity, and equivalence, as will 
 be indicated more fully in Chapter VIII. 
 
 In relation to the group principle, the concrete tends to form the 
 elements, especially those of lower order, and the abstract to form 
 elements and groups of higher order and ties of all groups but more 
 particularly those of higher order. 
 
 With respect to limitation, the concrete is more subject to limita- 
 tion as we ordinarily understand the term. Thus, for instance, that 
 species of limitation which we call impenetrability is prominent in 
 material and concrete things. Two material objects cannot occupy 
 the same portion of space at the same time, but two geometric dia- 
 grams may do so. In like manner a material object cannot be in 
 two places at the same time, but it is possible for an idea to be 
 simultaneously in a multitude of places. An acre of land cannot be 
 owned simultaneously by two persons, but the same view of life 
 may be possessed by many persons. 
 
 In that more advanced or pronounced form of the abstract which 
 
lo6 SOURCES OF EFFICIENCY 
 
 we have termed the efficiency abstract, the entities involved are still 
 freer from limitation than those included in the conventional ab- 
 stract, and consist essentially of the Efficients themselves. 
 
 In the table on p. ioo, by N we mean any possible sources of 
 efficiency beyond the Efficients themselves. Hence from our point 
 of view the term metaphysics means sources and modes of efficiency 
 beyond concrete, physical, or phenomenal ones. Hence N stands for 
 any possible and as yet unexplored region of efficiency. 
 
 Definition 
 
 Under certain circumstances, the following general definition will 
 be found useful. By the term multiplicative order of objects is 
 meant a series of objects each of which has a certain multiplicative 
 relation to the preceding object in the series. 
 
 METHODS OF APPLICATION 
 
 Number of Species 
 
 The order of materials and multiplicative group principles are so 
 closely related that much which was said in the preceding chapter 
 concerning the best methods of using multiplicative group systems 
 applies also to orders of material. Thus the great number of differ- 
 ent multiplicative series of objects is evident from the fact that 
 possible systems of multiplicative groups are so numerous. 
 
 Adaptation to Individual Situations 
 
 It also follows that it is important in given circumstances to try to 
 determine the best available gradation of materials and often, if 
 possible, to discover and utilize some hidden series of this kind in a 
 given field of work. For example, in taking physical exercise it is 
 an advantage to realize that gradations of efficiency exist in methods 
 of exercise, and that the most effective forms for mature persons 
 are those which with least effort produce a free circulation and 
 change of position of the fluids of the body. 
 
 To use another illustration, in an approximately rectangular 
 room the furniture and ornaments may be arranged in a variety of 
 artistic ways, but in a room of irregular shape they may usually be 
 arranged only in one best way. Hence the former shape is broadly 
 speaking on a higher plane of excellence. 
 
ORDERS OF MATERIAL 107 
 
 Emphasis on the Higher Terms in a Series 
 
 In using orders of material, in almost all cases it is a source of 
 increased efficiency to lay particular stress on the higher terms in 
 the series. Hence arises the prime value of knowing and controlling 
 centers of influence, strategic points, psychological moments, under- 
 lying causes, means of communication, and transportation routes. 
 
 Hence also the importance of the love of art for art's sake, or of 
 truth, or of any source of efficiency for its own sake. 
 
 Hence again the supreme importance of clinging to fundamental 
 ethical or other principles in times and places of unusual difficulty. 
 
 This principle of efficiency is also applicable to many of the details 
 of life. Thus the wise traveller frequently makes sure that his 
 money is in good shape. So the writer who desires to be clear and 
 forcible is at pains to use in the most effective way the particles 
 which denote time, space, and other prime groups, notwithstanding 
 the apparent insignificance of such words. 
 
 Importance of Dual Series 
 
 It is also well to note and take advantage of the great power 
 inherent in fundamental dual series such as those denoted by pairs 
 of terms like objective and subjective, concrete and abstract. Even 
 the baseball player makes use of this principle when he recognizes 
 the superior value of what he calls "inside baseball". 
 
 Self-corrective Power 
 
 In using multiplicative series of objects it is also desirable to keep 
 in mind the fact that, owing to the power of self-correction which 
 characterizes them as well as multiplicative group systems, even a. 
 crude series may often be used aggressively. 
 
 Groups of Series 
 
 Efficiency in the application of the principle in hand is often much 
 increased by dealing with orders of material in groups, or even as 
 group systems. In this connection orders of material propagated 
 from some central form of series are of especial importance. Thus 
 the series denoted by the terms solid, liquid, gas, ether, gives rise to 
 the sense perception series indicated by the words touch, taste, hear- 
 ing, vision ; also to a progressive set of terms denoting the sources 
 
108 SOURCES OF EFFICIENCY 
 
 of artificial light, viz.: tallow, oil, gas, electricity; also to the modes 
 of transferring heat indicated by the terms conduction, convection, 
 radiation. 
 
 Another example of parallel series is the following: country, conti- 
 nent, planet ; local, continental, planetary winds ; tornado, cyclone, 
 monsoon. 
 
 Symbolisms 
 
 Certain efficient symbolic methods of denoting a higher term in a 
 multiplicative series are already in use. Thus suffixes like -age, 
 -ism, and -ize cause a particular word to have a general meaning. 
 Examples are the words symbolism and symbolize as compared with 
 the word symbol. Similarly a higher order of material is sometimes 
 expressed by use of a noun in the singular instead of the plural 
 form. An illustration is honor as contrasted with honors, or profit 
 with profits. 
 
 Other symbolic devices to obtain a like end are the use of italics, 
 or of capital letters of various sizes and kinds, emphasis in oral 
 speech, the use of gestures, etc. Evidently many other forms of 
 symbolism might be invented to indicate multiplicative gradations. 
 
 Ideal Species 
 
 With orders of material, as with the other Efficients, it is impor- 
 tant to conceive of an ideal form a'nd to make the utmost use of it in 
 various ways including approximate and marginal uses. 
 
 For our purpose this ideal form is a series of efficiental terms 
 used for efficiental ends. 
 
 Summary of Chapter 
 
 The present chapter may be briefly summarized as follows. It is 
 advantageous, in certain connections, to condense an extended group 
 system into a simple succession of objects, each of which forms a 
 highly economical representation of a whole layer or order of the 
 given system. Frequently such a multiplicative series of representa- 
 tive objects arises or comes into effective use in a given domain 
 before any explicit group system has been worked out in this domain. 
 Also such a multiplicative series may, at times, be the resultant and 
 representative of several group systems. 
 
ORDERS OF MATERIAL 109 
 
 As to its form, every multiplicative series essentially constitutes a 
 line of objects, but from other points of view, a great variety of kinds 
 of series exist, owing to the fact that such successions of objects are 
 found in, or may be devised for, each domain of material or de- 
 partment of knowledge. 
 
 On the one hand, orders of material are sources of efficiency owing 
 to the extreme inclusiveness of each object in such a series, and 
 owing to the adaptability of these objects to directive management. 
 On the other hand, because of the comprehensiveness of these series, 
 they are especially adapted to deal simply and effectively with com- 
 plex data such as the stages of human progress. 
 
 In making use of multiplicative series, especial care is to be taken 
 to grasp their great number, to realize partially hidden or deceptive 
 species, and to lay emphasis on those terms which are high in a given 
 series. 
 
 EXERCISE 6 
 
 State the class or classes to which each of the following orders of material 
 belongs : 
 
 1. Steel frame, brick, wood, trimmings (as found in a modern office build- 
 ing)- 
 
 2. Percepts, concepts, ideas, laws. 
 
 3. Imitation, invention (or discovery), creation. 
 
 4. Farm, township, county, state, country, continent. 
 
 5. Fashion, principle. 
 
 6. Pint, quart, peck, bushel. 
 
 7. Water, blood. 
 
 8. (Chemistry) _ - (Art ) (Philosophy) 
 ] Physics j j Biology, Psychology j Sociology j { Rdig j on j 
 
 9. Bonds, preferred stock, common stock. 
 
 10. Standard, choice, fancy, extra fancy (as terms for grades of fruit). 
 n. Shell life, nest life, wing life 14. Physical courage, moral courage 
 
 12. Food, offspring, culture 15. Hand craft, brain craft 
 
 13. Starch, fat, protein 16. Property rights, human rights 
 
 17. Give a multiplicative series of six terms concerning periods of time of 
 different lengths. 
 
 18. Give the multiplicative series of implements whose function is to 
 thresh grain. 
 
 19. Give a multiplicative series of velocities in practical use. 
 
 20. Of weapons used in war. 
 
 2r. Of states in the United States with respect to area. 
 
1 10 SOURCES OF EFFICIENCY 
 
 Give an illustration of an order of materials which is 
 
 22. Artificial 23. Natural 24. Resultant 
 
 Give an illustration of : 
 
 25. Two or more orders of material which are parallel. 
 
 26. Of manifold cross orders of material. 
 
 27. Give an illustration of an order of materials used in some business 
 .as a result of the process of standardization. 
 
 28. Of an order of materials that is additive in appearance but is multiplica- 
 tive in essence. 
 
 29. Name a series of well known plateaus which are respectively Yz mile, 
 1 mile, 2 miles, 5 miles above sea level. Taken with a piece of land close to 
 Sea level in what respect is this an order of materials. 
 
 30. Give an illustration of the difference between concrete and abstract 
 utility. 
 
 31. Point out the advantages involved in being right handed (or left 
 handed), instead of ambidextrous. 
 
 32. Give two illustrations of the advantages of using abstract number in 
 arithmetic. 
 
 33. Also of the utility of abstract words in language. 
 
 34. If a given process be divided into a multiplicative succession of parts, 
 in carrying out this process it is made easy to stop when any required 
 degree of accuracy has been obtained. What economies or efficiencies 
 -result? Illustrate. 
 
 35. From the order of materials standpoint explain the efficiency meaning 
 of the statement "What one does not have in the head, one must have in 
 -the heels". 
 
 36. What order of materials is implied in the statement "strike me, but 
 iiear me". 
 
 37. State as fully as you can the principles of efficiency involved in the 
 -£erm "psychological moment". 
 
CHAPTER VII 
 
 EXTERNALITY 
 
 Illustration 
 
 It was remarked in Chapter II that an epoch in human progress 
 occurred when some primitive manlike creature first hit upon the 
 device of saving labor by keeping and using again a club which he 
 had found helpful in procuring food. It was a still earlier and per- 
 haps more important epoch in efficiency history when a club was 
 used for the first time without any thought of its repeated use; or 
 when any external object was first used by some animal as an aid 
 in obtaining food or protecting itself from its enemies, an illustration 
 being the use of a web by a spider. 
 
 General Statement 
 
 This explicit use of an object or objects external to a given 
 domain as a means of obtaining results constitutes the next primal 
 instrument for obtaining results which we shall investigate. This 
 source of efficiency often takes puzzling and extreme forms. This 
 fact is illustrated by various statements in common use such as 
 "The longest way round is the shortest way home", "There is a 
 point where economy becomes wasteful extravagance", and "There 
 is that which scattereth and yet increaseth". These as well as other 
 aspects of the matter, show the need and value of careful study of 
 the method of obtaining results which is under consideration. 
 
 The principle of efficiency involved in the use of objects or entities 
 external to oneself or to a given domain, we term externality. 
 
 CLASSIFICATION 
 
 Objects Usable as Externalities 
 
 As to the objects which may constitute an externality, we may say 
 in general that any object may be used as an auxiliary means to 
 efficiency in some way or ways, but not in all ways. Thus the 
 moon has often been an aid in determining the position of a ship at 
 sea, but the rocks on the moon cannot be used in building an irriga- 
 tion dam on the earth. 
 
112 SOURCES OF EFFICIENCY 
 
 Evidently also in determining whether an object is to be regarded 
 as auxiliary much depends on what is regarded as naturally and 
 inherently a part of any given object or domain. This is a matter 
 to be considered more fully later (see p. 123). Meantime it is well 
 to note that among the more important objects which are often 
 plainly used as externality agencies of efficiency are various material 
 Objects; in particular all tools and machines, and various physical 
 forces; plants as sources of clothing, as medicines, and in other 
 ways ; animals as beasts of burden, as sources of clothing, etc. ; other 
 persons, ideas, theories, symbols, efficiency and other principles, 
 categories like space and time; or complexes of these objects. 
 
 Many important individual objects which belong to those various 
 classes will be mentioned in the pages which follow. 
 
 Quantitative Species of Externality 
 
 It is also important to classify externalities with respect to the 
 forms which they may assume. 
 
 With regard to the categories of quantity and space, an externality 
 may be large or small ; near or remote ; a fringe, a background, or a 
 betweenness ; local, superficial, or pervasive ; and of various geomet- 
 ric shapes. 
 
 It is also important to remark that an externality may be of one, 
 two, or three dimensions. A long cable is said to be the life of a 
 ship. The cable in this case may be regarded as a linear or one- 
 dimensional externality. A three-dimensional externality is em- 
 ployed when the whole of a mass of water is boiled in order to kill 
 a few germs contained in it, or when practically all the carbon is 
 expelled from iron in one of the Bessemer processes of making 
 steel, so as to make it possible to introduce exactly the right per cent 
 afterward. 
 
 An externality may also take what may be called the point form. 
 We use this, for instance, when, in mastering a subject, we leap 
 ahead from one leading point to another, and afterward rapidly 
 fill in the intervening gaps or let them fill in themselves. A similar 
 instance is the mastery of any field by first mastering its strategic 
 points. 
 
 The importance of an infinite externality is illustrated in proofs 
 by exclusion in logic, and much more strikingly by the value of 
 religious ideas. A case of relatively infinite externality is that of 
 representing zero or absence of number by the symbol o. 
 
EXTERNALITY 113 
 
 What we may term matrix externality is often expressed by the 
 word "environment". 
 
 It is frequently useful to characterize an externality by means of 
 the category of number. Thus an externality may be dual in the 
 sense that it is composed of two elements as when both water and 
 heat are used in preparing food by the method of boiling. Similarly 
 an externality may be triple or %-fold. An illustration of the latter 
 is the repeated use of the pendulum in determining the force of 
 gravity at a given place. 
 
 Or an externality may be manifold in the sense that it is used in 
 many ways, or by many persons at the same time, as when a railroad 
 or an idea is used by many persons simultaneously. 
 
 Temporal Species of Externality 
 
 A case of externality may frequently be characterized by some 
 category of time. Thus a scaffolding is a temporary externality, 
 while the finished building may be a permanent one. When time is 
 used as a representative of what is contained in time, an externality 
 involved in time may conveniently be spoken of as temporal. Ex- 
 ternality of this kind is practiced by the man who is longheaded, or 
 forehanded, or patient. Another form of temporal externality is 
 illustrated by the manner in which the Rothschilds in London learned 
 of the results of the battle of Waterloo several hours before any one 
 else in the city and made the earlier knowledge the source of finan- 
 cial profit. All preventive and prophetic work is full of the extern- 
 ality of time. Another aspect of the matter is expressed by the 
 proverb "All things come to him who waits". 
 
 Still another case of temporal externality is that of suspended 
 operations in mathematics in order ultimately to save work by 
 cancellation or elimination of other kinds. The same mode of 
 obtaining efficiency applies in many other fields. 
 
 The result aimed at in any process also constitutes what is in one 
 respect a temporal externality. 
 
 Other Important Forms 
 
 If we combine the idea of number with that of order we get 
 the idea of reciprocity and hence of reciprocal externality. Illus- 
 trations of this are the two blades of a pair of scissors, man and 
 wife, mind and body, algebra and geometry, or the fruitful interac- 
 tion of theory and practice in any department as in engineering. 
 
ii 4 SOURCES OF EFFICIENCY 
 
 Similarly we may have triple or w-fold reciprocal externality, as 
 that existing among the five senses, or the various organs of the 
 body, the members of a family or community, the machines in a 
 factory, or the various departments of knowledge and action, as 
 agriculture, chemistry, biology, and mining. 
 
 An important special case is what is called the comparative 
 method of testing a principle in history or a problem in science. 
 Thus an important way of getting light on republican government 
 is to study all historic republics side by side. 
 
 As to force an externality may be reluctant or automatic. Thus 
 vision is characterized by certain large externalities which are 
 automatic and irresistible, as well as by others which are voluntary. 
 Motion often constitutes an efficient externality as when a teacher 
 enables a pupil to realize certain properties of a cone by means of 
 the rotation of a right triangle generating the cone, or when a 
 teacher unravels any complex matter by causing it to unfold from 
 certain unit principles. 
 
 Various adjectives of quality may be applied to externalities. 
 Among the most important are the terms homogeneous and hetero- 
 geneous. Thus an externality may be homogeneous (or hetero- 
 geneous) in itself, or in relation to the material to which it is 
 applied. The appliances used in keeping meat by cold storage are 
 heterogeneous in both of the above respects. An important case of 
 homogeneous externality is that of doing work on a large scale. 
 
 An extreme case of heterogeneous externality is that which may 
 be termed negative in character. In this species the datum and ex- 
 ternality are directly opposite in nature in some important respect. 
 Instances are a difficulty which leads to new discoveries and knowl- 
 edge, or a defeat or a misfortune which in the end imparts new 
 power. Of like nature is the making of a temporary sacrifice for 
 the sake of a future gain. 
 
 In relation to the directive faculty in man, externalities may be 
 classified as natural or artificial. Thus one hand is a natural ex- 
 ternality to the other. Machines and buildings are examples of 
 artificial externality. The results of a mechanical or biological 
 propagation are partly natural and partly artificial, and may be 
 termed genetic externality. The consequences or fruits of an act 
 or principle form externalities which may also be termed genetic. 
 In many cases, externalities of this last kind have an important func- 
 tion in determining the essential nature of an act or law. 
 
EXTERNALITY 115 
 
 Important cases of directive externality are the preparation and 
 use of reserves of any kind as of food, water, power, money, health, 
 knowledge. 
 
 With respect to the principle of limitation, an externality may be 
 vague, partial, or imperfect in any way. Thus in taking an oath in 
 court use is made of infinite externality, but usually of this in a 
 very obscure and general form. So mystics use unlimited exter- 
 nality in many forms all of which are more or less difficult to under- 
 stand. The ether, as used in physics, is a case of a valuable but 
 imperfectly understood externality in the field of science. 
 
 It is often an advantage to combine and use externalities in groups 
 or even in group systems. Thus in irrigating a large piece of land a 
 group of auxiliaries is used in the form of dam, ditches, pipes, tools, 
 men, and also of time, ideas, and experience. So a microscope 
 (or a telescope), and the various facts revealed by such an instru- 
 ment form a group of related externalities. In like manner if we 
 divide a set of externalities into two groups, viz. : natural and arti- 
 ficial, and subdivide each of these groups according to various 
 spatial, numerical, temporal, and other categories, we arrive at a 
 multiplicative group system of externalities. 
 
 Similarly an externality may be of high or low order. As an 
 example of a dual series of externalities we have the saying "The 
 pen is mightier than the sword". Space and time are auxiliaries of 
 a higher order than material objects. The order of excellence of 
 an externality may be determined in various ways, as by the number 
 of sub-externalities included in the given externality, or by its 
 dimensions, or by its general efficiency power. What is often called 
 "the ideal" in any department, even though it may be unattainable, 
 often constitutes a powerful and stimulating externality. 
 
 Complex Externalities 
 
 Evidently the different species of externality may be compounded 
 and complexed in many ways. Instances of such complex exter- 
 nalities are the aggregate of externalities found in a large factory, 
 or those used in connection with courts of justice in the punishment 
 of crime or the settlement of disputes. Vastly more extensive and 
 complex is the combination of externalities which are in operation 
 at each stage of human progress. 
 
n6 SOURCES OF EFFICIENCY 
 
 EFFICIENCY FUNCTIONS OF EXTERNALITY 
 
 In studying the advantages which accompany the use of external- 
 ity, it is evident at the outset that an extension of material and 
 methods in any process means additional opportunities for the for- 
 mation oi various species of groups and for reaping the efficiencies 
 which come from the use of groups. 
 
 Externality leads to Reuse 
 
 Looking at the matter in more detail, externality opens the way 
 to important cases of reuse. For instance the application of paint 
 to a wooden house keeps the material of the house from rotting 
 and thus prolongs the use of the house. It is to be noted also that 
 the house itself is an externality which prolongs the use of its 
 contents. So the immersion of a biological specimen in alcohol 
 leads to the preservation and repeated use of the specimen. 
 
 The combination of many business establishments into one is 
 frequently followed by the reuse by all the rest of what is best in 
 each one of the constituent businesses. 
 
 Externality also leads to more abstract and general forms of 
 reuse. Thus by showing that two objects are each equal to a third 
 object, we may show that they are equal to each other. The third 
 object in this case may be regarded as an externality the employ- 
 ment of which saves the labor of an often difficult direct comparison 
 of the two original objects. The extended use of this principle 
 leads to the method of measurement in dealing with objects and to 
 all the fruits of measurement. 
 
 Taking a wide view of things or doing things on a large scale 
 frequently opens the way to numerous economies and efficiencies 
 among the most important of which is prophetic reuse. For ex- 
 ample the U. S. Weather Bureau in the year 1903 observed tor- 
 rential rains on the Upper Missouri River and predicted a flood on 
 the Mississippi 28 days before it arrived at certain places and thus 
 saved many millions of dollars. The same bureau has diminished 
 the annual loss to shipping on the Great Lakes by fifty per cent. 
 
 Leads to Multiplicative Results 
 
 The externality of outflanking an enemy opens the way to the 
 multiplicative effect of an enfilading fire. In a much more general 
 way the consideration of a large domain of material gives oppor- 
 
EXTERNALITY 117 
 
 tunity for the discovery or invention of units and multipliers of 
 unusual excellence. 
 
 Economies 
 
 The use of auxiliary instruments results in a vast variety of 
 economies as of strength, time, space, and resources of all kinds. 
 At one time it took 78 men 1^2 minutes to put over the helm of a 
 large vessel ; later by the aid of steam, the work was done by 2 men 
 in 16 seconds. Every field of activity contains similar illustrations. 
 
 New Groups and Group Systems 
 
 General externality and special auxiliary objects are alike potent 
 aids in the formation of groups and of group systems. A simple 
 instance is the formation of a bundle by tying objects together with 
 twine. The use of a club, or of a bow and arrow, gave the savage 
 concentration of his strength both in time and space. The use of 
 the gun and bullet does the same in a far greater degree. The 
 externality of a copper wire on a railroad leads to the concentration 
 of many locomotives into one central power engine. 
 
 So the use of a clock gives us an accurate and detailed multi- 
 plicative grouping of time. In a far larger way the telegraph, tele- 
 phone, and various similar appliances of modern life make the world 
 one large group, and also a system of groups in many ways. With 
 reference to a special field like that of books, it has been remarked 
 that the "literature which enlarges the outlook, also transforms the 
 mind". Or, as Thoreau says, "Only that intellect makes any pro- 
 gress toward conceiving the essence of a matter which at the same 
 time perceives its effluence." 
 
 Accuracies and Delicacies 
 
 Externality frequently produces those uniformities and accuracies 
 which are the source of much efficiency (see Chapter VIII, p. 130). 
 Examples are the continuity of action obtained by the use of a fly- 
 wheel or a reserve of any kind, stability acquired by aid of ballast 
 or a bilge keel, or accuracy by aid of extra tests or apparatus. 
 
 In like manner auxiliary appliances are often a source of useful 
 diversity, fluidity, or sensitiveness. A simple instance is that of 
 making food tender by the use of heat. By the aid of the bolometer 
 a difference of temperature of less than .0001° may be detected. In 
 
n8 SOURCES OF EFFICIENCY 
 
 making glass the addition of soda lowers the melting point of sand 
 from 3000 to 2400 , and lime is useful in the same way in reducing 
 iron ore. By using the proper apparatus several thousand successive 
 photographs of a moving object may be taken in one minute and 
 the action of the corpuscles of the blood, for instance, traced in 
 detail. 
 
 A Source of Orders of Materials 
 
 Similarly the use of an externality is often a means of obtaining 
 a useful multiplicative gradation. Thus if two tracks are used on 
 a railroad in a given direction one can be used for fast trains and 
 the other for slow trains with many resultant advantages. 
 
 Some one has said that to get down to the pith of a matter one 
 must go round the matter and study it in all its bearings. Ex- 
 pressed in other words this means that a varied externality is neces- 
 sary in discovering the causes, sources, and essential efficientism in 
 any domain. Thus a consideration of the needs, rights, and op- 
 portunities of all classes of men leads to a multiplicative series of 
 ethical principles capped by what is at least an approximate or 
 efficiency absolute represented perhaps by a sense of oughtness 01 
 Kant's categorical imperative. 
 
 Thus also the combination at Jerusalem as at a focus, of the 
 various externalities represented by Egyptian, Assyrian, Persian, 
 Greek, and Roman civilizations was instrumental in leading to the 
 development at that place of the- Jewish and Christian religions. 
 In any field of work breadth of view as to ends aimed at is import- 
 ant in obtaining efficiency of a high order. Efficiency for selfish 
 ends is not efficiency at all in the long run. 
 
 New Powers of Management 
 
 A broad view of things is also a source of efficiency in that it 
 leads to a higher and more effective use of man's directive powers 
 (see Chapter XI, p. 192), and is productive of many valuable utili- 
 zations and substitutions. It gives a wider range of material to 
 select from, more space in which to act, and many aids in transfer- 
 ring objects in space. Thus a lampshade enables us to direct light 
 to a place of need and thus more fully to utilize the light. By the 
 use of salt, vinegar, tin, or cold storage, we can preserve food and 
 direct its use with respect to the categories of both time and place. 
 
EXTERNALITY 119 
 
 Externality is often a source of efficiency by enabling us to sub- 
 stitute a material or force that costs little for that which costs 
 much, as in the use of water-power instead of hand-power to saw 
 lumber. 
 
 Externality also assists in getting results by enabling us to apply 
 energies and resources at important centers. Thus Napoleon by 
 taking a large view of the field of operations was able to strike the 
 enemy in the rear at Marengo and thus to win the campaign by a 
 single battle. So in general a large view of matters reveals centers 
 of influence and also the means of reaching and mastering these, 
 centers and thus obtaining multiplicative results. 
 
 Prevention of Loss 
 
 The use of externality often produces important results in what 
 is at first a negative form. Thus a broad view of a given matter 
 may prevent error, sickness, or even loss of life. The use of an 
 arbiter to settle a dispute renders prejudice inoperative. The 
 breadth of view gained by education and travel is a safeguard 
 against hasty generalizations, or overuse of any one method. A 
 somewhat similar qualitative result springing from the use of ex- 
 ternality is the conversion of an obstacle into a stepping stone, or 
 of a defeat into a victory. 
 
 Unique Fruits 
 
 Some of the results obtained by the use of externality are unique 
 or transcendental in the sense that apparently they could not have 
 been obtained without the use of this principle in some form. Thus 
 the aeroplane enables a man to fly. The yellow fever parasite is so 
 small as to be invisible in the microscope yet it can be entirely con- 
 trolled by indirect means. The same is true of the germs of several 
 other diseases, as rinderpest, and pellagra. By the use of the 
 Roentgen rays the action of the heart and lungs may be seen and 
 photographed. By the same means when bismuth salts have been 
 added to the food the progress of this food during the whole process 
 of digestion may be watched. Religious conversions as produced 
 by the action of infinite externality upon the individual form an 
 illustration of beneficial results of an incomparably higher type. 
 
120 SOURCES OF EFFICIENCY 
 
 Complex Fruitages 
 
 It is scarcely necessary to add in this connection that the above 
 classes of efficiency functions may be compounded and complexed 
 in an endless variety of ways. For instance externality in the form 
 of an anticipation of future rewards often begets various efficiency 
 advantages. Such an anticipation, for example, arouses a feeling 
 of joy in the worker which increases his efficiency in a number of 
 ways as by stimulating his various activities, increasing his speed, 
 causing him to search for new knowledge, and perhaps leading him 
 to invent new methods. 
 
 Greater Use of Externality in Higher Organisms 
 
 If we wish to look at the fruits of externality in a more collective 
 and pictorial way we find, for instance, that the higher we go in the 
 scale of organisms the greater is the use of auxiliaries. The spider 
 has its web, and the bird its nest, but man has his cities, railroads 
 and philosophies. 
 
 If we examine the various definitions which have been made of 
 man for the purpose of discriminating between him and the lower 
 animals, we find that the essential part of each of these statements 
 is the conception of man as an animal using externality in some 
 explicit and conscious way. Thus man has been defined as the tool 
 using animal; as an animal looking before and behind; the cause 
 using animal (das ursachen Thier.) ; a rational animal; the animal 
 requiring the superfluous. 
 
 Greater Use by Greater Men 
 
 Furthermore it is to be noted that the greatest men are those who 
 have used the most and highest externality. A study of great men 
 in the schoolboy stage has shown that their most common charac- 
 teristic is a tendency to break out of ruts and discard conventions. 
 The use of this and other forms of externality increases as they 
 develop. 
 
 Time and tide, it is said, are always on the side of great men. 
 As a matter of fact such men have such an outside and comprehen- 
 sive vision of affairs that they are enabled to utilize time and tide 
 for their own purposes. 
 
EXTERNALITY I2 i 
 
 Human Progress Marked by an Increasing Use of Externality 
 
 Hence it is not surprising that each stage of human progress has 
 been marked by an increasing use of externality in its various forms. 
 The first club or stone used thus has developed into the present 
 mighty volume of machinery of all kinds, material, linguistic, social, 
 artistic and logical. 
 
 Furthermore an examination of each department of activity and 
 of each element of civilization reveals the same law of increasing 
 auxiliaries. Thus the knowledge required of the expert agricul- 
 turist has increased till at the present time he must use the 
 main principles and some of the details of chemistry, physics, 
 botany, biology, engineering, meteorology, commerce, and social 
 psychology. 
 
 Lack of Externality Means Loss 
 
 Another method of gaining an appreciation of the importance of 
 externality is to try to picture what life would be without certain 
 of the auxiliary instrumentalities now in common use. If, for 
 instance, in navigation we take away steam and gas we reduce 
 transportation by water to the use of sail vessels; if we take 
 away masts and sails, we have left boats propelled by oars ; if we 
 remove wood and skins, man must propel himself in the water by 
 swimming. 
 
 One reason why man has not been able to analyze the force of 
 gravitation into constituent elements is that this force is so perva- 
 sive that it has thus far been impossible to get an outside point from 
 which to view it ; that is, it has been impossible to apply any compre- 
 hensive externality to it. 
 
 Likewise in the higher mental world, the man without externality 
 is the narrow, selfish, and therefore blighted man. 
 
 Familiar Words Showing the Value of Externality 
 
 Still another way of obtaining an insight into the power of ex- 
 ternality is to recall the efficiencies connected with words or phrases 
 which denote certain more or less familiar forms of externality, 
 such for instance as tools, machinery, breadth of mind, reserves, 
 solidarity, outwit, undermine, correlations, larger horizon. 
 
122 SOURCES OF EFFICIENCY 
 
 Limitations in the Utilities of Externality 
 
 Finally in this relation mention should be made of the limitations 
 and often drawbacks connected with externality as a source of effi- 
 ciency. Externality, of necessity, means an added amount of ma- 
 chinery to carry and often the annexed toolage does not pay for 
 itself. It then becomes mere red tape or worse. Too much light 
 makes a confusing glare or even produces blindness. Wealth with- 
 out some higher externality often becomes a curse. At times a. 
 doubt has been expressed whether modern machinery as used thus 
 far has, on the whole, improved the condition of mankind. At 
 least we can say the burden of material mechanism carried by 
 modern civilization is as great as it can bear. Another class of 
 danger connected with the use of outside auxiliaries is the dwarfing 
 of one's powers of self reliance. Other aspects of this evil are 
 expressed by the proverb "Too many cooks spoil the broth", and 
 "What is everybody's business is nobody's business". In case an 
 externality results in a more extended multiplicative group system, 
 the drawbacks presented in a preceding chapter connected with 
 such systems will also be present. 
 
 It is well to note also that the dangers connected with an extern- 
 ality often correspond in size to the useful power of the externality. 
 The efficiency possibilities of unlimited externality for instance in 
 the best religious concepts seem to be boundless yet in many ways 
 the strength of religion has proved to be its weakness. Seemingly 
 as a consequence of the prodigious values in religion have come 
 pride, reluctance to use other sources of efficiency, hostility to gen- 
 eral culture, cruelty, and general persecution. Hence it has been 
 said, "The vision of a spiritual ideal is the most important single 
 element of efficiency, but one of the most dangerous". 
 
 Self-corrective Power in Externality 
 
 It should be observed, however, that externality contains within 
 itself the power largely to correct its own defects and evils. For the 
 high order of multiplicative power which results from such extern- 
 ality also means in large degree the power of self -correction and 
 self -development. 
 
 ANALYSIS 
 
 In order to get a more precise idea of the nature of externality 
 and hence to increase the advantages in its use, we shall now make 
 
EXTERNALITY 
 
 123 
 
 a more thorough examination of the elements which enter into it 
 than was made in the opening paragraphs of the chapter. 
 
 Space and Like Elements 
 
 A spatial element seems necessary to the idea of externality. For 
 the term implies outsideness to what is given or customary, and the 
 concept of something outside or beyond is a spatial one. 
 
 It is to be noted, however, that in the more abstract forms of 
 externality the idea of space is refined till in some respects this idea 
 seems to disappear altogether. An instance in point is the use of 
 an abstract quality or method of some kind as an auxiliary. Physi- 
 cally a quality may be as innerness, while in the domain of mental 
 attention it is outside of what was included in the consciousness of 
 the doer at the start. 
 
 The element of time is also present to some extent in externality. 
 For, at least with respect to the conscious apprehension of them, the 
 auxiliary used follows that which was first tried without the ex- 
 ternality, and hence we have in each use of externality some flavor 
 of succession or order. 
 
 The element of mind or consciousness is also usually present, 
 since the use of something beyond what is customary implies a 
 certain element of effort or surprise. Looked at in another way, 
 externality implies first an enlargement of the mind and then of the 
 material used or considered. 
 
 The meaning of externality may also be expressed in terms of the 
 group. From this point of view externality means an enlarged 
 group, the result being obtained by removing some limitation in 
 the datum group. 
 
 Relativity of Externality 
 
 From the preceding discussion it is evident that the element of 
 relativity is prominent in determining whether a given object or 
 process is a case of externality or not. What is externality from 
 one point of view may not be so from another. To the savage chief 
 the use of a messenger would be natural and the use of mails an 
 externality, while to a modern business man who has come to regard 
 the use of the mails as natural, the use of a special messenger would 
 usually seem an externality. Similarly the use of salt in one's food, 
 or of medicine, or of clothing, may or may not constitute an extern- 
 ality according to circumstances. 
 
124 SOURCES OF EFFICIENCY 
 
 The two extreme points of view, in this respect, with regard to 
 externality should here be stated. Thus from the point of view of a 
 single monad, the rest of the universe is an externality. But from 
 the universal point of view, there is no such thing as externality, 
 but all efficiency is an internal process in the universe as a whole. 
 These extreme conceptions are useful since they are themselves, 
 with respect to the customary use of this agent, special cases of 
 externality. However, under usual conditions it is an advantage to 
 divide a situation into what is ordinary and what is extraordinary 
 or external to the ordinary. 
 
 It is also well to remember that in externality as well as in each 
 of the other Efficients there is a characteristic or unique element; 
 something perhaps beyond analysis. 
 
 Auxiliaries vs. Externality 
 
 It may also be well in this connection to point out the essential 
 difference between the terms auxiliaries and externality. Auxiliar- 
 ies are usually subordinate in size and importance to the main 
 datum or method while an externality may be superior to the datum 
 and may dominate it. The term auxiliaries also implies a more 
 direct and immediate use than does externality. 
 
 In conclusion we have the following approximate definition: 
 
 Externality is a method of obtaining results by the application of 
 something outside of the customary data. 
 
 Also the outside object thus used is often termed an externality. 
 
 METHODS OF APPLICATION 
 
 Externality as a Group 
 
 Viewing externality as a larger group, and hence as essentially a 
 higher use of the multiplicative principle, is an aid to the efficient 
 use of externality in several ways. For it leads to an extended use 
 of this instrument by making evident the great value of this method 
 of work, by revealing the vast number of available auxiliary ob- 
 jects, and by putting such objects in an effective form. 
 
 Adaptation in its Application 
 
 Taking up the matter in more detail, externality is so broad a 
 principle that in its use, relativity, or special adaptation in peculiar 
 cases, needs to be studied carefully. 
 
EXTERNALITY 125 
 
 In many situations of great difficulty, rather than to use no extern- 
 ality, it is well to use the principle in some crude form. This may 
 be a blind kind of externality like patience, or an unformed kind 
 like agitation, or publicity, or the mere recording of facts while 
 waiting for laws to appear. Compromise is often a complex form 
 of crude externality since in it patience is exercised and results from 
 two or more simultaneous series of developments are awaited. 
 
 Externality by Doubling 
 
 A simple but widely applicable form of externality is that which 
 consists of doubling a given object or repeating a given process. 
 Nature has employed this source of efficiency in giving man two 
 hands and two eyes. Man utilizes the same method when he in- 
 stalls two engines in a power house, or checks the result obtained 
 from a computation by repeating the calculation. 
 
 Preference to Highly Developed Externalities 
 
 In using externalities it is evidently important to learn to recog- 
 nize those auxiliaries which are highly developed and therefore 
 unusually effective and to give the preference to such species. In 
 this connection it is to be noted that a high externality is usually 
 more or less abstract, and, for our purpose, closely related to the 
 Efficients. It has also in many cases acquired a tendency to act, 
 so to speak, of itself. 
 
 Even when an additive externality would answer a given purpose 
 it is often well to use a highly multiplicative process giving larger 
 results than are needed and to apply the extra results to the apices 
 of some other group system. 
 
 A small or superficial externality is often dangerous but one 
 cannot possess too much externality in its higher forms. One 
 reason for this is that the higher forms carry with them in an 
 unusual degree their own corrective, as well as more aggressive prin- 
 ciples of development. 
 
 Educational Sources of Externality Powers 
 
 In the process of acquiring externality powers it is well to remem- 
 ber that the study of a certain subject or some special form of 
 experience is often particularly fitted to give mastery of some 
 special kind of externality. Thus geography gives a grasp of space, 
 
I2 6 SOURCES OF EFFICIENCY 
 
 geology of time, astronomy of space and time, chemistry of quality, 
 physics of force, psychology of mind, and history of time and 
 mind. 
 
 The effective application of the principle of externality is also 
 often greatly aided by the use of certain of the primal sources of 
 efficiency to be studied in the chapters which follow. Thus the 
 analysis (see Chapter VIII) of a domain into different well se- 
 lected elements often opens the way to obtaining important extern- 
 alities by a mere extension of certain of these elements. Also 
 appropriate symbols (see Chapter X) are an aid in grasping large 
 externalities and in applying them. The use of symbols, for in- 
 stance, may lead to standard methods of transforming and adapting 
 auxiliaries and obtaining results from them by semi-mechanical 
 means. 
 
 Ideal Species 
 
 It is ever to be borne in mind that for our purpose the most im- 
 portant externality is that of the aggregate of the Efficients com- 
 bined in the most effective way and kept ready for use at any 
 moment. It is to be noted also that each individual person may 
 advantageously develop this general form into a special form or 
 shape adapted to his peculiar circumstances. It will also be recog- 
 nized that the use of the above ideal constitutes a use of externality 
 of externality. 
 
 Synopsis of Chapter 
 
 The principal results arrived at in this chapter are as follows. 
 Not only may the organization of given material produce efficiency 
 in its use, but an equal or even greater increase of efficiency may 
 often be obtained by going outside of the given situation and ap- 
 plying certain auxiliaries to the data in hand. Evidently the use 
 of outside material may be of innumerable kinds since it may in- 
 clude an endless variety both of objects and also of the forms in 
 which these objects may be assembled or viewed. 
 
 The fundamental source of new power in externality is that it, 
 from its very nature, opens the way to the formation of new and 
 larger groups, and hence means larger and higher forms of reuse, 
 multipliers, groups, and group systems, with the various consequent 
 fruitages of each of these. Of particular importance are the new 
 
EXTERNALITY 
 
 127 
 
 possibilities of directive management which arise. Many valuable 
 results otherwise impossible are also obtained. Hence human 
 progress has ever been marked by an increased use of externality of 
 various kinds. 
 
 So powerful is this source of efficiency, that it is especially im- 
 portant to realize the great number of forms which it assumes, and 
 the frequently large value of even its crudest and most elementary 
 species. At the same time the greatest stress should be laid on its 
 highest forms, and careful study be made of the sources from 
 which these may be obtained. 
 
 EXERCISE 7 
 
 State the class or classes to which each of the following externalities 
 belongs : 
 
 1. An axe 4. Darkness as a revealer of stars 
 
 2. Sunlight 5. A relay circuit on a telegraph line 
 
 3. Business capital 6. A name 
 
 7. Heat used to expand a wagon tire before placing the tire on the rim 
 of the wheel. 
 
 8. Heat used in making ice. 
 
 9. A line added to a diagram to aid in proving a proposition in geometry. 
 
 10. The third dimension of space, as utilized by a man riding in an 
 aeroplane. 
 
 11. An ambuscade. 
 
 12. Boiling water to kill the germs in it. 
 
 13. During the blizzard of the year 1888, a telegram was sent from New 
 York to Boston by the way of Paris. What externalities were employed 
 in this process? 
 
 14. Give an example of each of the principal kinds of externality. 
 State the principal kinds of externality 
 
 15. Gained by travel. 
 
 16. Afforded by an education in the ordinary sense of the term. 
 
 17. Used by an intelligent farmer. 
 
 18. By a teacher. 
 
 19. Employed in the manufacture of pottery. 
 
 20. In mining coal. 
 
 21. State the different kinds of externality involved in mental conscious- 
 ness. 
 
 22. Which of the mental powers (as memory, etc.) supply noteworthy 
 externalities? 
 
 23. What externalities are used in writing a letter and sending it by mail? 
 
 24. Explain altruism as a form of externality and the efficiencies which 
 result. 
 
128 SOURCES OF EFFICIENCY 
 
 25. Give three instances of the use of color as an externality. 
 
 26. Also of the use of heat in this way. 
 
 27. Also of water. 
 
 28. State the kinds of externality used by an ordinary bird. 
 
 29. In a certain factory 1000 yards of a given kind of cloth can be manu- 
 factured at a cost of $800, and 50,000 yards at a cost of $32,000. The 
 efficiency of the first process is what per cent of that of the second? What 
 externalities are here the source of efficiency? 
 
 30. Before the use of power machinery in making muslin, 1000 operators 
 could produce 10,000 yards in a certain time. After the introduction of 
 such machinery 50,000 operatives in the same time produced 4,000,000 yards. 
 Express the degree of human efficiency here involved. What externalities 
 were the source of this efficiency? 
 
 31. By direct computation obtain, to three decimal places, the numerical 
 
 value of /»— . Also compute this value after first rationalizing the denom- 
 
 V3 
 inator of the given fraction. State the degree of labor efficiency involved. 
 What externality is used in obtaining this efficiency? 
 
 32. If a man without a machine can plant 1 acre of potatoes in 1 day, 
 while a man with a machine can plant 3V2 acres, state the degree of human 
 efficiency in the second process and the source of the same. 
 
 33. Of what advantage is it to a boxer to keep in more or less constant 
 motion ? 
 
 34. State the advantages in the use of a large storage battery in connec- 
 tion with a city electric railway. 
 
 35. State the difference between parsimony and economy. 
 
 36. Point out the advantages in using a somewhat larger furnace than 
 is actually required in heating a house. 
 
 37. Also in the use of a fountain pen as compared with an ordinary pen. 
 
 38. State as fully as you can the externalities now used by physicians 
 which were not used by them one hundred years ago. 
 
 39. What kinds of externality are involved in publicity as to governmental 
 affairs, and what are the advantages which result? 
 
 40. Give an example where the use of externality results in a loss of 
 efficiency. 
 
 41. Show that reuse always implies externality. 
 
 42. Give three examples of groups formed by the use of externality. 
 
 43. What kinds of externality did Vergil use when he wrote many lines 
 in the morning and cut them down to a few by evening, and what were 
 the advantages involved? 
 
 44. Give an instance where the use of crude externality rather than of 
 none is advantageous. 
 
 45. Instead of telephoning a given message it is sometimes more advan- 
 tageous to send the message in a written form. Why? 
 
 46. What are the advantages to a business man in keeping a considerable 
 cash reserve on hand? 
 
 47. In carrying on commerce with another country (especially one low 
 
EXTERNALITY 
 
 129 
 
 in the scale of civilization) it has been found useful to learn the history, 
 geography, and customs of the country. What externalities and resulting 
 advantages are involved in this procedure? 
 
 48. State the externality involved in realizing the future rewards of pres- 
 ent work and the advantages of such realization. State also some efficient 
 ways of making such externality vivid to different classes of people, as to 
 pupils, or workmen. 
 
 49. What advantages result from reasoning a principle out to its logical 
 consequences before applying it? What forms of externality are here- 
 involved? 
 
CHAPTER VIII 
 
 UNIFORMITY AND DIVERSITY 
 
 Illustrations of Diversity as a Source of Efficiency 
 
 The separation of an object into parts with a view to the in- 
 dividual treatment of these parts is often a fundamental source of 
 efficiency. Watt's invention of a separate condenser changed the 
 steam engine from a toy to the most effective machine in man's 
 possession. Flight by the aeroplane was made a practical success by 
 dividing the wings of the machine into parts so that they could be 
 warped with such exactness as to make stability possible amid 
 shifting air currents. The triumphs of modern surgery come from 
 regarding the human body not as a lumpish whole but as made up 
 of separate cells, and also from keeping the germs of infection 
 away from wounds. 
 
 The source of efficiency thus illustrated, we term diversity. More 
 complex and abstract examples of its value are the beneficial results 
 arising from the separation of church and state, from individual 
 ownership of property, and from the distinction between what is 
 personal and impersonal. 
 
 Illustrations of Uniformity as a Source of Efficiency 
 
 In like manner, and often in a closely related way the principle of 
 uniformity or sameness is a highly important aid in obtaining use- 
 ful results. Thus the fact that the same units of money are used 
 in all parts of a given country saves the traveller much trouble and 
 expense in having one kind of money converted into another. The 
 perception by Newton that the moon falls toward the earth by the 
 same law that an apple does led to the establishment of the law of 
 gravitation with the many useful consequences that have resulted. 
 Similarly the equality of men before the law results in a general 
 sense of security which is productive of personal and social effi- 
 ciency in many ways. 
 
 Aids to other Efficients 
 
 The principles of diversity and uniformity are not only themselves 
 direct sources of efficiency, but they also act in important ways 
 
 130 
 
UNIFORMITY AND DIVERSITY 
 
 131 
 
 through the other Efficients. Thus in order to teach a group of 
 children at the same time, certain uniformities of age, development, 
 and interest must exist among the individual children composing 
 the group. In other words special uniformities and diversities 1 
 enter into the formation of a group, and hence into such particular 
 forms of the group, as reuse, the unit and multiplier, multiplicative 
 groups, and orders of material. In fact we shall find that uni- 
 formity and diversity are the raw materials, so to speak, out of 
 which groups and the various Efficients are formed. 
 
 In particular it is well to observe at this point that a uniformity 
 (and its accompanying diversity) in some cases form an incipient, 
 or rude germinal group, and in other cases a specially efficient final 
 form of group. 
 
 It will be noted that psychologically the perception (and treat- 
 ment) of diversities precedes that of uniformities ; while logically 
 the reverse is often the case. Hence in some places we treat di- 
 versities before uniformities, and in other cases follow the reverse 
 order. 
 
 CLASSIFICATION OF DIVERSITIES 
 Relations of Uniformity and Diversity 
 
 Before the classification of diversities and uniformities is at- 
 tempted, it should be stated that a uniformity always implies a diver- 
 sity (and vice versa), but that when one of the two is prominent 
 as a source of efficiency the other may be inconspicuous or practi- 
 cally hidden. It is especially important to bear this fact in mind 
 whenever, for certain reasons, we shall temporarily treat the two 
 categories separately. 
 
 It is useful to realize that diversities may exist among all possible 
 material objects, such for instance as those catalogued in the classi- 
 fication sections of the preceding chapters. It does not seem neces- 
 sary to repeat these lists at this point. 
 
 It will be advantageous, on the other hand, to consider in some 
 detail the classification of diversities as to their form. 
 
 Spatial Forms of Diversity 
 
 As to space and its related categories a given diversity may be 
 partial, entire, or partial in some special way, an example of the 
 last class being a mottled form. An illustration of efficiency ob- 
 
132 
 
 SOURCES OF EFFICIENCY 
 
 tained by a positional diversity is the fact that the sewing machine 
 was made possible by the transfer of the eye from the blunt to the 
 sharp end of the needle. A similar instance was the placing of a 
 rudder in front of the aeroplane. Spatially also a diversity may 
 be internal, in that it exists among the parts of an object as among 
 the parts of a locomotive; or it may be exterm'al, in that it exists 
 between one object and another external object, as between two 
 locomotives. 
 
 Numerical and Group Forms 
 
 A given diversity may be dual in that it contains two elements as 
 when objects differ in both shape and color; or triple, as when 
 motions differ in direction, velocity, and duration; or manifold, as 
 when two given objects differ in size, weight, color, form, position, 
 motion, density, utility, and with respect to other categories. 
 
 Hence it follows that diversities may occur in bundles or groups. 
 Important cases are those variations which in the process of evolu- 
 tion occur in aggregates or groups and which are termed saltations 
 or mutations. 
 
 It is evident also that diversities may be grouped multiplicatively 
 in various ways. Thus the differences between an amoeba and a man 
 may be treated as a multiplicative group system of differences. 
 
 Other Species of Diversity 
 
 Again, diversities may be artificial or natural; active or passive; 
 permanent or temporary; relative or absolute. 
 
 A temporary diversity is a diversity of diversity; that is, a 
 diversity of the second order. 
 
 In general it is most important for our purpose to remember that 
 one diversity may be of higher multiplicative order than another, 
 and as a consequence more vital and useful in many ways. Thus 
 the diversities which characterize a set of accounts kept in the card 
 form are in general of a higher order than those found among 
 accounts kept in the ledger book form. So a difference in the 
 mental power of two men is many stages above a difference in the 
 color of their eyes. 
 
 In brief we may say a diversity may be of high order because it 
 is manifold, or of several dimensions, or because it occurs in ma- 
 terial of a high order of efficiency, or exists between materials of 
 
UNIFORMITY AND DIVERSITY 133 
 
 widely different orders, or because the given diversity produces 
 especially important efficiency results. 
 
 Difficult and Complex Forms 
 
 Certain diversities are so peculiar as to be difficult to grasp and 
 characterize. Illustrations are the differences between the proper- 
 ties of certain alloys and those of their constituents, or that between 
 matter and mind, and that between uniformity and diversity them- 
 selves. Some of these diversities may be so ultimate that we lack 
 externality by which to determine them ; others of them are doubt- 
 less due to some untraced action of the multiplicative principle. 
 
 The various species of diversities may be complexed together in 
 many ways. An example of a complex diversity is that between 
 two personalities, or two civilizations, or two philosophies. 
 
 CLASSIFICATION OF UNIFORMITIES 
 
 As has already been stated, for every case of diversity there is a 
 corresponding case of uniformity. But in certain instances the di- 
 versity involved may be prominent while the related uniformity is 
 obscure, or vice versa. Hence cases often occur where the one of 
 these sources of efficiency is noteworthy, while the other is incon- 
 spicuous. Thus certain differences between the ideas of space and 
 time are evident but the connection or likeness between these two 
 concepts is more difficult to conceive. 
 
 It does not seem necessary to catalogue and illustrate those species 
 of uniformity which plainly correspond to species of diversity, such 
 as uniformities of color, size, shape, weight, etc. We shall limit 
 ourselves therefore to a consideration of the cases where uni- 
 formities are especially prominent and are relatively independent of 
 the diversities related to them. 
 
 Dual Uniformities 
 
 Besides the dual uniformity which consists of uniformity in two 
 respects such as color and size, another form of dual uniformity is 
 that which exists between two objects, as between two peas. Among 
 the most important dual uniformities of this class, are those equiva- 
 lences between objects or systems which are termed equalities, 
 equations, or identities. 
 
 Truth in one of its aspects viz. : as a correspondence between fact 
 and symbol is a dual uniformity of this general kind. 
 
134 
 
 SOURCES OF EFFICIENCY 
 
 Orders of Uniformity 
 
 Cases of uniformity of higher order, like those of diversity, 
 call for especial attention. Thus the uniformity with which the 
 earth rotates on its axis is more important than uniformity in the 
 speed with which a man walks. So equality of opportunity for 
 different men is of a higher order than equality of physical weight. 
 
 Important special cases of uniformity are those which are due to 
 some outside cause, and which may often be controlled through this 
 cause. An example is a likeness in the mental habits of pupils due 
 to certain qualities in a teacher, or uniformity in family traits due 
 to heredity. Mention should also be made of the uniformity which 
 arises when one set of forces is generated in order to balance or 
 counteract another set. 
 
 Approximate Uniformities 
 
 It is well to notice also that certain so-called uniformities are due 
 to limitations in our powers of perception. An example is the 
 apparent uniformity in the surface of a table. It is often profitable 
 to regard such a uniformity as a first group in a multiplicative 
 group system. 
 
 COMBINATIONS OF UNIFORMITIES AND DIVERSITIES 
 
 Evidently uniformities and diversities may be combined in a great 
 variety of ways. Only the most important of these will be here 
 considered. 
 
 Combinations Related Spatially 
 
 (i) In a given uniformity, the diversities may be internal. An 
 example is the uniformity of length during wide changes of tem- 
 perature in a bar formed of the metal called invar, due to the fact 
 that the bar is an alloy of two metals, nickel and steel; or steadiness 
 of bodily health due to the action of different organs in different 
 ways; or an equivalence relation of any sort between two objects 
 which differ in their composition or details. 
 
 (2) The diversities which are related to a given uniformity may 
 be external to the uniformity. Thus comparative uniformity of 
 the temperature is often maintained within a building by dividing 
 the walls which surround the building into several air chambers. 
 
 (3) A special variety of (2) is of sufficient importance to call 
 
UNIFORMITY AND DIVERSITY 
 
 135 
 
 for independent mention. The allusion is to that form in which 
 differences are distributed more or less symmetrically about a mean 
 or average. Illustrations are a series of groups formed by setting up 
 certain standards and including in a given group all the cases that 
 fall within certain limits above or below a given standard. Similar 
 cases are the grouping of places on the earth's surface by the use 
 of latitude and longitude, and the many varieties of symmetry in 
 mathematics, art, and common life. 
 
 Combinations Otherwise Related 
 
 (4) The uniformity and the diversity which are combined may be 
 of such a nature that the category of external or internal does not 
 apply to their relation. As an example we have that combination 
 of diversity in space with uniformity in time which is found in 
 markings on finger tips as used in identifying criminals. 
 
 (5) Finally we have those complex cases where uniformities and 
 diversities are combined in various ways at the same time. Thus 
 in a card index certain diversities are internal and others external 
 to the uniform size of the cards. Some of the uniformities and 
 diversities involved are also temporal in nature. The result is 
 a manifold and varying system of groups, productive of much 
 efficiency. 
 
 EFFICIENCY FUNCTIONS OF DIVERSITIES 
 
 Since uniformities and diversities are incipient or special forms of 
 groups and other Efficients, the efficiency functions of uniformities 
 and diversities are best expressed in terms of those of the other 
 Efficients. 
 
 Diversities as a Source of Reuse 
 
 In the first place it is to be observed that a diversity is often the 
 primal source of a case of reuse. For instance to recur to a former 
 illustration the separation of the engine of a steamboat from the 
 hull together with the transfer of this engine to a tugboat leads to 
 repeated use of the engine, and hence to the various economies and 
 efficiencies which characterize such reuse. To consider a more 
 general case, some diversity in the form of separation of parts is 
 evidently essential to all marginal reuse. Also a high degree of 
 diversity often leads to a high degree of marginal reuse. Thus the 
 
136 SOURCES OF EFFICIENCY 
 
 condyle on which the head of a bird rotates allows much greater 
 freedom of motion than that on which man's head is poised; hence 
 the work done by a bird in putting its body in a given position is 
 reused marginally to a much greater extent than is such work when 
 done by a man. 
 
 Diversities also open the way to other forms of reuse. Thus by 
 eating a meal composed of foods which differ as to the time of their 
 digestibility, the gastric juice and whole digestive apparatus may be 
 reused in the process of assimilating the meal. 
 
 Diversities lead to Groups and Group Systems 
 
 Similarly uniformities and diversities lead to the formation of 
 units and multipliers and of groups in general. These groupage 
 results often take many special and highly important forms. An 
 instance is the discovery by Joseph Henry that oiled silk will insulate 
 an electric wire and that consequently great lengths of such wire 
 may be wound around an iron core in concentrated form, later 
 results being of course the invention of the electric telegraph and 
 the dynamo. In like manner the tubular boiler is a case where a 
 diversity of material gives rise to a concentration of force in both 
 time and space and as a result has made the locomotive, for 
 instance, a practical success. 
 
 Not less important is the formation of multiplicative group sys- 
 tems by the utilization of diversities. For example the separation of. 
 the continuous manuscript roll into' the equal parts called leaves led 
 to several of the group systems which we find in a book. So owing 
 to chemical analysis the way has been opened to the systematic 
 group combination of elementary substances, the result being the 
 innumerable substances now in use which have been prepared by 
 chemical synthesis. 
 
 A diversity often leads to the formation of an order of materials 
 without any intervening multiplicative group stage. Thus the change 
 of seasons in the Temperate Zones results in a multiplicative grada- 
 tion of seasons and of corresponding life activities, winter being the 
 abstract efficiency season. The superiority of the inhabitants of 
 the Temperate Zone is doubtless in large part due to this fact and 
 its efficiency consequences. 
 
UNIFORMITY AND DIVERSITY 
 
 137 
 
 Lead to New Uniformities and Diversities 
 
 One diversity frequently leads to the formation or recognition of 
 another diversity and its fruits. Thus difference in soil should 
 mean difference in methods of cultivation and of products, and 
 hence to increased profits on the average. 
 
 Similarly a diversity may lead to a uniformity and its fruits. For 
 instance the fluidity which characterizes water causes the top of a 
 body of water to form a level surface and manifests itself in other 
 useful uniformity properties. Diversified farming makes profitable 
 returns more certain. Investment of funds in several different ways 
 adds to the likelihood of always having some income. 
 
 An Aid in Directive Work 
 
 Diversity in its various forms also facilitates directive efficiency 
 processes. Thus even the plant in order to transfer starch from one 
 part of its structure to another converts insoluble starch into sugar 
 which can be dissolved and made fluid. So in business fluid capital 
 of all kinds is directible. In another line of action, separation or 
 distinction of parts opens the way for the substitution of what costs 
 little for what is expensive. Also the separation of canned goods 
 for instance from surrounding causes of decay leads to the efficient 
 directive action of these foods both in time and space. The recog- 
 nition of diversity makes it easy to realize the needlessness of 
 throwing out the baby with the bath, and later the possibility of 
 developing the child without breaking its will. 
 
 Absolute Values of Diversity 
 
 The use of diversity often leads to certain absolute values ; that is, 
 to advantageous results which transcend the data incalculably, and 
 may be unique in that they are not otherwise attainable. Thus if 
 the division of a ship into compartments leads to the saving of the 
 lives of the passengers, the result is of the kind just described. 
 Similarly the isolation of persons sick of infectious diseases may 
 lead to like inestimable advantages. 
 
 Noticing differences in weight in samples of supposed nitrogen 
 was the means of discovering the chemical element argon and later 
 of other elements. The plasticity of maize made it possible to de- 
 velop varieties which ripen in the short summer of comparatively 
 cold climates. A diversity of parts in a landscape or work of art is 
 frequently a source of both esthetic charm and commercial value. 
 
138 SOURCES OF EFFICIENCY 
 
 Complex Utilities 
 
 The above efficiency functions may be combined in various com- 
 plex ways. An example is the great variety of useful results which 
 comes to the farmer who makes it a rule to keep the soil thoroughly 
 pulverized about certain growing crops. These complex develop- 
 ments may take extraordinary and unexpected forms. Thus from 
 the chance observation that light makes a smudge on silver has 
 sprung the whole science and art of photography. From the fact 
 that rubbed amber attracts a feather has arisen all of electrical 
 science. Of similar complex and dialectic character are the advan- 
 tages which have resulted respectively from the ownership of prop- 
 erty in severalty, from the division of labor, and from the atomic 
 theory of matter. 
 
 Words Illustrating Usefulness of Diversities 
 
 The benefits obtainable by the use of diversities may be realized 
 in another often effective way, viz. : by realizing the useful results 
 connected with certain more or less special and familiar forms of 
 diversity such, for instance, as analysis, variety, solution, indepen- 
 dence, detachment, ductility, delicacy, sensitiveness, freedom. The 
 advantages connected with diversity may also be realized in a nega- 
 tive way by recalling the evils and losses suggested by such words 
 as fixity, monotony, and fossilism. A concrete example is a railroad 
 accident caused by color blindness in an engineer. 
 
 Limitations to Values of Diversity 
 
 The presentation of the efficiency functions of diversities should 
 not be closed without a statement concerning the dangers and evils 
 connected with the use of diversities. Too much diversity, or mis- 
 placed diversity, may result in the impairment or destruction of 
 groups, or in difficulty in their formation. An example is the 
 diversity which characterizes a routed army. Another illustration 
 is furnished by the evil results of too pronounced a division of 
 labor. Often extreme diversities result in what is called license 
 or chaos. 
 
 EFFICIENCY FUNCTIONS OF UNIFORMITIES 
 
 Uniformity as a Source of Reuse 
 
 Uniformities also have their characteristic efficiency functions. 
 Thus the fact that the ocean is approximately the same the world 
 
UNIFORMITY AND DIVERSITY 139 
 
 over leads to reuse in all other places of knowledge of it gained in 
 any given place. The same statement applies to the atmosphere, a 
 geological stratum, or human nature. Permanence in time, gained 
 for instance by printed or phonographic records, or by monuments, 
 leads to the reuse of work and facts. The discovery by Van t'Hoff 
 that liquids and gases have important properties in common has led 
 to the reuse of our knowledge of one with respect to the other in 
 important cases. 
 
 Basis of Groups and Group Systems 
 
 Similarly a uniformity may be the basis of a group formation of 
 some sort, and hence be the source of the advantages which come 
 from the use of the group. For example, if a field is approximately 
 level, this uniformity opens the way to the use of a gangplow in 
 cultivating the field. Uniformity in the size and quality of a manu- 
 factured article leads to the wide use of that article. Justice and 
 honesty are the sources of many similar beneficial results. 
 
 The invariability in the time occupied by the earth in rotating once 
 on its axis is the basis of our multiplicative group system of time 
 measurement with its many ramifying utilities. Similarly various 
 social, political, and indeed all group systems are founded on certain 
 uniformities. 
 
 Other Uses of Uniformities 
 
 Uniformity and continuity, when realized, often make the use of 
 certain kinds of externality comparatively easy. An example is the 
 manufacture of an article on a large scale when the demand for the 
 object is certain and permanent. 
 
 Uniformities frequently open the way to profitable directive acts. 
 Thus uniformities in the parts of a watch or automobile facilitate 
 the substitution of a new part for any part that may be broken or 
 worn out. If we know that a certain volume of gas will give as 
 much energy as a ton of coal the substitution of one for the other 
 is often the source of valuable efficiencies. The fact that a network 
 of protoplasm connects the cells in a plant makes possible the opera- 
 tion of botanical grafting. 
 
 The use of uniformities as of diversities, in certain cases has 
 transcendental or absolute value, such as those of saving life, or 
 giving knowledge otherwise unattainable. 
 
140 
 
 SOURCES OF EFFICIENCY 
 
 Complex and Self-developing Values 
 
 The advantages resulting from the use of uniformity also often 
 take a complex and self-developing form. Such for instance are the 
 uses made of the straightness of a ray of light, or the advantages 
 arising from uniformity in weights and measures, or in language, or 
 from the correspondence of an organism to its environment. Some- 
 times these benefits are in part negative. Instances are the results 
 obtained from applications of the law of conservation of energy, or 
 from the principle that action and reaction are always equal. 
 
 Words Illustrating the Usefulness of Uniformities 
 
 We are aided in realizing the aggregate of efficiency values in 
 uniformities by noting those connected with certain special cate- 
 gories of uniformity as for instance with honesty, justice, constancy, 
 reliability, perseverance, durability, etc.; or by trying to grasp the 
 inefficiency that would characterize the world life if carried on 
 without the aid of these and similar categories. 
 
 Limitations to the Utilities in Uniformities 
 
 The use of uniformities however often brings certain drawbacks 
 or compensations. This fact may be realized by noting for instance 
 the evils connected with such words as monotony, fashion, custom, 
 panic, socialism. Ambiguities are an illustration of another class of 
 evils connected with the uniformity category. An important case of 
 the misuse of the principle of uniformity is what is termed hasty 
 generalization. This, in brief, consists of jumping to the con- 
 clusion that what is true in one or a few cases is true in all cases 
 of a given class. 
 
 The most important error of this kind is that of regarding some 
 special form of uniformity, such as reality or substance, or more 
 specifically matter, force, mind, or some other species of reality 
 uniformity taken as fundamental and inclusive, as the only route to 
 efficiency results. This view often leads to the further error of re- 
 garding uniformity in some form (as in that often termed truth) as 
 more fundamental and imp6rtant than the uses of uniformity. 
 Errors of this class will be treateed in more detail later. 
 
 Human Progress an Advance in Uniformities and Diversities 
 
 After what has been said as to the various efficiency values of 
 uniformity and diversity, it is not surprising to note that progress 
 
UNIFORMITY AND DIVERSITY 
 
 141 
 
 in each department of knowledge and action has been marked by a 
 progressive development of uniformities and diversities, both in 
 number and in degree of efficiency power. The child's mind begins 
 its unfolding process by the perception of differences and similari- 
 ties, and progresses by penetrating to and grasping diversities and 
 uniformities which are ever more comprehensive and vital. The 
 beginning of abstract and formal science is probably to be found in 
 the first perception by man of the difference between fixed stars and 
 planets, and all subsequent astronomical progress may be regarded 
 as a mere development of continuously better uniformities and di- 
 versities, leading to the generation of ever more efficient systems of 
 mutiplicative groups. A similar process has characterized progress 
 in every department of human life and thought, and hence progress 
 as a whole. 
 
 EFFICIENCY ANALYSIS OF UNIFORMITIES AND DIVERSITIES 
 
 In order to make the most efficient use of uniformities and 
 diversities it is important to analyze these concepts as closely as 
 possible, especially in terms of the other Efficients. 
 
 Relations to the Group Principle 
 
 With respect to the group principle, in general every diversity 
 means a new unit and hence often an order of units ; every uni- 
 formity means a new tie, or combination of units. Hence, from one 
 point of view, the diversity and uniformity aspects are the two 
 halves of the group concept. 
 
 Also it has already been remarked that uniformities and diversities 
 sometimes serve as crude, incipient groups, and at other times as 
 final highly finished groups. Hence from these various points of 
 view uniformity and diversity are to be regarded primarily as a 
 stage in the multiplicative system of things. 
 
 This method of regarding uniformities and diversities explains 
 why an animal, as a zebra, may be marked in a very peculiar way, 
 and yet be protected by its environment. For owing to our habit of 
 seeing things in groups, if the animal's markings fit, not its environ- 
 ment in all respects, but merely some one of the many group sys- 
 tems of which the environment is composed, we shall be likely to see 
 the animal as a part of this one system and not as distinct from its 
 surroundings. The multiplicative view of uniformity and diversity 
 
142 
 
 SOURCES OF EFFICIENCY 
 
 as contrasted with the vague, lumpish view often taken has many- 
 other advantages. 
 
 In uniformities and diversities the group principle involved is 
 built around with certain auxiliary categories, or efficiency handles, 
 which should at least be mentioned. 
 
 Relations to other Concepts and Efficients 
 
 As to the number idea, we find an implication at least of duality in 
 every uniformity; for a uniformity implies a comparison with 
 some other entity taken as a standard. Similarly a difference im- 
 plies at least two compared objects. This duality in a uniformity or 
 diversity has certain uses since, in effect, one of the two objects 
 constitutes an externality to the other. 
 
 Externalities of another nature are often implied in a uniformity 
 or diversity. Thus the evenness of the surface of a body of water is 
 the resultant or intersection of two opposite sets of forces, those 
 which draw objects together, and those which often cause objects to 
 repel each other. So the peculiar individuality of any object, as of 
 a piece of gold, is due to the convergence in the object of several 
 qualities or properties which are present in many other objects be- 
 sides gold, and hence in a measure are external to the gold. Simi- 
 larly any quality of an object may often be regarded as the focus of 
 several widely existent elements. 
 
 Uniformities and diversities imply or depend on certain limita- 
 tions. Thus objectively every uniformity is hedged in by certain 
 diversities, and correspondingly every diversity by uniformities. 
 Subjectively, the efficiency of uniformities and diversities is limited 
 by the degree in which we are cognizant of them. Hence in this and 
 other ways much relativity arises in their application. 
 
 Certain other relations between uniformities and diversities 
 should be mentioned. Thus with respect to order, as already stated, 
 diversity as a rule comes first psychologically, while uniformity is 
 first logically. With respect to the principle of orders of material, 
 diversity is more concrete (therefore individual and qualitative), 
 uniformity more abstract. With respect to force, diversity is more 
 active, and uniformity more passive. 
 
 Diversity relates primarily to quality, uniformity to quantity. 
 
 In relation to the idea of efficiency, diversity is directly essential 
 to this idea (since efficiency means surplusage) while uniformity is 
 an indirect route to it. 
 
UNIFORMITY AND DIVERSITY 143 
 
 Definitions 
 
 The terms in current use for various kinds of uniformity and 
 diversity are loose, overlap, and are often difficult of precise defini- 
 tion and coordination. However in the course of different discus- 
 sions it is frequently necessary to use some of these terms, and it is 
 therefore important to define them as accurately as possible with 
 reference to uniformity and diversity as sources of efficiency. 
 
 The following are among the most important terms of the uni- 
 formity class. 
 
 Uniformity means primarily oneness of form, amid various diver- 
 sities such as those of position, material, color. Hence it is pri- 
 marily a spatial uniformity. However its meaning is often refined 
 and extended so as to include almost every kind of oneness. Thus 
 we may speak of objects as uniform in color or in any other quality. 
 
 Equivalence means primarily sameness with respect to weight; 
 stated more generally it means, equally availing. Hence it is pri- 
 marily a dynamic term. As often used however it has outgrown its 
 original limited significance. 
 
 Continuity means literally a holding together (against opposing 
 forces). Hence it has spatial and negative dynamic aspects. It is a 
 relation without gaps, that is, an unbroken relation, and usually 
 contrary to certain appearances. It may also be one, two, or three 
 dimensional. 
 
 Similar efficiency descriptions might be given of other terms 
 belonging to this general class such as accuracy, analogy, adapta- 
 tion, conservation, consistency, constancy, consecutivity, certainty, 
 equality, evenness, homogeneity, immobility, identity, likeness, mo- 
 notony, monism, necessity, oneness, persistence, parallelism, parity, 
 reality, reliability, resemblance, similarity, stability, simultaneity, 
 sameness, truth, unity. 
 
 Of terms in the diversity class the following call for particular 
 mention. 
 
 Diversity means literally a bearing or turning apart. Hence the 
 term originally had a dynamic as well as a spatial aspect. But in 
 its present generalized form it may be used to express almost any 
 difference. 
 
 Change means diverse forms of the same object occurring in 
 succession. Hence it involves an element of time. Its meaning in 
 other respects is vague and general. 
 
144 
 
 SOURCES OF EFFICIENCY 
 
 Similar efficiency descriptions might be given of the other di- 
 versity terms in current use such as of alteration, conversion, devia- 
 tion, discontinuity, dissimilarity, flexibility, fluidity, freedom, 
 heterogeneity, instability, manyness, mobility, modification, muta- 
 tion, plasticity, relativity, sensitiveness, unevenness, unlikeness, 
 variation, variety. 
 
 METHODS OF APPLICATION 
 
 Group View an Aid 
 
 The view of uniformity as not mere vague lumpish likeness and 
 of diversity as not accidental or capricious difference, but of both 
 as essentially groupish in nature, and when taken together, as form- 
 ing certain useful stages in the multiplicative system of things, is an 
 important aid in using these instruments in the most efficient way. 
 
 Great Number of Forms 
 
 Thus the multiplicative view is an aid in realizing the vast num- 
 ber of diversities and uniformities which exist or may be generated. 
 For example in order to form some idea of the different kinds of 
 apples which are possible we may consider the following product : 
 
 (no. possible sizes) X (no. shapes) X (no. colors) X 
 (no. flavors) X (no. durations). 
 
 It is also well to remember that some of the above factors are also 
 multiplicative group systems. Such a method of treating diversi- 
 ties enables the farmer for instance to forecast the great variety 
 of ways in which a horse or fertilizer may be defective, or a teacher 
 to grasp the immense diversity in young minds, and of methods 
 and devices which may be employed to meet special needs. 
 
 Illustrations of Extreme Cases 
 
 In reinforcement of the above conception it is important to bear 
 in mind certain facts or principles like the following: The divisi- 
 bility of matter is practically without limit, for the molecules in a 
 cubic centimeter of gas if placed in line would go many times round 
 the world and would take 265 billions of years to count and yet a 
 molecule is composed of many ions. Also different kinds of matter 
 interfuse so that it is said that "a perfectly pure chemical element is 
 the dream of the ignoramus". Also relations of kinds of matter are 
 
UNIFORMITY AND DIVERSITY 
 
 145 
 
 in a constant state of change since motion is the normal law of the 
 universe. Even the force of gravitation on the surface of the 
 earth is constantly changing as the earth shifts its position with 
 reference to the sun and moon. The number of diversities man can 
 create or conceive of in like manner is without limit since for in- 
 stance the grey matter of the human brain contains 5,000,000,000 
 cells each of which apparently may be a center or modifier of idea- 
 tion in many ways. A cubic millimeter of blood contains 5,000,000 
 red corpuscles, or the blood in a human body on the average con- 
 tains 22,500,000,000,000 of them, and with changes in these, the 
 bodily health and mental processes vary. 
 
 With respect to uniformity no one as yet has been able to discover 
 a variation in the atomic weight of any chemical element. In color 
 photography of a certain kind, two successive laminae in a gelatine 
 plate are separated by a distance of only one one hundredth mil- 
 lionth of an inch, yet those laminae retain their exact position dur- 
 ing the process of applying chemical solutions to fix them. We also 
 have the general principle of continuity, often embodied in the 
 statement that nature never proceeds per saltum. 
 
 The principle of multiplying relations also enables us to realize 
 the extraordinary power in a small diversity. Thus a difference of 
 one-tenth of one per cent in the amount of carbon in steel may 
 render worthless an otherwise good piece of metal. 
 
 The Multiplicative Principle an Aid in Other Ways 
 
 The multiplicative principle also aids us in utilizing crude and 
 imperfect uniformities and diversities when better forms are not 
 available. For, as has been pointed out in other connections, the 
 multiplicative principle in a measure is both self corrective and has 
 the power to develop the imperfect into something better. An 
 illustration is the use in combination of our crude theory of atoms 
 (or diversity) and the ether (or unity) and the vast number of, 
 useful results thus obtained. A still broader case is the employment 
 together of monistic and pluralistic theories as toolage aspects of 
 the universe. 
 
 Externality an Aid to Greater Results 
 
 Externality is often a powerful aid in discovering a uniformity 
 or diversity in a difficult situation. For within a large area of facts, 
 
146 SOURCES OF EFFICIENCY 
 
 one is more likely to find a spot or spots where some important 
 diversity or uniformity is unmasked and exposed to view than in a 
 narrow area. So subjectively the externalities afforded by a broad 
 education or by wide travel are fitted to break up the permanences 
 of habit and tradition. 
 
 To look at the matter in more detail, the externality of time has 
 enabled men to discover the change in position of many so-called 
 fixed stars, and to learn that mountains rise and fall, and that some 
 rivers are more stable than mountains. So the externality of travel 
 and study enabled Darwin and Wallace to establish the fact of the 
 variation of species and to assign an adequate reason for the same. 
 By the aid of the gelatine culture plate Koch was able to isolate 
 different species of bacteria. Externality in the form of a fly wheel 
 may give uniformity and continuity to the motion of an otherwise 
 unstable machine. 
 
 A more abstract form of externality in this connection is that 
 whereby we get a diversity by the use of another intermediate di- 
 versity as when we form a conception of a new kind of space by 
 analyzing the ordinary space concept into its essential elements and 
 varying or changing one or more of these elements. 
 
 Treatment of Difficult Cases 
 
 In forming or discovering diversities in difficult cases it is often a 
 help to try to obtain a diversity .with respect to certain important 
 categories taken in succession. Thus in such cases attempts may be 
 made successively to form, for instance, diversity as to space, quan- 
 tity, number, or time; or a diversity of velocity, force, order, color, 
 mentality, or any other quality or category. A similar remark 
 applies to uniformities. 
 
 It may also be well to remark at this point that the discovery of 
 diversities usually precedes that of uniformities. 
 
 In this connection something should also be said as to the impor- 
 tance of determining whether to give a uniformity or a diversity the 
 leadership in a given situation, which species of each to use, and 
 how best to combine them. For instance it is sometimes necessary 
 to decide whether it is best to put all of one's eggs in one basket (as 
 in making investments) ; or to determine whether, in a given case, to 
 live each day by itself, or to treat life as a whole. Externality, 
 especially the externality of consequences, is useful in such cases. 
 
UNIFORMITY AND DIVERSITY 147 
 
 Other Efficients as Aids 
 
 The various categories of efficiency which have been investigated 
 in the preceding chapters, as well as those which are to be studied 
 in the chapters which follow, may also be used to advantage in con- 
 nection with uniformities and diversities. Thus it is well to remem- 
 ber that it is advantageous to master and reuse certain important 
 types of uniformity and diversity, and also that every case 
 of reuse produces a uniformity along its path. Again by the appli- 
 cation of predictive reuse we realize that certain uniformities and 
 diversities are in a sense omnipresent. Thus we may argue that, 
 in order to survive, every organism must reach a certain level of 
 efficiency. Hence we may anticipate that every existing organism 
 possesses its own characteristic instruments for obtaining results ; 
 that this instrumentalism differs widely in its forms but approxi- 
 mates a certain uniformity of power. 
 
 The method of multiplicative groups is also an aid in grasping 
 (or inventing) a large variety of uniformities or diversities and in 
 selecting that particular one in the array which is best fitted for a 
 given purpose. It also leads to the use of uniformities and diversi- 
 ties in other and more aggressive ways. Negatively it prevents the 
 ignoring and dread of using the profusion of uniformities and di- 
 versities which exist. 
 
 It is also important to apply the principle of orders of material 
 to uniformities and diversities as an aid in discriminating between 
 higher and lower forms. Thus the caste system of India is charac- 
 terized by a uniformity and diversity both of which are of a low 
 order. For the uniformity involved is so concrete and fixed that it 
 interferes with useful change, while the diversity is of such a nature 
 that it prevents uniformity of reward for efficient action. Another 
 illustration of somewhat different kind is the contrast between the 
 kind of diversities which are utilized when a drug is dissolved and 
 absorbed through the stomach and general fluids of the body, and 
 the diversities which are involved when the drug is first ionized 
 outside of the body and then driven by an electric current into that 
 particular part of the organism where it is needed. The former 
 method because of the many unnecessary disturbances which it 
 produces (that is, its lack of uniformity) must be regarded as of a 
 distinctly lower order of efficiency than the latter. 
 
 In connection with the limitations which hem in the useful func- 
 tions of uniformity and diversity (see pp. 138, 140) it is well to 
 
148 SOURCES OF EFFICIENCY 
 
 remember that in many domains a certain average or normal degree 
 of uniformity and diversity are desirable. Thus in certain rela- 
 tions the peculiarities or bizarre features of the English system of 
 weights and measures make it more highly educative than the more 
 uniform metric system. A similar remark applies to the English 
 language as compared with an artificial language such as Ido or 
 Esperanto. 
 
 Ideal Species 
 
 Finally, it is well to realize and work toward the ideal system of 
 uniformities and diversities. For our purpose this consists of uni- 
 formities and diversities in one or more of the Efficients, applied in 
 efficiental ways, for efficiental ends. 
 
 It is also well to have constantly in mind the best form of uni- 
 formities and diversities which is directly applicable to affairs in 
 general. This consists of uniformities and diversities combined as 
 a multiplicative group system and in such a way that each uniformity 
 will interfere with the diversities to the least possible extent, and 
 vice versa. Contrasted with absolutism at one extreme and laissez- 
 faire individualism at the other, the form just described constitutes 
 a federal system characterized by the utmost freedom and the utmost 
 law and order. Practical success of a high order in any calling con- 
 sists primarily in realizing the enormous number of diversities in- 
 volved, the great number of uniformities or ways in which groups 
 may be formed, and in uniting and utilizing these diversities and 
 uniformities by means of multiplicative group systems of a higher 
 order. 
 
 Summation of the Chapter 
 
 A condensed statement of the principles discussed in this chapter 
 will now be of service. The perception and use of uniformities and 
 diversities form a source of efficiency which is often of fundamental 
 importance. Owing to their general and comprehensive nature, the 
 principles under discussion exist in a multitude of forms, though, 
 much study is often necessary to uncover certain of these. The 
 simple and complex forms which they assume are alike numerous. 
 
 Uniformities and diversities in some cases, in essence constitute 
 crude, incipient groups ; in other cases they are a highly finished 
 final form of the group. Consequently in all cases they have the 
 
UNIFORMITY AND DIVERSITY 149 
 
 efficiency properties of groups in special forms. They are especially 
 useful as first steps in developing more elaborate efficiency organi- 
 zations or processes. Often, apart from any consideration of the 
 group idea, uniformities and diversities lead directly to reuse and 
 other forms of efficiency and even to transcendent results. Numer- 
 ous more or less familiar words like analysis and mobility illustrate 
 the uses of diversity; and similarly words like justice and reliability 
 suggest the values in uniformity. The progress of the individual 
 and that of the human race alike, are marked by the perception and 
 use of more and more vital and comprehensive uniformities and 
 diversities. 
 
 The general multiplicative principle is an aid in realizing both the 
 vast number of kinds of uniformities and diversities and the ex- 
 treme forms which these may take. The self-developing and self- 
 corrective powers inherent in the multiplicative principle also con- 
 stitute an aid in using crude forms of uniformities and diversities. 
 It is important to be able to realize the highest types of resem- 
 blances and differences, and to use these with the utmost effective- 
 ness. Especially important is it to realize that the highest species 
 of all is the combination of those uniformities and diversities which 
 are individually most efficient, which aid each other the most, and 
 interfere with each other the least. 
 
 EXERCISE 8 
 
 1. Give an example of each of the principal species of diversity. 
 
 2. Also of each of the principal species of uniformity. 
 
 3. State some of the advantages in having two engines in a factory 
 instead of a single larger engine. 
 
 4. Give a similar instance where duality is the source of efficiency. 
 
 5. State some of the advantages in being able to separate water into 
 small particles of vapor. 
 
 6. State the uniformities and diversities which enter into the structure of 
 a Zeppelin airship. 
 
 7. State some of the advantages which follow from the fact that the action 
 of one force, as gravitation, is independent of that of another, as light 
 or heat. 
 
 8. In some factories the accounts for the year are kept in terms of 
 thirteen periods of four weeks each (instead of the twelve calendar 
 months). State the advantages in this. 
 
 9. Ascertain some of the peculiarities of different kinds of Jena glass, 
 and the corresponding efficiency properties. 
 
150 SOURCES OF EFFICIENCY 
 
 10. Define each of the following terms with reference to the principle of 
 diversity, and give an example of the efficiency value of each : flexibility, 
 plasticity, mobility, adjustability. 
 
 ii. In a very dry summer at the Kansas Experiment Station, on ground 
 prepared merely by disking, only 4 bushels of wheat per acre were produced. 
 On ground deeply plowed and thoroughly pulverized, the yield was 38 
 bushels per acre. If the cost of cultivation per acre in the two cases was 
 $.75 and $4 respectively, and the wheat produced was worth 90c per bushel, 
 what would have been the gain from the more thorough pulverization of 
 1000 acres? 
 
 12. Give in detail some of the advantages in thorough pulverization of 
 the soil in raising crops. 
 
 13. Describe the block system of managing a railroad, and state some of 
 its advantages. What elements of uniformity and diversity are here 
 involved? 
 
 14. What are the advantages to a large railroad company in having all 
 the stationery used in its offices reduced to a few standard types? 
 
 15. State some of the advantages in knowing that the different forms of 
 energy in action on the earth's surface are, with slight exceptions, trans- 
 formed sun force. 
 
 16. Give some of the advantages of regarding a given form of work, 
 as that of laying brick, as a succession of parts or motions. 
 
 17. In what ways does the use of machines give uniformity and accuracy? 
 Show that this uniformity is sometimes excessive. 
 
 Give an example where a diversity leads to 
 
 18. Marginal reuse 22. Another diversity 
 
 19. Prophetic reuse 23. A uniformity 
 
 20. Formation of a group 24. A useful directive act 
 
 21. Of a multiplicative group system 25. A transcendent result 
 
 26. Complex self-developing results 
 
 27. Give examples where uniformities produce the results indicated in 
 Exs. 18-26. 
 
 28. Give an example where a diversity is obtained by the use of externality. 
 
 29. Where a uniformity is obtained by externality. 
 
 30. State the advantages in preparing lumber in pieces of small thickness 
 and nailing these together when heavier pieces are needed. Also state the 
 disadvantages. 
 
 31. State some of the different ways in which the lights of light houses 
 differ, and also state the resulting advantages. Why are light ships or 
 buoys sometimes used instead of light houses? 
 
 32. By what means is the effect of solid space produced by a flat picture? 
 
 33. In terms of the Efficients studied thus far, state the efficiency advan- 
 tages of honesty. 
 
 34. Give an example where an excessive amount of diversity results in 
 loss. 
 
 35. Another where diversity misused in some other way results in loss. 
 
 36. Where an excessive amount of uniformity results in loss. 
 
UNIFORMITY AND DIVERSITY 151 
 
 37. Where uniformity misused in some other way results in loss. 
 
 38. State some of the disadvantages which result from the fact that the 
 gold dollar fluctuates in value. Suggest some means by which this evil 
 might be diminished, if not altogether remedied. 
 
 39. How are the values of the uniformity and diversity principles illus- 
 trated by the use of the wheel? 
 
 40. What uniformity and diversity principles are illustrated in a cream 
 separator? 
 
 41. Why is it that a snake can swallow an object larger than its own 
 head (thus a boa constrictor can swallow a calf) ? 
 
 42. If each State in the United States should have a different system of 
 weights and measures point out some of the disadvantages which would 
 result. 
 
 43. How does the principle of diversity help give sea power the superiority 
 over land power? 
 
 44. Explain standard time with reference to uniformity and diversity 
 principles. 
 
 45. Arthur Young says "the magic of property turns sand into gold'*. 
 State the source of efficiency which is involved in this case. 
 
 46. Give an example where two diversities are combined to form a 
 uniformity. 
 
 47. Also where two diversities when combined make a greater diversity. 
 
 48. Discuss the value of accuracy in terms of the other Efficients. 
 
 49. State some of the advantages of isolating oneself or one's employees 
 from distractions when at work. Give also instances where such isolation 
 results in loss. 
 
 50. Give an example showing the value of knowing that action and re- 
 action are always equal. 
 
 51. What is meant by uniformity of the laws of nature? Illustrate. Also 
 give three illustrations of the efficiencies which result from the utilization 
 of this uniformity. 
 
 52. Illustrate the advantages which result from the fact that the atomic 
 weights of the chemical elements do not vary. 
 
 53. State the successive kinds of freedom which have been obtained by 
 the people of the United States, and the new groupings and other advantages 
 which have resulted from each. 
 
CHAPTER IX 
 
 EXPENDITURES AND RESULTS 
 
 General Statement 
 
 In Chapters II to VIII primary attention has been paid to 
 methods by which to attain increased efficiency; that is, to the rela- 
 tions or apparatus which intervene between an expenditure and 
 the result obtained, rather than to the expenditure and result them- 
 selves. It will be an advantage also to give some primary consider- 
 ation to the data and results. For instance, it is often an aid to 
 efficiency to make it a rule to. strive after those results which are 
 most inclusive and multiplicative in value while at the same time 
 making the data employed as inexpensive as possible; in other 
 words, to realize that the efficiency of a process is in proportion to 
 the gap between the expenditure and the result. A comprehensive 
 review of the various aims and ends of processes will be useful as 
 a means of forming even an approximate scale of values in any 
 situation. Since the result of one process may be data of another 
 process, the study of possible expenditures and results should also 
 facilitate the linking of such processes together so as to form more 
 or less comprehensive systems for obtaining desired ends. If even 
 a rude common essence of value's could be obtained, other equally 
 or even more important advantages would follow. Accordingly the 
 expenditures and results of efficiency processes will be the main 
 object of investigation in the present chapter. Primary attention 
 will be given to results aimed at, expenditures being considered 
 largely by implication. 
 
 CLASSIFICATION 
 Results Grouped according to Materials 
 
 We shall first classify the aims and results of efficiency pro- 
 cesses according to the materials of which they are constituted. 
 Proceeding thus we obtain the following groups of aims : 
 
 Physical objects or forces, including, for instance, land, buildings, 
 mines, tools, machinery, light, heat, mechanical power, speed, and 
 all other species of so-called material inorganic wealth. 
 
 152 
 
EXPENDITURES AND RESULTS 153 
 
 Biological results, as plants and animals and their useful products, 
 as food, warmth, shelter, life, offspring. 
 
 Personal or psychological results, as pleasure, power, health, 
 leisure, knowledge, education, comfort, welfare, well-being. 
 
 Social results, as position, fame, friendship, love, service; social 
 means to these ends, as social and political organization; and com- 
 plexes of these results, such for instance as are included under a 
 term like civilization. 
 
 Ethical and religious results, as character, the approval of one's 
 conscience, and religious conversion. 
 
 Abstract formal results, as space, time, freedom, reuse, groups, 
 and the various categories and Efficients both as means to ends, and 
 also, from certain points of view, as ends in themselves. In the 
 past the uniformity or equivalence aims which come under this 
 head, such as peace, truth, and reality, have been unduly empha- 
 sized as ultimate ends, though perhaps they cannot be too greatly 
 emphasized as means to ends. 
 
 Evidently one of the above results (especially some item in one 
 of the later classes) often includes or quickly brings others. Thus 
 good government often means wealth, health, education, and happi- 
 ness to many citizens. 
 
 Results Grouped according to Forms 
 
 The results of efficiency processes may also be classified with 
 reference to their form. 
 
 Thus with respect to size results aimed at may be large or small ; 
 one, two, three, or ^-dimensional. With reference to other spatial 
 categories, they may be local or omnipresent ; may have various 
 shapes ; may occupy different positions, as when they are internal 
 or external to data. With reference to number, they may be single 
 or manifold. 
 
 In this connection it is especially important to observe that they 
 may be direct or indirect. Thus adaptation to one's environment is 
 not so much an end in itself as a means to an end. From our 
 point of view, as has already been remarked, equivalence results (as 
 truth, reality, accuracy, justice) are not ultimate, but proximate 
 and intermediate. A mere means to a result often becomes of such 
 importance that it comes to be regarded as itself a more or less 
 ultimate end of action. This being the case, from certain points 
 
154 SOURCES OF EFFICIENCY 
 
 of view it is often useful to sum up the equivalence and more 
 ultimate ends of action in couplets like the following: light and 
 sweetness, truth and love, science and sentiment, the universe as 
 mechanism and the universe as idea, certitude and utility, realism 
 and idealism. 
 
 With reference to time results may be temporary or permanent, 
 and may come quickly or slowly. Similarly they may be reciprocal 
 (with the data) ; positive or negative; simple or complex. Instances 
 of complex results are all the beneficial changes included in a case 
 of wholesome growth, as for instance the change from the acorn 
 to the oak, or the results of civilization. 
 
 The beneficial results of an efficiency process may occur in a 
 grouped or multiplicatively grouped form. An illustration of 
 grouped results is knowledge as including health, wealth, fame, 
 service, and happiness. Often in this connection relativity is pres- 
 ent. Thus each item in the list of the results just mentioned may 
 lead to or include the others. Thus health often leads to knowl- 
 edge, wealth, happiness, etc. In this manner groups are obtained, 
 which may be regarded as sub-groups in a larger system. 
 
 By-products 
 
 A somewhat important method of classifying results in this con- 
 nection is that which makes a distinction between direct results and 
 by-products. Thus cattle are slaughtered primarily for the meat 
 which they supply as food. But when the process is rightly con- 
 ducted a host of by-products is also obtained such as hides, oils, 
 oleomargarine, stearine, tallow, soap, fertilizers, medical extracts,, 
 dye stuffs, buttons, glue, bone, charcoal, some hundreds in all. 
 The externality of carrying on work on a large scale often makes 
 by-products particularly important. In highly competitive work, 
 the by-products may become the chief source of profit. Much 
 relativity frequently comes into play in determining what is a main 
 and what a by-product. The side results are often abstract and 
 scarcely observed, but at the same time of prime importance. Such 
 for instance are experience gained, particularly knowledge and 
 power concerning efficiency processes. 
 
EXPENDITURES AND RESULTS 155 
 
 Scales of Results 
 
 As a continuation of this line of thought it follows that the dis- 
 tinction between results as of higher or lower order is of the first 
 importance. A graded series of results may be obtained with refer- 
 ence to various categories. Thus with reference to the perpetuation 
 of the race, the aims and ends of processes in the order of their 
 importance are self-preservation (including food, shelter, life) ; 
 self -propagation (offspring) ; happiness; self-sacrifice. 
 
 The matter of arranging all results in a general and inclusive 
 multiplicative scale will be considered in connection with the analysis 
 of surplusages as a whole and their comprehensive marginal multi- 
 plicative grouping. 
 
 Before taking up this topic, it will be of advantage briefly to 
 analyze certain terms which are often used to express the results of 
 processes. One of the most important of these terms is the word 
 value. 
 
 Value and Worth 
 
 The term value as currently used has two widely different mean- 
 ings, which are often confused, viz. : ( 1 ) an equivalence meaning 
 and (2) a surplusage meaning. Thus in the phrase "the value of a 
 gallon of oil" the first or equivalence meaning of the word value is 
 the amount of money that may be obtained by selling the oil (i.e., 
 money value) ; or the amount of heat generated by burning the oil 
 (i.e., fuel value) ; or the amount of coal which when burned will 
 produce the same amount of heat as the oil (i.e., coal value). 
 
 The second or surplusage meaning of the words is the superior- 
 ity of oil with respect to another kind of fuel (which is equivalent in 
 heat value), as the superiority of the oil in concentration, lightness, 
 rapidity of combustion, and power to give a war vessel a large radius 
 of action and consequent capacity to win naval battles. In like 
 manner it may have meanings of these two kinds in other ways 
 and in comparison with other substances, for instance as a kind of 
 lubricant or an insecticide, or as a source of coal tar and its pro- 
 ducts, or as a means of calming stormy waters at sea. 
 
 In this book the term value is used as far as possible in the 
 second or surplusage sense. 
 
 The term worth has two similarly contrasted meanings. These 
 
156 SOURCES OF EFFICIENCY 
 
 are illustrated in the sentences, "This house is worth $2000", and 
 "Mr. X. is a man of great worth". 
 
 ANALYSIS AND MULTIPLICATIVE GROUPING OF THE AIMS 
 OF EFFICIENCY 
 
 If we attempt to tabulate the aims and ends of efficiency pro- 
 cesses in a comprehensive, hierarchical, and completely filial form 
 by the customary method of progressively including sub-aims in 
 larger and larger aims, we are hindered by the complexity and cross 
 relation of many of the value concepts involved and by their quali- 
 tative incommensurability. However, we may make what is, in 
 some respects, an even more useful systematization of the aims and 
 ends of efficiency processes by analyzing efficiency aims into a scale 
 of constituent elements and, by use of these elements, building 
 up values or aims into a marginal multiplicative group system, gen- 
 eral and undeveloped in some respects, but serviceable in many 
 more or less fundamental ways. 
 
 Four Elements in Valuable Results 
 
 The first and most fundamental constituent in the result aimed 
 at in any efficiency process is that of non-equivalence with respect 
 to the datum or expenditure, or a certain disproportion between 
 means and ends. This non-equivalence may be positive or negative, 
 that is, may represent gain or loss. It may be quantitative or quali- 
 tative. When it is quantitative it may be named a surplusage. 
 When it is qualitative (as when physical exercise produces good 
 health) it is useful to realize it as a fact, to regard certain cases of 
 it as units or elements', and to reuse, group, and extend them 
 systematically. 
 
 The second constituent in the results with which we are particu- 
 larly concerned is a certain positive or plus quality. It often re- 
 quires much externality to determine this, yet it is an important 
 source of efficiency to recognize it as a distinctive element in results 
 sought after, and to regard it in its most fundamental forms as 
 primarily impersonal or subpersonal. Thus groups as such and 
 as a whole have values and uses which are practically universal and 
 only occasionally in the systematic scheme of things take personal 
 form. 
 
EXPENDITURES AND RESULTS 157 
 
 The third principal constituent in efficiency results is that supplied 
 by the element of personality in its various forms. It is this which, 
 when annexed to positive non-equivalence, causes it to become 
 happiness or well-being. 
 
 The fourth class of constituents are those more or less concrete 
 elements which when annexed cause positive non-equivalence to 
 take such special forms as food, or offspring, wealth, or fame; or 
 which cause personal positive non-equivalence to take the form of 
 special sensations of pleasure as that of warmth, or some form of 
 pleasure which is related to any special organ of the body or faculty 
 of the mind. 
 
 It is not necessary that all of these four classes of constituents 
 be present in a given result. Thus if a process produces a new 
 and better system (or groupage) only the first two constituents 
 are present in the result obtained. In a sensing of beauty or sub- 
 limity only the first three are present. 
 
 This analysis at least makes possible an approximate multiplica- 
 tive group system of values in any given situation and opens the 
 way to many directive and other efficiency processes in the treat- 
 ment of such values. 
 
 Illustrations of the Four Elements 
 
 Specific illustrations will aid in making clear the meaning and 
 general uses of the above analysis and the multiplicative group 
 synthesis thus made possible. A careful examination of the acts 
 of a boy, for instance, shows that the dominant source of pleasure 
 in a boy's nature is fundamentally that of generating or obtaining 
 a surplus as such, any immediate concrete gain to himself being 
 a secondary matter. Many of his acts of mischief are performed 
 not because he delights in destructive deeds as such, but because 
 he finds his greatest pleasure in a mere disproportion between 
 means employed and the results which follow. Hence by sufficiently 
 tactful treatment he may, if he is normal in body and mind, almost 
 always be led to conduct which will give this same sort of pleasure, 
 but will also be profitable in other ways to all concerned. For a 
 like reason a child is often more interested in working out and 
 operating a puzzle which has no concrete use than by making 
 money by raising crops in a garden. In like manner the able busi- 
 
158 SOURCES OF EFFICIENCY 
 
 ness man frequently finds more pleasure in business as a game, 
 that is as a mere means of obtaining marvellous results, than in the 
 yacht or paintings which financial profits enable him to buy and 
 enjoy. So, also, many persons read the newspapers primarily for 
 the new sensations which they thus experience, that is the new 
 pleasure which they obtain from the perception of new and strange 
 diversities, externalities, and groupages, rather than from the direct 
 concrete utility of the new facts which are assimilated. The dom- 
 inant surplusage principle in both of these cases is sound as far as it 
 goes but it needs careful safeguarding and directive treatment in 
 connection with the other constituents of efficiency results. 
 
 A somewhat higher case is that in which a more fundamental 
 pleasure is found in harmony, beauty, and sublimity, or in living a 
 highly moral and broadly sympathetic life (that is, in highly de- 
 veloped forms of groupage and externality) than in food or money, 
 which indeed are often mere detailed consequences of the primal 
 efficiency principles involved in the former cases. 
 
 Advantages in the Use of the Four Elements 
 
 The efficiency advantages which flow from the preceding analysis 
 and systematization of values, call for some more formal and ex- 
 tended statement. 
 
 In the first place it is to be noted that the first and more funda- 
 mental and therefore comprehensive constituents in values (viz. : 
 positive non-equivalence or groupage) are practically omnipresent 
 and in a vast number of cases may be had at little or no cost; also 
 that by obtaining them thus the more specific forms, those which 
 are usually expensive when sought for individually, may be obtained 
 at slight cost by the use of the marginal reuse. Thus every occupa- 
 tion, however humble in its conventional rating, as cooking or- 
 boot-blacking even, is saturated in many ways with the various 
 Efficients which may become sources of the highest pleasure when 
 properly understood. For all persons also the sight of a sunset 
 costs nothing, and when to this is annexed some knowledge of the 
 principles of esthetics and art gained from books or art galleries at 
 small cost, highly specialized forms of pleasure and value are 
 obtained at slight expense. By pursuing methods like these the way 
 is also often opened for the attainments of results more or less in 
 groups instead of singly. 
 
EXPENDITURES AND RESULTS 159 
 
 It follows also that the prime source and method of social ef- 
 ficiency is to generate or create positive non-equivalence constantly 
 and in all possible ways quite regardless of all personal considera- 
 tions, or at least putting all such considerations in a secondary place. 
 New light is thus thrown for instance on ethical principles. For 
 the method of life thus indicated includes as a detail the doing of 
 good to those who have annoyed us. At one stroke it eliminates 
 revenge, selfishness, heartless fun, pessimism, and substitutes some- 
 thing better. It puts constructive work and plusness in all forms 
 in the foreground actively and constantly. Personal considerations 
 are set apart but are always within hailing distance. It makes it 
 possible for each individual to enjoy the primal essence of all 
 things not only without interference with others but rather by pri- 
 marily aiding others. It follows, of course, that this view makes 
 .one expectant of and ready to utilize all new forms and kinds of 
 useful results. 
 
 Other Advantages 
 
 One or two matters of detail should also be mentioned in this 
 connection. If positive non-equivalence is the primal essence of 
 values it follows that a method, at least approximate, is thus sup- 
 plied of ranking and ordering the various means of obtaining 
 results in a given field and hence of accelerating and otherwise 
 improving the attainment of these results. Thus in educational work 
 •those studies, as a rule will be most valuable which give the greatest 
 surplusage and groupage, or the greatest groupage powers. The 
 same remark will apply to other callings or departments of life 
 and work. 
 
 A still more general result is that the above treatment of values 
 gives a comprehensive, sound, and vital scheme of efficiency, all 
 parts of which reinforce each other. 
 
 Drawbacks and Their Remedy 
 
 At the same time mention should be made of the fact that the 
 above method of viewing and treating the results aimed at in ef- 
 ficiency processes has certain drawbacks. One of these is a fre- 
 quent coldness and lack of force due to the absence of personality. 
 Another is the fact that putting non-equivalence (instead of some 
 
160 SOURCES OF EFFICIENCY 
 
 form of uniformity) in the first place may open the way under 
 some cases to incoherence and lack of system as when each person 
 in a community tries to form his own system of values. However, 
 a closer view of the matter will show that these defects are largely 
 superficial. For the outgoing power inherent in the multiplicative 
 principle will be in the end remedy the first of these defects and the 
 corrective power which is also inherent in the multiplicative princi- 
 ple will check and remedy the second. 
 
 Advantages Illustrated by Human Progress 
 
 As a general illustration of the advantages to be gained in effi- 
 ciency processes by making subpersonal positive non-equivalence 
 the primary and most fundamental element in the results sought, 
 it may be well to point out that during the last five hundred years 
 human progress in general has largely been determined by the 
 progress of science, and that the most important factor in the 
 increase of scientific knowledge has been that of making the sub- 
 personal point of view fundamental. Thus modern chemistry 
 arose after the spirits of the medieval alchemist had been discarded. 
 The astrologist regarded the planets as animated and personal. 
 Even Kepler viewed the earth as analogous to a huge animal, and 
 Newton was able to establish the law of gravitation only by disen- 
 tangling the problem from all immediate considerations of personal- 
 ity. On the other hand science perhaps has erred at times by trying 
 to eliminate the category of personality altogether, instead of 
 putting it, at least for the time being, in a secondary place. That 
 is, it has reacted too far from the medieval point of view. Appar- 
 ently also it has erred frequently by exalting mere equivalence 
 (or "truth") above the fruitful results of equivalence, that is above 
 positive non-equivalence and the various special forms which this 
 assumes. Hence the results obtained by the scientific method in the 
 past would seem to be but an imperfect glimpse of those obtainable 
 by a broader and more exact view of efficiency. 
 
 Relation to Chapter I 
 
 Before concluding the present chapter it will be well to consider 
 briefly its relation to Chapter I. In Chapter I the main discussion 
 related to quantitative homogeneous efficiency. Cases of hetero- 
 
EXPENDITURES AND RESULTS l6l 
 
 geneous or qualitative efficiency were treated only by the ratio or 
 comparative method. In the present chapter the intention has been 
 to treat qualitative efficiency by a more direct method, viz. : by a 
 comprehensive view of such cases, an analysis of them into a pro- 
 gressive series of elements, and the synthesis of them into a more 
 or less complete multiplicative group system. This method includes 
 the methods of Chapter I as special details and hence gives a more 
 comprehensive and aggressive view of the whole matter under 
 consideration. 
 
 Summary and Outlook 
 
 The substance of the present chapter may now be briefly stated. 
 The study of the aims and ends of efficiency processes is important 
 both in itself, and also as a means of improving these processes. 
 Aims and ends may be classified as to the materials composing 
 them (viz., as mineral, psychological, social, etc.) ; and also ac- 
 cording to their form. An important distinction in the latter respect 
 is that between the main result and a by-product. 
 
 Aims and ends of all kinds are analyzable into four principal 
 elements, viz.: (i) non-equivalence (between datum and result); 
 (2) a positive quality; (3) the element of personal application; (4) 
 all other constituents. By means of this analysis we find that, with 
 respect to efficiency processes, the most important and omnipresent 
 constituent is positive non-equivalence. The subpersonal nature of 
 this aim enables us to strive to create and utilize values in an un- 
 limited variety of ways and with great freedom. In particular it 
 prevents much waste, opens the way to the utilization of many com- 
 paratively costless sources of pleasure, and to an ordering of and 
 grouping of values in cases where such a process would otherwise 
 be difficult or even impossible. It also gives that breadth of view 
 without which the highest and most continuous efficiency processes 
 are impossible. Hence it is not surprising, that, as the world has ad- 
 vanced this view of the aims and ends of conduct has become more 
 and more prominent. 
 
 In the present chapter and those which precede it we have dis- 
 cussed the meaning of the term efficiency the principal general 
 methods by which efficiency may be obtained or increased, and the 
 ends and aims of efficiency. In the chapters which immediately 
 
162 SOURCES OF EFFICIENCY 
 
 follow we shall investigate certain more special methods of obtaining 
 results than those considered in the preceding chapters. The first 
 of these more individual efficiency agencies relates to man's cognitive 
 faculty. Others that follow are related more particularly to his 
 powers of volition or action. 
 
 EXERCISE 9 
 
 Give an example of each of the following classes of the fruits of ef- 
 ficiency processes : 
 
 i. Inorganic material 6. Imaginative n. Spatial 
 
 2. Dynamic 7. Moral 12. Reciprocal 
 
 3. Biological 8. Religious 13. Negative 
 
 4. Emotional 9. Social 14. Indirect 
 
 5. Intellectual 10. Temporal 15. Grouped 
 
 16. Multipiicatively grouped 
 
 17. Give a set of results which form an order of materials series as to 
 their relative importance. 
 
 18. State the different beneficial results (including efficiental ones) involved 
 in shelter. 
 
 19. In wealth 20. Knowledge 21. Power 22. Health 
 
 23. Give a case where a means to an end has become, in effect, an end 
 in itself. 
 
 24. Give a by-product in the manufacture of butter. Of pig iron. 
 
 25. Give a set of desirable results each of which, in some respects, includes 
 the others. 
 
 26. Name some of the by-products -which accompany the manufacture of 
 kerosene for illuminating purposes. 
 
 27. Name the by-products of some other process with which you are 
 familiar. 
 
 28. Give an instance where a by-product has become more important than 
 the original principal product. 
 
 29. Give an instance of the conversion of a source of loss into a source 
 of gain. 
 
 30. Explain the different possible meanings of the word value in the 
 phrase, "value of a bushel of wheat". 
 
 31. Give an example of the use of the word "worth" both in an equiva- 
 lence and in a surplusage sense. 
 
 32. Why is it that a man who receives, at the end of a year, 5 per cent 
 in addition to his principal, is often regarded as receiving an equivalent for 
 his investment; a man who receives 8 per cent., as making an efficient use 
 of his money; and a man who tries to obtain 300 per cent (as by investing 
 his money in mining stocks), as attempting to obtain something for nothing. 
 
 33. Discuss the various ways in which pleasure in one's work is a source 
 of efficiency and give illustrations. 
 
EXPENDITURES AND RESULTS 163 
 
 34. State the various kinds of pleasure which a carpenter may experience 
 when building a house. Also state in some detail the efficiency results of 
 such pleasures. 
 
 35. Make a similar statement concerning a teacher and his or her work. 
 
 36. Discuss some of the various devices which an employer may use in 
 causing his workmen to take pleasure in their work. 
 
 37. Also those which a person in a given calling can use in developing his 
 own interest in the same. 
 
 38. Discuss the subject of attention in connection with efficiency. 
 
 39. Name a number of efficiental sources of pleasure which are widely 
 present and cost little or nothing. 
 
 40. Explain the distinction between : "value in use" and "value in ex- 
 change", as used by political economists. 
 
 41. The term truth has come to include both equivalence relations and 
 also the surplusage fruits of such relations. State certain truths and also 
 the equivalence and surplusage elements in each of these. 
 
 42. State the various useful results, both immediate and more remote, 
 which may be the outcome of a successful teacher's work. 
 
 43. State the same for money expended in improving the water supply of 
 a city. 
 
 44. Ascertain what is meant by the term "epigenesis" and show how it 
 illustrates the idea of surplusage. 
 
 45. Explain what is meant by synthetic judgments, and in what respect 
 they illustrate the principle of surplusage. 
 
CHAPTER X 
 
 SYMBOLISM 
 
 Introductory Illustrations 
 
 When a merchant in Chicago wishes to buy goods in New York, 
 by writing a letter he can often save himself the expense of a 
 journey to New York. Or, going a step farther by sending 
 a telegram he can diminish in an important degree the time required 
 for obtaining the goods. This latter advantage often leads to other 
 advantages, such as the rapid reuse of capital or the making of a 
 sale that would otherwise be lost. When a scientific investigator 
 makes a discovery, by publishing the fact in a journal he opens the 
 way to its immediate and wide reuse. Also he often finds that in 
 the process of stating his discovery in terms of concepts in general 
 use, he develops and extends the new fact or principle. When a 
 surveyor enters in his notebook a drawing of the route surveyed 
 and also numerical and descriptive facts relating to it, he prevents 
 mistakes which he might make if he trusted to mere memory, fre- 
 quently saves himself the labor of making a resurvey, and also 
 puts the facts obtained in such a form that they can readily be 
 grouped in various forms and made the basis of efficient action by 
 himself and others in different ways, as in building a railroad. 
 
 The above instances illustrate the fact that the use of symbols may 
 be an important aid in obtaining useful results. Accordingly sym- 
 bolism is the next primary agent of efficiency which we shall study. 
 
 CLASSIFICATION 
 
 Cases of symbolisms might be grouped and named according to 
 the objects or materials represented by the given symbols, but such 
 a classification is not important for our purpose. It is well to 
 observe however that any object or entity may be denoted by a sym- 
 bol and usually by many different kinds of symbols. Extreme but 
 important cases are the representation of nothing (absence of 
 material) by some sign, as the absence of a number by the zero mark ; 
 or of an unknown object or number by a sign, as x ; or of a partially 
 known object by a symbol, as in certain cases in chemistry. 
 
 164 
 
SYMBOLISM 165 
 
 Objects Usable as Symbols 
 
 More valuable for our purpose is the classification of symbolisms 
 according to the material of which they are composed. 
 
 In the first place we find many material inorganic objects employed 
 in whole or part as signs or marks. Examples are dress, flags, ink, 
 paper, pencil marks, paint, idols made of stone, certain fetishes, 
 incense, clouds, the wind, the ocean, the barometer, thermometer, 
 etc. Such symbolisms are further illustrated by quotations like the 
 following: "He is pure gold", or "He is a star". 
 
 Also a physical force, as gravitation or electricity, may be used as 
 an expressive representation of some other kind of power. Thus 
 we speak of a weighty idea, of a magnetic person, or say that a 
 man is a live wire. 
 
 Of especial importance in this connection are light, color, and 
 sound. Examples of the employment of light and color in symbol 
 form are the black and white of the printed page, color as it appears 
 in paintings, flowers, the warning colors of animals, and certain 
 signals in railroading. Color often has abstract and conventional 
 meanings. An instance in the use in art of red and green to denote 
 the concrete, and of blue to express the abstract. 
 
 Among the sounds which are recognized or used as symbols are 
 thunder and various other sounds made by inorganic objects, the 
 sounds made by birds and other animals, the cry of a baby, the yell 
 of a savage, the drum signals of the African, spoken articulate 
 language, and an organization of sounds such as is found in a 
 symphony or fugue. 
 
 A living object or a combination of living objects may often form 
 a useful symbol. Thus green grass denotes the presence of water, 
 and a buzzard the proximity of carrion. Living objects are used 
 as symbols in a more abstract way, as when we say, for example, 
 that a certain man is a lion or an eagle. 
 
 In like manner it is often advantageous to use a part of a 
 living object as a symbol for the whole object. Examples are the 
 recognition of a plant by means of its leaves or flowers, or an 
 elephant by his trunk. So a beard is sometimes a convenient symbol 
 for a man, and a criminal may be identified by the marks on his 
 finger tips. So a smile or a gesture may express a state of mind. 
 Similarly a mind, or a mental state, attribute, or product frequently 
 
1 66 SOURCES OF EFFICIENCY 
 
 forms an effective symbol. Thus a feeling of pain often represents 
 danger or loss ; and a certain feeling of pleasure indicates gain or 
 advantage. 
 
 Certain sensations are in some way representative of the outside 
 world and must be interpreted as such. Thus some sensations of 
 taste or smell indicate foods, and others represent poisons. 
 
 So certain acts symbolize certain degrees of knowledge or states 
 of feeling. Also a mental peculiarity may represent the past educa- 
 tion of a person, or his early environment, or, in a measure, his 
 parentage. 
 
 An entire personality may also be a symbol as when an ambassa- 
 dor represents a nation. In certain cases a personality may repre- 
 sent more or less impersonal data. Instances are the use of a 
 personal concept like angels, devils, demons, gods, to represent 
 a natural force. 
 
 Spatial Objects as Symbols 
 
 The different spatial categories furnish material for symbols in 
 various ways. For example a group of points is frequently used 
 to represent a set of objects of any given kind. Or one point may 
 stand for a number of points or objects. Such a point is often 
 termed a focus. The Braille printed alphabet for the blind consists 
 entirely of aggregates of points. So a line may be made to stand for 
 an object in various useful ways, or for a motion, a velocity, dura- 
 tion, relation, etc. Specific illustrations are supplied by various 
 diagrams used in scientific works. Similarly we have lines of force 
 and lines of cleavage. The bounding lines of an area, as of a 
 country, frequently form a useful symbol for the whole area. 
 Similarly a solid object may be denoted by its bounding lines. 
 The letters used in writing and printing are made up essentially of 
 lines. Punctuation marks are points and small lines which indicate 
 to the eye the main parts of the group structure of a sentence. 
 
 An area may represent the product of any two factors. Thus 
 the distance passed over by a moving body may be represented 
 by an area, in which one dimension stands for the time occupied 
 by the motion and the other dimension represents the velocity of the 
 moving body. In common life and perception the visual surface 
 of a physical object is used in countless ways as a representative of 
 
SYMBOLISM X 67 
 
 the whole solid object. Similarly a volume may be used to stand 
 for the product of any three factors. Thus interest on money may 
 be represented by a volume whose three dimensions are principal, 
 rate, and time. Also in a less definite way volume or size is 
 employed to express power, influence, or efficiency in any form. So 
 a part of a geometric object is often used to represent the whole. 
 
 Shape or form may have an almost innumerable number of 
 different symbolic meanings. The closely allied category of posi- 
 tion also has many symbolical uses. For instance superiority in 
 power or influence is often represented by a higher position of 
 some kind, as a seat on a platform in a public meeting. In music 
 gradations in pitch are indicated by a series of positions on a printed 
 scale ; also simultaneity of sound is denoted by placing on the same 
 vertical line the marks which represent the given sounds. Position 
 is also used as a principle of symbolism in other highly conventional 
 but important ways, as in the arrangement of words in a sentence, of 
 digits in a number such as 78562, or of symbols in various combina- 
 tions of which the following are illustrations, 5 2 , 52, 25, 2 5 , ,,5. 
 
 Neighborhood Symbolism 
 
 The important case where the meaning of a symbol is largely 
 determined by its surroundings we shall name neighborhood sym- 
 bolism. Thus in 78562 the meaning or value of the 7 depends 
 mainly on the number of symbols which follow it. A similar case 
 is that of a word like bill which may have a number of distinct 
 meanings and whose particular meaning is determined in any given 
 case by the context, that is, by the position of the given word with 
 reference to adjacent words. As an illustration we may take the 
 word bill in the two sentences, The woodcock has a long bill ; and, 
 I will not pay this bill. 
 
 Other Abstract Symbols 
 
 Number is used as a symbol in many ways. Thus it may express 
 volume, size, position, power, or efficiency of any kind. An example 
 of the latter kind is contained in the statement, An opportunity in 
 early life is not one but a thousand. 
 
 Similarly time and its various categories often constitute useful 
 symbols. Thus time may represent space as when we say that two 
 
1 68 SOURCES OF EFFICIENCY 
 
 cities are eight hours apart. Time may also represent growth, 
 for instance a person's age indicates on the average a certain stage of 
 development. A more complex case is the use of time as representa- 
 tive of various forces operating in time, as when we say that time 
 cures all ills. 
 
 Motion is a useful symbol in a variety of ways. The motion of 
 a cloud indicates the direction and velocity of the wind in the 
 stratum of air which contains the cloud. The flight of a person is 
 often a sign of guilt or of fright. Certain kinds of motion indicate 
 the presence of life. The motions of a workman are expressive of 
 the amount of bodily energy he is expending. 
 
 Motion symbolism may take an elaborate, articulate form. Ex- 
 amples are wigwagging as practised in the signal service of an 
 army, various kinds of dancing, finger reckoning, and the various 
 forms of deaf and dumb gesture language. 
 
 The order in which one well known set of objects is customarily 
 arranged often constitutes a simple and effective means of indicating 
 the order which holds among a less familiar set. Thus on a geo- 
 logical map the order in time of the geological strata is often con- 
 veniently denoted by the order of the colors of the spectrum. Simi- 
 larly on a topographical map the parts of the ocean are frequently 
 denoted by blue, lands little above the sea level by green, and moun- 
 tains by red, the various intermediate colors and shades of the 
 spectrum being used to express yarious intermediate degrees of 
 elevation of the land surface. In like manner the order of letters 
 in the alphabet, and of numbers in the number scale are frequently 
 used as symbols for other cases of order, as of order in a multiplica- 
 tive series scale. 
 
 Efficients as Symbols 
 
 Entities of a still more abstract and general kind may be employed 
 as symbols. In general, any Efficient, or any part of an Efficient, 
 may be used as a brief and comprehensive symbol of other things. 
 Thus an element may represent a group, or one group may stand for 
 any other group or form of groupism. Any diversity may be repre- 
 sented by a diversity of any other sort as by an irregular mark like 
 < or -— ■>. So we often represent any uniformity by any other more 
 convenient or powerful uniformity. An important case, already re- 
 
SYMBOLISM 169 
 
 ferred to in different places is that in which an equivalence of some 
 particular kind stands for ubiquitous available surplusage, as when 
 peace is used as a symbol for constant potential happiness. So any 
 instrument may be a symbol for the fruits of that instrument. 
 
 Absence as a Symbol 
 
 An extreme case of efficiency in symbols is that in which mere 
 absence of anything represents some particular object or entity. 
 Thus empty space may be a sign for some number agreed upon ; 
 x when used for ix 1 is a twofold illustration of this principle. 
 Absence or silence may indicate dislike, forgetfulness, suspicion, or 
 have any prearranged meaning. Thus we have the saying "Silence is 
 more eloquent than words." A convenient and widely applicable 
 symbolism of this sort is the representation of the absence of 
 obstacles and the resulting speed or power by a vacuum. Thus a 
 railroad system may be conceived of as a branching vacuum con- 
 necting important places which are stores and sources of positive 
 surplusage. 
 
 Symbols Formed of Complex Materials 
 
 Evidently the above materials out of which symbols are formed 
 may be compounded and complexed in many ways. An illustration 
 is the combination of symptoms in the human body which indicates 
 health or the presence of some particular disease. This combina- 
 tion may consist of a coating on the tongue, feelings of pain or 
 pleasure, sounds of different kinds, lines in the face, color of the 
 complexion, temperature, position of the bodily parts, action of the 
 pulse or heart, absence of appetite, changes of growth or decay. 
 
 Symbols Classified according to Forms 
 
 It is often also an advantage to characterize certain symbolisms 
 according to their forms or some other prominent quality. 
 
 Thus with respect to personality and directive processes it is 
 often useful to discriminate between symbols which have been de- 
 vised by a person for his own use {private or subjective symbol- 
 isms), and those which are objective and general. 
 
 In a still more general way we can distinguish symbols which 
 are artificial like the alphabet and those which are natural like the 
 colors of a bird or the beard of a man. 
 
IjO SOURCES OF EFFICIENCY 
 
 Spatial and Like Forms 
 
 A spatial element is often prominent in a symbolism. In particu- 
 lar, it is useful to note that, from the relative point of view, a dia- 
 gram (or other symbol) may be larger than the material represented, 
 as in diagrams of molecular structure, or smaller, as in most maps, 
 printed language, etc. 
 
 A symbol or symbolism may be of one, two, three, or no dimen- 
 sions, examples of the last species being the use of a point or 
 empty space as a sign of something. An important special dimen- 
 sional case is what may be termed the semilinear form of symbolism. 
 This consists of a set of symbols dominantly linear but with some 
 width varying according to circumstances. As examples, we have 
 a line of print, or mathematical symbols, or the symbolisms which 
 are found in a person's stream of consciousness. 
 
 As to time and allied categories, various symbolisms may be 
 characterized as temporary (provisional), permanent, survivals, 
 prehistoric, prenatal, or hereditary. 
 
 With reference to the category of number, the specific char- 
 acter of a symbolism may be determined in several different ways. 
 For example the number of its fundamental symbols is often an 
 important distinguishing characteristic of a given system. Thus 
 the Arabic system of notation for numbers contains ten symbols. 
 This numerical element in a symbolism varies greatly owing to the 
 fact that in certain cases greater efficiency is obtained by using 
 only a few primary symbols, and in other cases by using many. 
 
 Manifold Symbolisms 
 
 Also we may obtain what we may term a dual, triple, or w-fold 
 symbolism by symbolizing a given domain of material in two, three, 
 or w-different ways. In a mine a danger signal often consists 
 both of the ringing of a bell and of the flashing of a light of some 
 kind. The policemen of a city are denoted by their names, by their 
 numbers, and as a whole by their uniforms. A country may be 
 described in common language, or by maps, or diagrams, or tables 
 of numerical data, or a series of pictures, each method having its 
 own special uses, and all combining multiplicatively to produce 
 expressiveness of a high order. 
 
 A reciprocal symbolism is a combination of two objects or of two 
 domains of material such that each may be used as a symbolical 
 representative of the other. An example is furnished by the music 
 and words of a good song. 
 
SYMBOLISM 171 
 
 Symbolisms Characterized by an Efficient 
 
 An important class of symbolisms with respect to the category of 
 force are the records automatically made by certain machines. 
 
 A species of symbolism is often best characterized by that Effi- 
 cient which is most prominent in its form or structure. Thus it is 
 frequently best to regard a case where the whole is represented by 
 a part as a unit and multiplier symbolism. A special instance of this 
 form is a prize of any kind given as a representative or specimen 
 of other larger rewards to come later. 
 
 Similarly certain important species of symbolisms have a marginal 
 reuse form. Thus a conductor on a railroad train instead of re- 
 cording by pencil the fact that a certain passenger has paid his fare 
 saves time and labor by simply making a hole in the passenger's 
 ticket. 
 
 A symbol may be systematically grouped in its inner structure; 
 and in like manner individual symbols or symbolisms may be com- 
 bined so as to form a multiplicatively grouped aggregate. The fact 
 that a sentence as used in ordinary language is essentially a multi- 
 plicative group structure is indicated by the term "articulate 
 language". 
 
 Orders of Symbolisms 
 
 One symbol may often be represented by another and frequently 
 briefer and more efficient symbol; hence symbolisms may be of dif- 
 ferent orders. Thus ordinary language may be converted into short- 
 hand (as used by a stenographer in reporting a speech), or stated 
 in terms of the Morse telegraphic code, or expressed in some species 
 of cryptography. Hence all of these devised systems are of the 
 second order. When a telegrapher reads a message by sound, the 
 set of sounds utilized by him constitutes a symbolic system of the 
 third order. 
 
 One symbol may also be of higher order than another owing to 
 its aggregate superior efficiency. Thus among civilized peoples, a 
 word like Jehovah is superior in significance to a wooden image in 
 representing a divine principle. 
 
 Scale of Departure from Appearances 
 
 The classification of symbols (or symbolisms) according to the 
 degree of their departure from the object represented, is of funda- 
 
172 SOURCES OF EFFICIENCY 
 
 mental importance. In this respect we have the following principal 
 types : 
 
 (i) Cases where such departure is slight, as in photographs, 
 maps, geometric outlines, or in verbal contractions, as the use of 
 U. S. for United States. In such symbols the transformations in- 
 volved consist essentially in a reduction of size, or a syncopation 
 (or in some cases of an expansion) of the object represented. Often 
 also a slight reluctant departure from the form of this object is 
 involved. The largest departure from phenomenal appearance 
 allowable in this respect is found, perhaps, in the representation of 
 a solid object by a drawing on a flat surface. 
 
 (2) Diagrams in which there is not only a change in size, but 
 also a considerable change in form, as in a diagram of the human 
 heart with the parts rearranged so that the process of the heart's 
 action can be studied in consecutive detail. Similar cases are a 
 diagram of the structure of a molecule, or of the parts of a sentence. 
 
 (3) Symbols in which the departure from the form of the object 
 represented is preferential and aggressive. Instances are the word 
 "man" as compared with what the symbol represents ; the use of x 
 to denote the volume of a box ; and the sign = instead of the word 
 "equals". All ordinary verbal language, whether spoken or written, 
 shorthand, telegraphic codes, etc., are of this class. In this connec- 
 tion, special mention may be made of symbols which involve an un- 
 limited or infinite departure from so-called reality. Examples are 
 the representation of infinity by the sign 00 and zero by o. So 
 certain religious teachers have enforced the inferiority of matter 
 and evil by declaring them to be non-existent. 
 
 Transcendent Symbols 
 
 Symbols often appear in a more or less unanalyzable, mysterious, 
 and even transcendental form. An instance is the combination of 
 marks on a plant by recognizing which, even before blossoms have 
 been produced, a plant breeder like Luther Burbank is able to 
 select from 10,000 individual plants of a given variety the two or 
 three which will develop specified desirable qualities. Certain physi- 
 cians have like powers in reading symptoms of diseases, and certain 
 other persons in reading minds and characters. Often a work of art, 
 as a painting by Turner, is a complex and a more or less transcenden- 
 tal symbol. 
 
SYMBOLISM 
 
 173 
 
 Complex Forms of Symbolism. 
 
 It is evident that the above forms may be compounded and 
 complexed together in various ways. An instance is found in a 
 scientific book which contains not only ordinary language but also 
 mathematical or logical formulas, pictures, diagrams, and numerical 
 tables. Its statements and formulas often also contain implicit 
 expressions of truths and facts not yet fully unravelled and perhaps 
 beyond our full comprehension. 
 
 Two General Types of Symbols 
 
 Before closing the discussion of species of symbolisms, it will 
 be well to note that it is often useful to group different kinds of 
 symbolism into two main classes as follows : 
 
 I. Geometric, graphic, or pictorial symbols. These are preferentially 
 single (or integral), concrete, depart reluctantly from appearances 
 and appeal primarily to the sense of vision. They are characterized 
 by vividness, immediacy, and force of action. 
 
 II. Algebraic symbols. These are characterized by an aggressive 
 departure from appearances, are, in general, abstract in nature, and 
 composed of numerous small parts which are combined in multipli- 
 cative group fashion. They are related to the hand and higher 
 mental faculties as well as to the eye. They are marked by their 
 comprehensive grasp, ease of formation, and many-sided efficiency. 
 
 These two general classes of symbols may also be briefly de- 
 scribed as direct, and indirect. 
 
 Efficiental Essences 
 
 An important form of the first of these two classes is what may 
 be termed the efficiental essence of an object or domain. By this is 
 meant the Efficients which together form the dominating structure 
 of the object, or to which it can be reduced, and which often can 
 advantageously be used in place of the object or domain. A simple 
 example is the set of lines which is often used to represent a box. 
 Another is the group of fundamental ideas which form the essence 
 of a book. A more complex case is the aggregate of special efficiental 
 methods which characterize any particular nation, as the English, or 
 which maybe regarded as representing a given type of civilization. 
 
174 SOURCES OF EFFICIENCY 
 
 EFFICIENCY FUNCTIONS OF SYMBOLS 
 
 The efficiency functions of symbolism are presented to best ad- 
 vantage by stating them in terms of other leading principles of 
 efficiency. 
 
 Symbols a Means of Economy 
 
 Thus many of the advantages connected with the use of symbols 
 appear in the form of economies or groups. For instance a symbol 
 usually contains far less material than the object represented. A 
 hundred dollar bill weighs much less than one hundred gold dollars 
 and still greater is the disparity between the bill and one hundred 
 bushels of wheat. Economy of this kind is often practically infinite, 
 as when a house is represented by certain diagrams, or by the word 
 "house". 
 
 Closely connected with economy of material is economy of force 
 or energy. For example it is much easier to transfer to a distant 
 place a picture of a house than the house itself. 
 
 This economy often takes a wide and complex form. An illus- 
 tration is the saving of energy involved in reading a book of travels, 
 instead of making the actual journeys described in the book. 
 
 Closely connected with economy of material and energy is economy 
 of time and all that time represents. In fact the proper use of sym- 
 bols may beget an economy in each and every element employed in 
 producing results. These economies are often combined in complex 
 forms. For example the colored petals of a flower form a sign to 
 the bee, which leads to a saving of pollen in cross fertilization, 
 hence to a saving of energy to the plant, and to a saving of time in 
 the evolution of the plant into a higher form. 
 
 An Aid in Foming and Using Groups 
 
 Symbolisms are also a means of producing more positive inclusions 
 or groups than economy. Thus the symbols which represent objects 
 can often be collected into a small portion of space or time where 
 it would be impossible to collect the objects themselves. An example 
 is the summation in figures of the coal deposits of the United States 
 as compared with a physical combination of all this coal in one heap. 
 Signs and signals also lead to concentrations of strength and action, 
 as in games, or war, business, or governmental processes. 
 
SYMBOLISM 
 
 175 
 
 A Means to Reuse 
 
 The employment of symbols often leads to reuse on a large scale. 
 A printed description or picture of a building often produces exten- 
 sive multuse of the principles embodied in the building. If it were 
 not for oral or printed language or pictorial representations of an 
 object, only those actually witnessing an event would ever know of it. 
 
 This useful function of symbols is increased by the ease with 
 which they can be preserved on account of their conciseness. This 
 quality makes it possible readily to inscribe them on lasting materials 
 or to shelter them. Symbols lead to reuse not only in these ways 
 but also because they facilitate the action of the imagination and 
 reason. 
 
 When we say that a certain orator is a star, we employ reuse of 
 still another kind. In this case the reuse involved is that of work 
 done in assimilating the meaning of a star. This gain also takes the 
 form of added force and vividness in the process of communicating 
 ideas. 
 
 Symbols Auxiliary to Multiplicative Group Systems 
 
 The use of symbols often facilitates the formation of multipli- 
 cative group systems. An example is the organization of an army 
 by the aid of uniforms, and various flags and standards. So widely 
 separated objects may often be grouped multiplicatively by 
 affixing proper tags or marks to them;. Many systems of biologi- 
 cal classification are obtained essentially in this way. An important 
 illustration from the business world is the coordination of several 
 lines of work in a machine shop or other establishment by means 
 of carefully prepared charts. This process often in effect consti- 
 tutes the combination of several linear group systems into a com- 
 prehensive areal one. Similarly the tabulation of the results of any 
 large and many-sided investigation facilitates the discovery of laws 
 governing these results, and the use of checks, tests, and various 
 cross multiplicative groupings. Also the multiplicative grouping 
 of a given domain of material in terms of a certain few units taken 
 as fundamental is facilitated by expressing these units in symbolic 
 form. Thus as soon as a national consciousness has adopted certain 
 ideas as standard or primal and expressed these in words, other 
 experiences and ideas will be expressed in terms of these standard 
 ones, and the national life will be correspondingly systematized. 
 
176 SOURCES OF EFFICIENCY 
 
 An Aid to Other Efficients 
 
 In like manner the employment of symbols develops orders of 
 material. Thus in business processes the construction of efficiency 
 curves and charts facilitates the working back to causes and sources 
 of efficiency or waste and the formation of improved processes of 
 work. In some cases, the symbolism itself acts as a higher grade 
 of material with reference to the objects represented. 
 
 In the use of symbols, uniformities are developed by the inten- 
 tional making of different symbols of the same general size, by the 
 reuse of symbols, by the discovery of like efficiental essences in 
 different domains, or by the permanence conferred on the data 
 represented. Symbols also furnish diversities in the form of differ- 
 ences between the symbol and the object represented, and frequently 
 also in the spatial detachment of the symbol from the object. These 
 diversities are often the sources of important characteristic advan- 
 tages. In certain cases a name or symbol confers a kind of substan- 
 tial individuality upon an otherwise vague and uncertain entity. 
 Other persons before the time of Priestley had obtained oxygen but 
 he is regarded as its discoverer, in part because he first gave it a 
 name. 
 
 The development of uniformities and diversities in connection 
 with symbols also leads to the fruits which are characteristic of 
 uniformities and diversities. 
 
 Symbols Mean Various Externalities 
 
 Symbols are not only themselves a useful auxiliary but they 
 facilitate the application of other externalities in connection with a 
 given domain of material. Thus by their conciseness they open the 
 way for the formation of short tabulations or other brief combina- 
 tions of various materials, and for the use of reciprocal externality 
 among these materials and the application of outside externality to 
 them in group ways. An important special case of this source of 
 efficiency is the use of maps and charts of various kinds. The 
 use of symbols frequently leads to externality in the form of sus- 
 pended operations, and consequent economies such as are involved in 
 cancellations for example. 
 
 Also the process of contracting material into symbols often leaves 
 vacant space where externalities can be annexed, or indirect routes 
 or methods followed. 
 
SYMBOLISM 
 
 177 
 
 By taking advantage of the detachment of symbols, the mind also 
 acquires a certain freedom and largeness in its operations which are 
 attended by many useful results. 
 
 The externalities inextricably inwoven with our visual habits and 
 those due to the permanency and easy motion of symbols may also 
 be mentioned in this connection. 
 
 The above species of externality often occur in complex form. 
 Thus in solving a given problem, the use of symbols often enables 
 one to plunge into the middle of the subject, and to work in several 
 directions at once, using many auxiliaries simultaneously. 
 
 Facilitate Directive Work 
 
 The smallness and lightness of symbols facilitate the directive 
 use of them and hence, in effect, of the materials which they repre- 
 sent. The useful results of such directive use are discussed in 
 Chapter XI (p. 192). Symbolism, especially in the form of the effi- 
 ciental essence of an object, often leads to important directive 
 efficiency acts of other kinds. This consists in regarding an object 
 as a multiplicative group structure in which the efficiental essence 
 is the prime group. Often the essentials of a desired object can 
 be found in some accessible or cheap form, and the supplementary 
 details treated in some special way. 
 
 Unexpected and Self-developing Results 
 
 The use of symbols often also leads to certain unexpected and self- 
 developing results. These dialectic results often spring from the 
 unrealized manifold nature of symbols, from their concentration, 
 reciprocal action, and the various uniformities and diversities which 
 characterize them, or to which they give rise. This dialectic 
 development is often vague and uncertain, in other cases it is 
 standard and to a certain degree dependable as in the processes of 
 mathematics or other calculuses. 
 
 It is well to note in this connection that the dialectic power in a 
 calculus in large measure may be resolved into the dialectic proper- 
 ties of symbolisms outlined above. Thus the approximate uniform- 
 ity in the size of the symbols employed in an algebraic equation leads 
 to many important results which we cannot stop to point out in detail. 
 The same is true of the uniformity in the size of the letters of the 
 alphabet, and of Arabic numerals. For these and like reasons, in 
 
178 SOURCES OF EFFICIENCY 
 
 mathematical work a symbolism often seems to move forward to 
 new results by some intrinsic, uncanny, and irresistible power. Hence 
 the mathematician Euler, for example, remarked that his pencil 
 seemed at times to surpass himself in intelligence. 
 
 Transcendent Results 
 
 Some of the fruits obtained by the use of symbols are transcen- 
 dental and absolute, in the sense that they cannot be measured. 
 An instance is the saving of lives of the passengers on a sinking 
 ship by the aid of wireless telegraphy. Others are unique in the 
 sense that apparently they could not have been obtained in any other 
 way. Thus it is scarcely conceivable that certain highly developed 
 forms of multiplicative groups could have been obtained or kept 
 in operation without the aid of symbolisms. 
 
 Another illustration of a like high order of fruitage is the pleasure 
 afforded by a symphony or great painting. Still another of widely 
 different character is the power conferred on us by symbols to use 
 together toolages apparently contradictory, and to get the advantages 
 belonging to each with a further dialectic of advantageous results. 
 An illustration is the use in combination of the atomic and ether 
 theories of matter. 
 
 The above functions of symbols may be complexed in many 
 ways. Illustrations of such complex useful results are given in the 
 paragraphs which follow. 
 
 Increasing Use of Symbols 
 
 The value of symbolisms may be realized in other more pictorial 
 ways, as by noting that increasing civilization has been marked 
 by an increasing volume and variety of symbolisms. This value 
 may also be made evident by trying to conceive what the modern 
 world would become if its various languages, signs, and symbols 
 were removed. Evidently the most elementary processes of life 
 would be greatly diminished in efficiency while, apparently, the 
 higher and complex processes would crumble and disappear. 
 
 Words which show the Value of Symbolisms 
 
 The value of symbolisms may be realized from another point of 
 view by recalling and massing together the utilities implied by 
 such words as language, plans, scheme, outline, diagrams, metaphors, 
 paintings, sculpture, photography, pictures, art, telegraph, telephone. 
 
SYMBOLISM 179 
 
 Dangers and Limitations 
 
 The dangers and limitations connected with the use of symbols 
 are especially prominent on account of the abstract, detached, and 
 often highly transformed character of this instrument of efficiency. 
 The following diagram will be an aid g 
 in grouping and grasping these draw- 
 backs. In the diagram O stands for the 
 object symbolized; S means the symbol 
 for O ; S' is the symbol after it has 
 been transformed or shifted in position 
 for some purpose; and O' is the object 
 
 again but often in a new relation or condition. This diagram 
 makes clear that there are three main classes of dangers connected 
 with the use of symbols : 
 
 (1) Those in going from O to S (that is, from the object to the 
 symbol) ; 
 
 (2) Those in going from S to S' (that is, from the symbol to the 
 symbol in a new position or state) ; 
 
 (3) Those in going from S' to O' (that is, from the symbol back 
 to the object). 
 
 Errors in Going from Object to Symbol 
 
 In class (1) are included all those cases where the symbol fails 
 to correspond to the object which it is supposed to represent. A 
 common example is the over-capitalization of a stock company. The 
 lack of correspondence between fact and symbol may be due either 
 to unconscious error or to intention. In the latter class would come 
 various misrepresentations, lies, and swindles. An extreme case is 
 that where a symbol is wholly deceptive and stands for nothing, 
 or what is worse than nothing, as in some cases of forgery. 
 
 Errors in Manipulation of Symbols 
 
 As illustrations of class (2) we have the errors made in 
 transcribing and combining symbols in mathematical calculations, or 
 those made in processes of reasoning carried on in oral or printed 
 language. Details concerning such errors are given in Chapter 
 XVI. In this class also belong losses due to difficulties in preserv- 
 ing symbols till the time is ready for their translation back into the 
 data represented. As instances we have the cases where paper 
 
180 SOURCES OF EFFICIENCY 
 
 money and various memoranda and securities have been destroyed 
 by fire, flood, insects, or rodents before the valuable symbols named 
 could be converted into some concrete and permanent form of wealth. 
 Alterations made in symbols for the purposes of deception, as when a 
 check is raised, also belong to this class of dangers and losses. 
 
 Errors in Going from Symbol back to Object 
 
 Class (3) includes all errors and misrepresentations made in the 
 process of converting the symbol into the material represented, or 
 some datum more or less like this material. An important case 
 in this class is that which assumes that the object will have all the 
 properties of the symbol, as that a bridge will be as strong in pro- 
 portion to its size as in the model which has been made to repre- 
 sent the bridge. Another special case in this class is the ignorant 
 selling of stock certificates for less than they are worth, or signing 
 any important document under the impression that one's signature 
 has an entirely different meaning from the actual one. 
 
 An extreme case in this class is the error of regarding the symbol 
 as not representative but ultimate. Instances are the common error 
 of mistaking paper money for real money, or of exalting a religious 
 image or ceremony above the reality represented. This conception 
 of the symbol as an objective reality rather than as an instrument 
 for attaining results often takes partial and elusive forms. Thus 
 many of the difficulties in the mastery of mathematics come from 
 regarding such symbols as 
 
 as objects rather than as instruments. 
 
 The Tongue of Efficiency 
 
 On the whole, however, it is evident that the advantages con- 
 nected with the use of symbols far outweigh the disadvantages. 
 In fact symbolism may be termed the tongue of efficiency, and in 
 some respects also its brain. 
 
 SOURCES OF EFFICIENCY IN SYMBOLISM 
 
 Our study of symbolism up to this point has made it clear that a 
 symbol is a special form of group, and that the utilities which flow 
 from the use of symbols are special forms of the benefits which 
 
SYMBOLISM 181 
 
 accompany the employment of groups. Hence as an aid to using 
 symbols in the most efficient way it is important to investigate as 
 closely as we can the relation of symbols and symbolisms to the 
 group idea. 
 
 The Symbol as a Group 
 
 The word symbol means something thrown together; that is, a 
 contraction, abbreviation, or syncopation. Hence primarily symbol 
 means a group formed by the process of inclusion. Special mention 
 should be made of the fact that this contraction is made in such 
 a way as to bring in front of the user and within the scope of a 
 single act of vision, data that may have been lying in many direc- 
 tions and at various distances from the observer. 
 
 The process of contraction by which symbols are formed may be 
 carried on in such a way as to make the resulting symbol a multi- 
 plicative group structure ; or later, by use of externality, the symbol 
 may be developed into this form. Also, as has been pointed out, 
 different symbols are frequently combined so as to form a systemat- 
 ically grouped aggregate. The symbolic multiplicative group system 
 is often parallel to a multiplicative group system of material in the 
 object represented. 
 
 A Symbol as a Unit 
 
 In some aspects or cases, a symbol is a unit which has various 
 multipliers or multuses. For example a gesture which causes an 
 entire audience to rise to its feet is a unit motion with respect to 
 the motion of the audience which follows. So a word in some re- 
 spects is a unit with respect to the object represented by the word. 
 A symbol may also be a multiplier. Thus a gold reserve is in effect 
 multiplied many times by the large amount of paper money circu- 
 lated with reference to it. 
 
 Relation of Symbolism to other Efficients 
 
 With respect to the principle of orders of material, symbols are 
 usually high in the scale of efficiency, and often indeed belong to 
 the efficiental abstract grade. 
 
 Externalities of various kinds are present or implied in symbols. 
 Beside the various species of related externality spoken of in the 
 preceding pages mention may be made of the fact that a symbol 
 
1 82 SOURCES OF EFFICIENCY 
 
 implies a wide range of application, and also certain auxiliaries to 
 safeguard the use of the symbol. 
 
 In addition to the various uniformities and diversities which 
 have already been considered as prominent in symbolisms, special 
 mention should be made of the exact correspondence, or uniformity, 
 which should exist between symbol and object, and between symbols 
 representing the same object. 
 
 Some element of limitation is always a contributing cause to the 
 formation and use of symbols. Thus if it were not for our limited 
 grasp of objects in space and time, we should not need to use sym- 
 bols. This limitation factor varies greatly in degree and form. 
 Hence a special study of it will be an important aid to the most 
 efficient use of symbols in different cases. For this special study 
 see Chapter XV (p. 265). 
 
 Relativity of Symbols 
 
 This brings us to the general matter of relativity in the nature 
 symbols. With reference to different individuals and to the 
 same individual under different circumstances there is often much 
 variation as to what is to be taken as a primal datum of experience 
 and what is to be regarded as an artificially formal symbolism. 
 Thus the colored surface of an object from one view point is an 
 original datum of experience which may usefully be denoted by 
 symbols (described in words, or expressed in units of area) ; 
 from another standpoint this colored surface is but a symbolic repre- 
 sentation of the certain molecules and forces. 
 
 A symbol also contains an element of unique individuality, not 
 statable in terms of other concepts or primal modes of efficiency. 
 This often becomes the source of unexpected uses and values. 
 
 Definition 
 
 As a summary of the results of our study of the nature of 
 symbols we may make the following definition : 
 
 A symbol (or symbolism) is a group (or system of groups) whose 
 function is the efficient expression and transfer of other groups and 
 which acts mainly through the eye and ear. 
 
 METHODS OF APPLICATION 
 
 A realization of the essentially multiplicative nature of symbolism 
 is an aid in many ways in making the most effective use of signs and 
 
SYMBOLISM 183 
 
 representatives. Many of these methods are obvious and we shall 
 discuss only those which are most important or most likely to be 
 overlooked. 
 
 Vast Number of Possible Symbolisms 
 
 By an application similar to that made with the other Efficients, 
 the multiplicative principle aids us in realizing the great number of 
 possible materials and combinations of material which can be utilized 
 in making symbols. It also aids us in conceiving the vast number 
 of forms which symbolisms may assume. The multiplicative group 
 principle is likewise a powerful help in systematizing these materials 
 and forms and holding them ready for use. 
 
 Potency of Symbolisms 
 
 The great power in the multiplicative principle enables us to realize 
 also the extreme extent and efficiency to which even a limited or 
 crude species of symbolism may be developed. Illustrations are 
 the power of the tactual symbolisms employed by a person like Helen 
 Keller, and those special forms unconsciously employed by un- 
 tutored lightning calculators. As a more abstract illustration we 
 have the power of the equation ax 2 -J- bxy -f- cy 2 -\- dx -\- ey -f- 
 f = to represent all the properties of the straight line, circle, 
 ellipse, parabola, and hyperbola. 
 
 Adapting Symbolisms to Special Circumstances 
 
 Owing to the great variety of forms which symbols and symbolisms 
 may take, and the wide differences in the circumstances attending 
 their use, in any specified case it is of especial importance to study 
 the limitations and possibilities involved in order to select or devise 
 the most desirable symbolism for use in the given situation. In this 
 process much use of externality is often desirable. Thus in making 
 a graph, or realizing an efficiental essence, especially in a difficult 
 case, externality is frequently helpful. This may take the form of 
 getting at a distance from (or holding at arm's length) the material 
 considered, or of viewing it from all sides, or of allowing time 
 to work upon it. Also when a wide domain is studied, the efficiental 
 essence is apt to come to the surface in certain spots, or a natural 
 symbolism to be revealed. 
 
 Cases illustrative of the advantage and need of special symbolisms 
 
1 84 SOURCES OF EFFICIENCY 
 
 under different circumstances are the use of adapted marks and 
 signs on clay tablets in Babylonia and Assyria, on papyrus and 
 granite in Egypt, and parchment and marble in Greece. A modern 
 instance is the difference between day and night signals on railroads. 
 An illustration from the world of commerce is the fact that cotton 
 and wheat may be sold by standard (that is, technical verbal descrip- 
 tion as Grade A, etc.), while wool cannot be sold in this convenient 
 way but is bargained for by sample. 
 
 Relations of Graphic and Linguistic Symbolisms 
 
 As to the use of more general kinds of symbolisms under different 
 circumstances, it should be observed that algebraic symbolism 
 (Class II, p. 173) is preferable as a general or standard method 
 of expression, while graphic or pictorial symbols are to be used 
 locally or occasionally for the sake of special advantages. Examples 
 of such local use are the employment of flags in the management 
 of an army, or of diagrams in the teaching of grammar. 
 
 Careful study must often be made as to when and how to 
 combine these two main classes of symbols. A rhythmic or alternate 
 use of the two will often be found very advantageous., 
 
 Form and Color in Symbolisms 
 
 Also in devising and using symbols it is to be noted that, in 
 general, the form of a symbol is a more effective element than the 
 color. This is one reason why algebraic symbolism, as a rule, is 
 superior to the graphic form. For a somewhat similar reason spoken 
 language is more efficient than gesture language as a standard method 
 of expression. Vocal language also, since it employs certain organs 
 in the mouth and throat, has the advantage of leaving the arms and 
 hands free for use in other ways. 
 
 Standard and Special Symbolisms 
 
 In the field of objective symbolisms (that is, of those used not for 
 private purposes, but in connection with other people) it is desirable 
 to give the preference to standard and conventional symbols. At 
 the same time it is important to acquire the power and form the 
 habit of improvising symbols for one's private use, since such 
 symbols may often be highly efficient in special situations. 
 
SYMBOLISM 185 
 
 Preference to Symbols of High Order 
 
 It is scarcely necessary to say that it is desirable to make all 
 symbols and symbolisms of as high an order as circumstances will 
 permit. In the first place the material to be symbolized should be 
 selected and transformed so as to make it as efficient as possible. 
 Again individual symbols should be as efficient as possible both in 
 form and in other ways. As examples of superior symbolisms in 
 this respect we have the phonetic alphabet as compared with the 
 
 Egyptian hieroglyphs, the Leibnitzian — ±- as contrasted with the 
 
 dx 2 
 
 Newtonian y, and the use of a word like Jehovah in expressing 
 infinite external multiplicative power as compared with a heathen 
 idol. 
 
 Also in a symbolism of high order the individual symbols are 
 combined in effective ways, as for example in a multiplicative group 
 system. By this method,' for instance, a few symbols rightly used 
 are made to take the place of a large number combined in an 
 inefficient way. An example is the English alphabet as compared 
 with the Chinese syllabic system. A more specific instance is the 
 Linnean method of naming species of plants and animals. Before 
 the time of Linneus one name of common blue grass was "gramen 
 pratense paniculatum majus latiore folio poa theophiasti". In 
 the Linnean system of nomenclature this name is reduced to "poa 
 pratensis". The swift and vast progress of botany and zoology 
 since the time of Linneus is largely due to the simplicity and power 
 which characterize the binomial method of naming species. 
 
 A high order of symbolism often takes the form of a symbolism 
 of a symbolism, as when shorthand is used instead of ordinary 
 language. Again it may take the dimensional form, as when a 
 solid is represented by a flat picture, or in some cases by a set of 
 points, or even by one point. 
 
 In this connection it is to be remembered that neighborhood sym- 
 bolisms (see p. 167) are of a high order of efficiency, and that they 
 can often be utilized not only in private provisional symbolisms, but 
 also in giving added economy and power to certain applications 
 of objective language. 
 
 Similarly a manifold symbolism is of a high order of efficiency. 
 An example is that of expressing the fact that a given bottle con- 
 tains poison by printing the word poison on the label, annexing a 
 
1 86 SOURCES OF EFFICIENCY 
 
 picture of a skull and crossbones, and making the surface of the 
 bottle rough to the touch. 
 
 Auxiliaries in Making and Using Symbolisms 
 
 In applications of symbolism, other forms of externality than 
 those already indicated are often extremely useful. For instance 
 the use of some auxiliary often makes it possible to obtain pictures 
 or other representations of an object not otherwise possible. A 
 striking instance of this are the skiagraphs of the bloodvessels of 
 the brain obtained by the injection of mercury into these blood- 
 vessels, and the application of X rays. In other cases extra and, 
 from the strictly logical point of view, superfluous symbolism fre- 
 quently results in quickness and vigor of action with a consequent 
 dialectic of values. Instances of this are the method of denoting the 
 end of a sentence by a period or dot and also by the use of a capital 
 letter at the beginning of the next sentence ; or the employment of 
 difference of shape as well as size in forming a symbol as when 
 A is used instead of & as the capital form of small a. A combination 
 of color and form in a symbol when either alone would be adequate 
 is a like instance. 
 
 A more general and important case is supplied by the manifold 
 and various, even profuse, symbolism in a language like English as 
 compared with a minimal language like Esperanto or Volapuk. Here, 
 as has been said, "luxury is economy", and, we may add, efficiency. 
 
 This apparent excess of symbolism is useful not only as a direct 
 source of efficiency but often also in a negative way as a means of 
 preventing error. For example it often furnishes simple means of 
 checking a given statement or process. 
 
 Utilization of the Self-developing Power in Symbolisms 
 
 Especially important also is it to recognize and utilize the self- 
 corrective and self-developing property which is peculiarly charac- 
 teristic of symbolism as a source of efficiency. This principle will 
 be found particularly useful in cases of limitation and difficulty, as 
 when we express in language all that we know about partially under- 
 stood matters and find by development of this symbolism that our 
 language proves to possess a far wider expressiveness than we had 
 supposed. In its higher forms this principle is illustrated by the 
 extraordinary power of certain symbolic forms of deductive 
 reasoning. 
 
SYMBOLISM 187 
 
 Ideal Species 
 
 It follows from what has been said in the preceding pages that 
 our ideal form of symbolism would be a representation of efficiental 
 data in efficiental form for efficiental ends. 
 
 Summary of Chapter 
 
 An illustration of the great efficiency value of symbols is the fact 
 that making a written record of a result opens the way to the reuse 
 of the given result in many lines. Among the most obvious kinds of 
 symbolisms are written and oral language, pictures, maps, tabula- 
 tions, motions, and combinations of these. More extreme species 
 are neighborhood symbolism, and the expressive use of absence or 
 emptiness. Symbols are thus not only composed of a great di- 
 versity of materials, but they also occur in an endless variety of 
 forms. Among the most important forms of symbolisms are the 
 different linear and areal species, and those which are built upon 
 each other in succession. The two most general types are the 
 geometric and algebraic (or the direct and indirect). Its efficiental 
 essence is often a highly important representative of an object or a 
 domain of material. 
 
 The economy attained by using the symbol of an object instead 
 of the object itself is often practically infinite. Other values which 
 frequently result are speed, organization, ease in directive manage- 
 ment and in the application of externality, the fruits of these, and 
 other useful results which are often transcendent. Each particular 
 form of symbolism has its own special efficiency powers. However, 
 owing to the detached and abstract nature of most symbols their use 
 is exposed to peculiar dangers which must be guarded against. 
 
 Owing to the great variety of existing or possible symbolisms and 
 their extreme power, great care is often needed in order to select or 
 invent the particular species which, in a given case, will be most 
 effective. Especial attention is to be paid to the use of different 
 kinds of symbolism in combination, as in the alternate use of the 
 two principal kinds. The application of externality is useful in 
 different cases. Preference is to be given to standard forms of high 
 order, the highest form of all being that which is as efficiental as 
 possible both as to data, form, and aim. 
 
1 88 SOURCES OF EFFICIENCY 
 
 EXERCISE 10 
 State the class or classes to which each of the following symbols or sym- 
 bolisms belongs : 
 
 i. A smile 3. Footprints 5. A trade mark 
 
 2. A flag 4. Ditto marks 6. A weather vane 
 
 7. Sounds made by sleigh bells. 
 
 8. The word rock in "He was a rock in defence of his position". 
 
 9. A curved line showing the fluctuations of the price of wheat from day 
 to day. 
 
 10. The sign + as use d to express addition. 
 
 11. A coat of arms as used in heraldry. 
 
 12. The cry of an infant when in pain. 
 
 Give an example of the use of each of the following as a symbol : 
 
 13. Some bird 17. Heat 21. Some other fluid 
 
 14. Some quadruped 18. Flame 22. The air 
 
 15. Some flower 19. Some metal 23. Smoke 
 
 16. Some tree 20. Water 24. A leaf 
 
 25. A physical force to represent a mental power 
 
 26. State the advantages involved in the use of each symbol given in Exs. 
 1-12. 
 
 27. Name all the audible symbols you can. 
 
 28. All the visible ones. 
 
 29. All the mental ones. 
 
 30. Give an example of order used as a symbol. 
 
 Give an example of the following classes of symbols or symbolisms : 
 
 31. Natural 35. Neighborhood 39. Multiplicatively grouped 
 
 32. Artificial 36. Inherited 40. Semi-linear 
 
 33. Semi-artificial 37. Dual . 41. Of second order 
 
 34. Negative 38. Triple 42. Of third oider 
 
 43. What different kinds of symbolism are combined in a rocket fired as 
 a signal? 
 
 44. In a flash light as used by a light house? 
 
 45. Name some of the most important signs of spring, and state the class 
 or classes of symbols to which each of these belongs. 
 
 46. If it costs $3000 per year to maintain a given light house and $150,000 
 worth of property is saved by means of the light house, state the degree of 
 efficiency involved. 
 
 47. During one year the expenses of a certain business were $10,000 and 
 the returns were $16,000. The next year $1000 additional spent in advertising 
 increased the profits of the business by $4000. State the degree of efficiency 
 of the business the second year as compared with the first. State the de- 
 gree of efficiency of the additional money spent in advertising. 
 
 48. State the advantages in the use of a set of signals in playing football. 
 Also the disadvantages. 
 
 49. Discuss the principles of symbolism involved in moving pictures. Also 
 the efficiental and other advantages which result. 
 
SYMBOLISM 189 
 
 50. Answer the question "What's in a name". 
 
 Give an instance where the use of symbols leads to 
 
 51. An economy of material 54- Reuse 
 
 52. An economy of force 55. Multuse 
 
 53. An economy of time 56. Formation of a group 
 
 57. Formation of a multiplicative group system 
 
 58. Formation of an order of materials series 
 
 59. Self-developing efficiency results 
 
 State approximately the degree of efficiency involved in the use of 
 
 60. "Five" as a substitute for "four and one more". 
 
 61. 6792 for "six thousand seven hundred and ninety-two". 
 
 62. 4 -\- 2 = 6 for "four and two are six". 
 
 63. In 1,987,653 the figure 3 expresses three units and it also helps the 
 figure 5 to express tens, 6 to express thousands, etc. How many items of 
 work does it do in all? How many kinds of symbolism are combined in this 
 instance ? 
 
 64. Give an example of symbolism of the third order with a statement of 
 the efficiencies connected with it. 
 
 65. Give two examples of the use of protective coloration in animals, and 
 explain its benefits. 
 
 66. What is the smallest number of points needed in order to represent 
 a straight line? A plane surface? What is the degree of efficiency in each 
 of these cases? 
 
 Name as many advantages as you can connected with the use of 
 
 67. Maps 68. The electric telegraph 69. Wireless telegraphy 
 
 70. What is the semaphore and what principles of symbolism are em- 
 bodied in it? 
 
 71. State the different forms of symbolism which are often used in 
 making an exhibit of the expenditures of a city, and the results obtained. 
 What are the advantages of such symbolic summations? 
 
 72. Discuss the advantages in the use of a trade mark. 
 
 73. Give two examples of graphic (or geometric) symbolism. Also two 
 of algebraic symbolism. 
 
 74. Give an example where graphic and algebraic symbolism are used to 
 advantage in alternate succession. 
 
 75. State as many different kinds of symbols as you can which can be used 
 in advertising a business, and illustrate each. 
 
 76. By numbering the parts of a ship and keeping a model of the ship 
 at some shipyard, it is often possible quickly to repair the ship while at a 
 distant place. Explain how this may be done and what principles of sym- 
 bolism are utilized in the process. Name some other objects besides ships 
 to which the method is applicable. 
 
 77. State what is meant by routing a piece of work in a factory, the ad- 
 vantages involved, and how routing is aided by symbolism. 
 
 78. What kinds of symbolism are involved in social etiquette? What ad- 
 vantages result? What disadvantages? 
 
190 SOURCES OF EFFICIENCY 
 
 79. Give an example of a symbol which has erroneously come to be used 
 as a reality. 
 
 80. Discuss the disadvantages in the use of symbolisms implied in the 
 statement, "talk is cheap". 
 
 81. Give two illustrations of errors or losses arising from the use of 
 symbolisms. 
 
 82. State as many checks as you can on the abuse of symbols. 
 
 83. Express as well as you can the unused wealth of symbolic power in 
 the alphabet. 
 
 84. Explain the Dewey method of classifying books and the principles of 
 symbolism utilized in it. Indicate other fields in which this method of 
 classifying objects is used or is usable. 
 
 85. In what respects do actions speak louder than words? 
 
 86. It was the habit of Clerk Maxwell from early childhood to try to 
 discover what he called the "go", or the "particular go", of any machine or in- 
 strument which he saw. In terms of the ideas of the present chapter explain 
 the meaning of the word "go" as thus used. 
 
 87. Discuss the relation of symbolism to efficiental essence. For instance, 
 which of the two terms is broader? 
 
 88. Why should the letters in a written word be connected or run to- 
 gether, while those in a printed word are distinct? 
 
 89. Explain the principles of symbolism embodied in some system of print 
 for the blind. 
 
 90. Give an example of some kind of equivalence used as a symbol for 
 surplusage or profit. 
 
 91. Give an instance where the removal of an object or domain of ma- 
 terial to a distance aids in revealing its efficiental essence. 
 
 92. Give an instance where the form of a symbol is more efficient than 
 its color. Also give one where the reverse is true. 
 
 93. Discuss the relative values of audible and visible symbols. 
 
 EXERCISE 11 
 Review 
 
 1. Of 4000 eggs which were placed in a given incubator, 2400 hatched. 
 State the degree of efficiency involved. 
 
 2. A girl can write 15 words per minute by hand and 60 words by type- 
 writer. Express in two ways the degree of efficiency involved. State some 
 of the sources of this efficiency. 
 
 3. Make up and solve a problem of your own concerning the degree of 
 efficiency in a given case and the sources of this efficiency. 
 
 4. Instead of paying for each article as purchased, it is often an advan- 
 tage to run an account at a store, and to pay for purchases occasionally by 
 check. State the Efficients involved in the latter method. 
 
 5. What principle of efficiency is utilized in the wedge form of attack in 
 warfare? 
 
SYMBOLISM 
 
 191 
 
 6. Why is it often an advantage for a baseball player to train himself for 
 batting by swinging Indian clubs many times heavier than the bat which he 
 is to use? What principle of efficiency is involved? 
 
 7. Explain the addition of numbers in arithmetic as a combining of multi- 
 plicative groups. What advantages result? 
 
 8. Treat in like manner the multiplication of numbers. 
 
 9. Explain division of numbers with reference to the principles of groups. 
 
 10. In a certain county clerk's office under the elective system in a given 
 year the receipts were $13,968 and the expenditures $23,928. Later under the 
 appointive system the receipts were $31,355 and the expenditures $20,200. 
 Compute the degree of efficiency involved. State some of the possible 
 sources of the increased efficiency. 
 
 11. What principle of efficiency is most prominent in the following pre- 
 cept : Be sure you are right and then go ahead ? 
 
 12. What principles of efficiency are involved in the case of a straw which 
 shows which way the wind blows? 
 
 13. What principle of efficiency is involved in the use of a baggage check 
 for a trunk, and what advantages result? 
 
 14. In language study what efficiencies are involved in using the principal 
 parts of a verb as representative of all the forms of the verb? 
 
 15. A boy, sick of the hook worm disease was found to be 12 per cent 
 efficient. If a normal boy could work 8 hours a day, how long could the 
 sick boy work? 
 
 16. In the business world what are the signs of the beginning of a period 
 of commercial prosperity? State some of the advantages of being able to 
 read these signs. 
 
 17. Discuss the efficiency values of artistic surroundings in a store or fac- 
 tory, especially of those symbolisms which convey an appreciation of the 
 Efficients in some way. 
 
 18. What principles of efficiency are involved in Emerson's statement "The 
 key to every man is his thought". Give illustration of the uses which may 
 be made of this statement. 
 
 19. As a result of the use of Dalton's chemical units, exact methods of 
 making sulphuric acid have been substituted for guess work and rule of 
 thumb. State the Efficients involved and the useful results obtained. 
 
 20. Discuss the relation of the classification of objects to the principles 
 of multiplicative grouping. 
 
CHAPTER XI 
 DIRECTIVE 
 Illustrations 
 
 It has been estimated that by stocking the rivers of France with 
 black bass brought from America the value of the fish taken annually 
 from the French streams has been doubled. The transfer of the 
 eucalyptus tree from Australia to other lands as California and 
 South Africa has produced even more important results. These in- 
 stances illustrate the efficiency value of man's power to change the 
 position of objects including himself. Often this principle takes 
 various complex and apparently qualitatively different forms, such 
 as the changing of the forms of objects, the selection and cultiva- 
 tion of plants, and the cooking and preservation of their products. 
 But the primary and fundamental principle involved in all such 
 cases is that of changing the position of objects or parts of objects. 
 This principle of directive action constitutes the next fundamental 
 source of efficiency which we shall study. We shall denote it by the 
 single word directive. 
 
 The ways and forms in which this category of efficiency comes in- 
 to play are so numerous and so often complexed with other Effi- 
 cients that we shall call particular attention only to those cases where 
 the directive principle is prominent as compared with the other 
 prime sources of efficiency which are involved. 
 
 CLASSIFICATION 
 
 Objects which may be directed 
 
 Cases of directive action may be classified according to the mater- 
 ials moved or directed in them. In general we may say that any- 
 thing may be moved, changed, or directed in some respects, but no 
 object can be moved in all respects. For example we cannot change 
 the position of the moon in its orbit, but by shifting our position 
 on the earth we can change the position of the moon in the sky with 
 reference to other heavenly bodies. We cannot change the amount 
 of rain which falls from a cloud but by irrigation or the processes 
 
 192 
 
DIRECTIVE 
 
 193 
 
 of dry farming we can in part change the route by which water 
 travels from the cloud to the ocean with very beneficial results to 
 mankind. We cannot live over the past directly, or make two plus 
 two equal five, but we can do both of these things in some indirect 
 sense. 
 
 As a result of what has been said it is evident that a special 
 science of directive action may exist in each of the principal fields 
 into which human affairs are usually divided. Thus we have civil 
 engineering, mechanical engineering, electrical, social, educational, 
 and similar departmental species of management. 
 
 Other methods of classifying directive acts are, however, more 
 important than this for our purpose. 
 
 Directive Agents 
 
 One of these is a grouping of directive cases according to the 
 directive agents, that is, the directors involved. All the various 
 forms of what is called a living matter have some directive power 
 both over themselves and over some objects external to themselves. 
 
 Thus various plants are able to turn themselves (as a whole or in 
 part) toward the sun (heliotropism), or toward moisture (hydro- 
 tropism), or toward the earth (geotropism), and in other ways. 
 Highly specialized forms of such powers are illustrated by the 
 sensitive plants and the Venus flytrap. Plants also have power to 
 draw food from the earth and air, and also to move such food for 
 considerable distances in opposition to the force of gravitation. Im- 
 portant special cases are the power which protoplasm has to direct 
 sunlight and which certain plants have to fixate nitrogen. 
 
 Individual animals have many different ways of moving themselves 
 and external objects. A primitive case is that of the sea urchin 
 covering itself with sea weed to protect itself from its enemies. 
 
 An aggregate of individuals may also constitute an important 
 directive agency. Examples are a flock of birds, a pack of wolves, 
 a society, nation, or corporation. 
 
 Similarly it is often useful to regard certain parts of individuals as 
 independent directors. Examples are the cells and organs in a living 
 body, and the different so-called faculties of the mind. 
 
 More abstract entities also have what constitutes for our purpose 
 directive power; illustrations of these are the spirit of the age, the 
 weltgeist, or any aggregate of efficiency agencies. 
 
194 SOURCES OF EFFICIENCY 
 
 Also in efficiency processes allowance must be made for unknown, 
 or imperfectly known, or even transcendental efficiency agencies. 
 
 It is important to note in this connection the wide range in direc- 
 tive powers both in the individual agent, and in different directors 
 when compared with each other. The oyster when young has con- 
 siderable self-directive power, but when mature has very little. 
 With man the reverse is true. 
 
 In self-directive the material moved and the agent are one. 
 
 Directive Acts Classified according to Form 
 
 Most important of all for our purpose is the classification of 
 directive acts according to their form. 
 
 A simple case of spatial directive is that of changing the position 
 of an object. Changes in the position of the parts of an object may 
 result in a change of shape. With regard to the category of space 
 (or quantity) a directive act may also be narrow or comprehensive. 
 More important still it may be a separating or a collecting act ; that 
 is, it may be an act of analysis or one of synthesis. It may be partial 
 in that it is directive of some part of an object, or in that it is a 
 transfer of an object in some specifically limited way. It may be 
 indefinite as when a situation is merely agitated or stirred up, the 
 motive being a vague hope that something useful may result; or 
 definite, as when every step and the reason for it are carefully 
 calculated. 
 
 An act of directive may be characterized according to the cate- 
 gory of number in various ways as by the number of objects moved, 
 the number of directors, or the number of parts in the given act. 
 
 A simple case of a temporal directive act is the transfer of an 
 object from one point in time to another. An example is the saving 
 of money to be used at some future date. A much broader case is 
 the conservation of national resources. With respect to time a direc- 
 tive act may also be brief and temporary, or of long duration. The 
 adjectives prophetic, preventive, or well timed are also often applic- 
 able. An important temporal species is that termed initiative, that 
 is, the act or power of making a start (or doing all that the be- 
 ginning of an act implies) under any given circumstances, especially 
 those which are difficult. 
 
 As to motion and force, directive acts may be characterized as 
 feeble, delicate, energetic, automatic, slow, or swift. 
 
DIRECTIVE 195 
 
 An important species is what may be termed reciprocal directive. 
 In the simplest form of this case each of two agents moves, directs, 
 or influences the other or something belonging to the other. A large 
 part of trade, exchange, and commerce belongs to this form of 
 directive action. 
 
 With respect to the categories of mind, various cases of directive 
 may be characterized as conscious, unconscious, and subconscious ; 
 or even voluntary and involuntary. Thus certain kinds of personal 
 influence are unconscious and often involuntary. 
 
 As to quality a directive process may be homogeneous or hetero- 
 geneous either as to material, directors, or form. It may also be 
 continuous or discontinuous. An important case of heterogeneous 
 directive is that in which the result is noticeably different in some 
 respect from the datum, as when carbon is converted into diamonds, 
 heat into light, or the useless into the useful. 
 
 Directive in the Form of Inaction 
 
 Another important species of directive is that which may be 
 termed negative. This consists essentially of absence (in whole or 
 part) of action on the part of the agent, or in his motion away from 
 an object, or in his keeping an object from motion, while at the 
 same time some other process which in the end will prove beneficial 
 is allowed to go on. Special cases of negative directive are inaction, 
 patience, persistence, removal, prevention, rejection, withdrawal, 
 self-sacrifice, restraint. The -utility of negative directive is illus- 
 trated by Napoleon's maxim never to disturb an enemy while he is 
 making a false move, by the frequent success of what is called the 
 Fabian policy, and by all cases of the removal of waste. 
 
 Grouped Directive Acts 
 
 It is often advantageous to perform directive acts in groups. 
 Thus in a well organized shop by pulling a single lever many 
 machines may be set in operation simultaneously. A case of unit 
 and multiplier directive is that of changing the course of an entire 
 vessel by a movement of the rudder only. Also when a ship is 
 steered in the region of a favorable trade wind, owing to the con- 
 tinued action of the wind the initial directive act receives a multiplier 
 of still higher order. When a gun is fired the directive work of 
 aiming the gun and pulling the trigger is multiplied in complex ways. 
 
196 SOURCES OF EFFICIENCY 
 
 It is even more advantageous to combine directive acts in multi- 
 plicative group systems. An important case is that of superintending 
 a group of persons each of whom exercises directive functions over 
 a group of other persons and so on. Illustrations are the super- 
 vision and direction of an army by a general, of a railroad by its 
 head, and of the government and people of the United States by 
 its president. 
 
 Other less homogeneous cases of multiplicative group directive 
 are the work of irrigating a large tract of land, or the shaping of 
 public opinion by means of a variety of agencies. 
 
 Directive Acts of High Order 
 
 It is an important aid to efficiency to be able to recognize a 
 given directive act or process as of high or low order, and 
 more important still to be able to determine its exact place in a 
 given scale. In such a determination various factors must be con- 
 sidered. Thus an act may be of high order if it moves highly 
 efficient material, as the germs, sources, or underlying causes of 
 things, or if it influences leading or governing men. This kind of 
 directive is recognized in the proverb, the hand that rocks the cradle 
 moves the world. 
 
 A case of somewhat different kind is the control of the business 
 of a country maintained by means of a domination of its transporta- 
 tion routes. 
 
 A more abstract case and often a very useful one is directive of 
 the marks or symbols which represent objects instead of the objects 
 themselves. 
 
 Highly efficient directive is also often obtained by moving an 
 object to an apex or controlling point in a system or domain. Thus the 
 dog jumps at the throat of his victim, and the bee tries to sting the 
 eye. Von Moltke went from Denmark to Berlin in order to practise 
 the art of war. Jesus went to Jerusalem that he might the better 
 influence the religious thought and practice of the world. 
 
 Other directive acts of high order are those of converting what is 
 harmful or useless into what is valuable. On this same plane of 
 high efficiency are directive acts which cost little or no effort, ex- 
 amples being negative directive and results obtained by unconscious 
 influence. Acts which proceed in an automatic or self -regulating 
 way are of the same high grade. In such cases we are often utiliz- 
 
DIRECTIVE 
 
 197 
 
 ing work done by other men at some distant time or place or in 
 some obscure way. 
 
 On the highest plane of all perhaps are directive acts which produce 
 groups or other fundamental efficiency machinery of some kind. 
 Several of the above elements of high efficiency may of course be 
 present in a single act or process. 
 
 From the preceding discussion it follows that directive acts in a 
 given department may often be arranged as a multiplicative series. 
 Thus in military evolutions we have tactics and strategy, the terms 
 being placed in ascending order. In like order in agriculture are 
 found the cultivation of nearby and familiar plants ; the search for 
 and cultivation of the best existing plants to be found anywhere in 
 the world ; and the breeding of new and better species of plants. 
 
 In work in general we have as a multiplicative series, imitation, 
 invention (or discovery), creation. 
 
 Indirect Management 
 
 With respect to externality directive acts may be characterized 
 as direct or indirect. An example of indirect directive is the removal 
 of an obstacle in order that another object may be moved. A still 
 more indirect case is that of undermining an obstacle in order to 
 remove it. 
 
 Another form of indirect directive is that of moving an object by 
 means of power exerted through some auxiliary object, as when a 
 man moves himself by moving the locomotive on which he is stand- 
 ing, or by attaching a weight to a window sash utilizes at a later time 
 (when raising the sash) the energy generated by the falling of the 
 sash. Another form of directive characterized by externality is 
 work performed on a large scale. 
 
 Complex Species of Directive 
 
 Evidently the above species of directive may be compounded and 
 complexed in many ways. Examples of complex directive are any 
 comprehensive piece of engineering, the directive processes involved 
 in agriculture, or in the manufacture of various articles, in education, 
 or in the various departments of life and work in a highly civilized 
 community. Plainly the work of the so-called efficiency engineer, 
 when fully developed, is not only of far-reaching importance but of 
 cumulative complexity. 
 
198 SOURCES OF EFFICIENCY 
 
 EFFICIENCY RESULTS OF DIRECTIVE ACTION 
 
 General Illustrations of Uses of Directive 
 
 If we bake clay and thereby make a dish, we perform a directive 
 act which has a variety of advantageous results. One result is the 
 separation of the moisture from the clay (diversity), with the con- 
 sequence that the dish may be permanent in shape (uniformity). 
 Hence result other diversities such as the separation of food into 
 portions and of each portion from the table and other contaminat- 
 ing matter. Also the dish thus formed is capable of much reuse. 
 A still more general efhciental result is an increased refinement in 
 the multiplicative group organization of society. Looked at from 
 another point of view, the making of dishes leads to an improve- 
 ment in human health, an increase of happiness, and often to pro- 
 longed life. The latter class of results is however largely 
 determined and dominated by the former, and primary attention 
 should therefore be paid to the former class. 
 
 A Means to Group Formations 
 
 A directive act may result in the formation of a group in a single 
 and direct way, as when a useful assemblage of articles is obtained by 
 packing a number of articles in a satchel. But directive acts always 
 result in group formations in much more general and manifold ways. 
 Thus when any object is moved from position A to position B the 
 result will be the separation of the moved object from all points and 
 materials near A, and also its greater proximity to those near B. 
 Hence many groups will be dissolved and others will be formed ; or 
 stating the matter more generally, many new uniformities and diver- 
 sities will be generated which will serve as the raw material for 
 group formations. 
 
 It is also to be noted in this connection that the selection of an 
 article means the rejection of all other articles, and that the forma- 
 tion of one group means the formation of an infinite negative or 
 matrix group. 
 
 Economies 
 
 In various cases the result of the above process is the formation 
 of groups which are especially efficient in different ways. Thus im- 
 portant economies may result. An example is the utilization in gas 
 engines of the gases given off by a blast furnace with the consequent 
 
DIRECTIVE 
 
 199 
 
 economy of fuel in the factory. When salmon are left to propa- 
 gate themselves in a state of nature more than 98 per cent of the 
 ova or young fish are destroyed by other fish or by birds. In 
 artificial hatcheries only 15 per cent are lost. Or the result may 
 take the form of a saving of time. Thus it is estimated that Luther 
 Burbank in the breeding of new plants has attained results in a 
 single life time which, if left to the processes of nature, would have 
 required millions of years. 
 
 A Means to Other Efficients 
 
 In like manner the gain may take a unit and multiplier form. 
 Thus when a window sash is raised in order that a breeze may blow 
 through the room, the work of raising the sash may be said to be 
 multiplied by the breeze. Telegraph operators express a like result 
 when they say that multiplex telegraphy produces "phantom lines" 
 of wire on which messages are carried. 
 
 The application of forced draft to a tubular boiler produces both 
 a concentration of motion in a small portion of time (increased 
 velocity) and also a concentration of force in a small portion of 
 matter. 
 
 The importance of the diversity and uniformity results of di- 
 rective is illustrated by chemical analysis and synthesis, and the 
 products obtained by means of them. Examples are the artificial 
 production of camphor, quinine, and salvarsan, the specific for 
 syphilis. An important special form of uniformity which may 
 result from a directive action is that obtained by dovetailing to- 
 gether two or more irregular objects so as to make one that is uni- 
 form in some way. 
 
 The result of directive . may also be the production of an article 
 of a higher plane of excellence in an order of materials scale. Ex- 
 amples are the superior qualities of cheese, butter, and tea obtained 
 by the careful manipulation of ferments. 
 
 Directive acts or processes may result in the formation of a new 
 and more powerful symbolism or calculus, or it may open the way 
 to other directives. Thus the manufacture of iron supplied iron as 
 an aid in later directive processes. Or it may produce new extern- 
 ality. Thus travel gives breadth of view and knowledge of new 
 auxiliaries. 
 
200 SOURCES OF EFFICIENCY 
 
 Self-developing Fruitage 
 
 The dialectic fruitage of directive is especially prominent. Thus 
 the man who first combined steel and concrete could not foresee all 
 the advantageous results which would follow. In a much more 
 fundamental field those who first obtained mathematical results by 
 moving geometric objects and applying them to each other could not 
 forecast all the principles of geometry which would be discovered as 
 a consequence and the many applications of these in engineering and 
 various departments of science. 
 
 In this connection the fact is to be emphasized that in directive 
 acts we are either dealing with material objects or with entities the 
 substantial aspect of which has been made prominent. Hence the 
 result of a directive act has that peculiar permanency which is 
 characteristic of the categories of materiality and substance and 
 which often constitutes a new dimension of efficiency. Actually 
 performing a process (as compared with the theoretical achievement 
 of results) also has a valuable reflex effect on the doer. He is 
 compelled to realize and observe limitations in the world about him, 
 and learns to recognize and avoid certain common errors. Also 
 owing to limitations in his hands, eyes, and nerves, and to other 
 limitations in his powers of conscious grasp, and owing to still 
 others in objects, he must divide a concrete directive process into 
 parts and perform the whole as a linear or semi-linear series or 
 group system. He thus acquires group neighborhood symbolism and 
 other habits adapted to the efficient manipulation of such a series. 
 With practice these powers in time often become so well disci- 
 plined that they adjust themselves to given conditions more or less 
 automatically. 
 
 Transcendent Results 
 
 Many of the results obtained by the directive method are absolute 
 or infinite in the sense that in value they immeasurably exceed the 
 data employed. In a sense also they are transcendent in that they 
 cannot be analyzed so as to be statable in terms of the data or of 
 other Efficients. Also some of them are unique in that they cannot 
 apparently be obtained without the use or aid of directive. 
 
 As illustrations we have the saving of life by the directive use of 
 mosquito netting to exclude the malaria carrying mosquito; or by 
 the use of antiseptic surgery; and the making visible of otherwise 
 
DIRECTIVE 20I 
 
 invisible objects by the invention of the microscope and telescope. 
 A further illustration is the artificial fertilization of the eggs of 
 certain species of animals by the use of chemicals, or even by the 
 prick of a needle. 
 
 Hence many directive acts become in effect what may be termed 
 acts of creation. Thus Watt for efficiency purposes created the 
 steam engine. Afterward the use of the steam engine gave coal most 
 of its value. So lignite which when burned directly is relatively 
 worthless becomes valuable by being converted into gas. 
 
 Special Fruitage of Each Species of Directive 
 
 Each particular species of directive action has its own peculiar 
 efficiency functions in addition to many of the more general ones 
 given in the preceding discussion. One of the most important 
 forms of directive in this respect is the species termed initiative. 
 An act of this kind gives a certain priority in time to one's work 
 and this priority often means an inclusiveness or groupism which ulti- 
 mately leads to many valuable results. Initiative also means a break- 
 ing into new ground and hence a new diversity, often a new unit, 
 radically new externality, and other efficiency materials or results. 
 
 Advantages of Management in Each Department of Life 
 
 An important way in which to realize the vast amount of fruitage 
 already obtained by the use of the directive principle, as well as to 
 appreciate the complex forms in which these fruits appear, is to try 
 to grasp the results from this source in each department of life and 
 activity. For instance the value of directive in agriculture may be 
 realized in a general way by raising the question as to what would 
 be left of this department of activity if all directive were eliminated 
 from it. In manufacturing it is estimated that the one form of 
 directive called scientific management, alone has doubled the output 
 obtained from a given number of workmen in establishments where 
 it is used. A more comprehensive way of realizing the sum total 
 of the values of directive is to note that human progress throughout 
 has been marked by an increasing amount and progressively higher 
 order of management. For instance each epoch of history has been 
 a new epoch in directive processes, examples being the periods 
 marked by man's control of stone, wood, organs of speech, iron, 
 fire, and electricity. 
 
202 SOURCES OF EFFICIENCY 
 
 Looking at the matter from another point of view it has been 
 stated as a law that "other things being equal, progress is in propor- 
 tion to control". Thus man's control in the fields of chemistry and 
 physics being greater, progress in these sciences has been much 
 more rapid than in botany, zoology, psychology, and sociology. 
 Similarly the supremacy of the Anglo-Saxon in the world's civiliza- 
 tion at the present time is largely due to the great energy which is 
 characteristic of this race, and which is especially noticeable when 
 contrasted with oriental fatalism. 
 
 Words Illustrating Value of Directive 
 
 In grasping the efficiency importance of the directive principle, it 
 is also an aid to note the values connected with certain special and 
 relatively familiar species of directive as analysis, synthesis, substi- 
 tution, utilization, management, engineering, superintendence, trade, 
 exchange, control, and executive work in all forms. 
 
 The increasing employment of directive and the growing appre- 
 ciation of its value are indicated by the increasing use of such 
 terms as social engineer, educational engineer, light, chemical, or 
 efficiency engineer. 
 
 Limitations to Utilities in Directive 
 
 Certain limitations in the fruitage of directive acts arise from 
 man's circumscribed control of objects. Illustrations are man's ina- 
 bility to cause rain in the time of droughts, or to compel a horse to 
 drink though we can lead him to the water. 
 
 The direct losses connected with cases of directive take two 
 principal forms, thus we have 
 
 ( i ) Unconscious or unintentional losses, such as are indicated by 
 words like mistake, and often also by the words misdirect, misuse, 
 misapply. 
 
 Illustrations are the mistakes made in introducing the gipsy moth 
 and the English sparrow into the United States, and wholly uncon- 
 scious errors like that of transporting the phylloxera to France and 
 the Hessian fly to Great Britain. 
 
 Losses of this class may take many special individual specific 
 forms, such as excessive directive (as in meddling, domineering, 
 etc.) ; or too small an amount of directive; or in directive of a low 
 
DIRECTIVE 203 
 
 order, where a high order is possible, as in the use of war instead of 
 arbitration. 
 
 (2) The second important form of evils connected with directive 
 are conscious and intentional misuse and misdirection, as in swind- 
 ling, cheating, corrupting, and similar acts and processes. 
 
 Often classes (1) and (2) are combined in cases which are 
 difficult precisely to analyze, as in many forms of sin and crime. 
 
 The Hand of Efficiency 
 
 However after full allowance for all limitations and drawbacks 
 has been made, we still find a high surplusage of value in directive 
 acts and processes. This we may sum up in the statement that just 
 as symbolism is the tongue of efficiency, so directive is the hand of 
 efficiency. 
 
 EFFICIENCY ANALYSIS 
 
 From the preceding discussion it follows that directive is essen- 
 tially a group-making process, but that it is this process considered 
 from a peculiar and limited point of view. 
 
 Directive as a Group-making Process 
 
 Thus as compared with reuse (1) in directive special attention is 
 paid to the beginning or incipiency of group formation, the process 
 of use and the matter of results being often left in the background 
 for the time being: 
 
 (2) Directive also, to a greater extent than reuse, implies or is 
 exerted in opposition to resisting forces or conditions ; 
 
 (3) Hence directive lays emphasis on personality and especially 
 on the will exerted in overcoming difficulties. Hence courage, per- 
 severance, knowledge of human nature and similar qualities are 
 specifically prominent in executive work as compared with other 
 group work. 
 
 In other words directive is the group-making process considered 
 from the incipient, concrete, subjective side. 
 
 In this separation of the directive part from the rest of the group- 
 making process, the principle of diversity is utilized. This has the 
 advantage of making it possible to group these new incipiencies and 
 treat them in various efficient ways as by applying externalities to 
 
204 SOURCES OF EFFICIENCY 
 
 them. Hence in the end it adds greatly to the efficiency of the 
 group principle in its various forms. 
 
 Other Elements in Directive 
 
 Certain other special sources of efficiency in directive should also 
 be mentioned. 
 
 For instance, motion implies space, and a knowledge of the 
 properties of space, especially of its efficiency properties, is often a 
 source of power in carrying on directive processes. 
 
 Similarly it is important to recognize that directive implies time 
 in the general way in which all motion implies it, and also in the 
 special way indicated by the word incipiency. 
 
 Limitation is also present in the form of opposing forces or condi- 
 tions. Hence a knowledge of force and limitation may be a source 
 of added efficiency in directive processes. 
 
 Unique Element 
 
 Also there is present in directive a unique element, not statable, 
 in terms of the other Efficients or categories. This is present par- 
 ticularly in the ethelistic element involved in directive. We glimpse 
 this element in the power which living matter has to initiate motion, 
 to move itself, and in what we call freedom of the will, all difficult 
 of analysis, yet all important possible sources of new efficiency at 
 any time. 
 
 Definitions 
 
 It will be well also to define as closely as we can certain more or 
 less familiar species of directive to which we shall have occasion to 
 refer at times. 
 
 Initiative is a species of directive in which the ideas of incipiency 
 and usually of opposition are emphasized, all other elements being 
 left vague and indefinite. 
 
 Substitution is the dual directive act of removing one object and 
 putting another in its place. 
 
 Utilization is the act of transforming that which has been unused 
 into something directly useful. 
 
DIRECTIVE 205 
 
 METHODS OF APPLICATION 
 
 The most fundamental way in which to utilize directive to the 
 utmost as a source of efficiency is to realize and apply the fact that 
 directive is essentially groupish and multiplicative in nature. Many 
 details of this method suggest themselves at once as a result of the 
 preceding discussion, but particular mention may be made of the 
 following. 
 
 The Multiplicative Principle an Aid in Many Ways 
 
 The multiplicative aspect of the matter is helpful in realizing the 
 great variety of objects or entities which may be directed, the many 
 different routes and ways in which they may be moved, and also in 
 holding all these data in mind in a panoramic form in readiness for 
 use as opportunity may arise. This principle also enables us to 
 realize and anticipate the extreme power and extraordinary results 
 of directive action in its developed forms. It should also cause us 
 to keep in mind the possibly great destructiveness of unwise direc- 
 tive. Any artificial method of work, even that of the cultivation of 
 plants, particularly on a large scale, is exposed to great dangers 
 since as some one has said such a process upsets the balance of 
 nature. In other words, in all directive work the universe is to be 
 regarded as in an almost even balance between gigantic opposed 
 multiplicative systems, and hence as composed of enormous oppor- 
 tunities and of equally great dangers. 
 
 Adaptation to Special Situations 
 
 In certain situations careful study needs to be made in order to 
 determine the most efficient available species of directive action. In 
 some cases only vague directive such as merely breaking up or 
 shaking up a situation is possible, more definite action being post- 
 poned till the immediate results of such incipient action become 
 apparent. Another limited form of action is that which is implied 
 in the injunction to cast one's bread upon the waters. Among the 
 most important but most difficult species of directive are those in- 
 volved in the management of other workers, in the full utilization of 
 the power peculiar to each individual, in eugenics, and in the equit- 
 able distribution of the profits of modern methods of work. Knowl- 
 edge not only of the general principles of efficiency but of a great 
 variety of technical facts is called for in dealing with such problems. 
 
206 SOURCES OF EFFICIENCY 
 
 Certain cases of definite, stubborn, and wide-spread limitation, 
 such as the fact that sunshine reaches the earth in a scattered 
 diffused form., must often be dealt with in a number of different 
 directive processes. The investigation of methods of meeting such 
 cases takes the form of a study of sciences like physics, chemistry, 
 and agriculture. Similarly a knowledge of the special limitations 
 and possibilities of reciprocal directive, as in exchange and com- 
 merce, requires a knowledge of the technical facts and laws of 
 psychology and sociology. 
 
 Relations of Action and Inaction 
 
 In this connection attention should be called to the importance of- 
 studying the relation of negative directive (or inaction) to positive 
 directive processes. Efficiency is often gained by knowing laws of 
 limitation and the peculiarities of special situations well enough to 
 be able to determine when to apply active directive and when to 
 leave matters to the dialectic processes of nature. Often it is best 
 to use these two methods in alternate succession. As an illustration 
 we have the fact that it is often a source of efficiency not to try at 
 first to make one's work too finished and complete, but to leave 
 something to the self-developing power of circumstances, and later 
 to apply methods of correction and adjustment. 
 
 A special form of combined positive and negative directive work 
 is that in which the directive process has in large part become auto- 
 matic and self-regulative. As has been pointed out elsewhere such 
 forms are of a high order of efficiency. 
 
 Superiority of Constructive Work 
 
 Particular attention should also be called to the fact that in 
 directive processes constructive work should always if possible be 
 dominant, and destructive work such as punishment and surgery, 
 incidental and secondary. This principle constitutes a directive of 
 directive in that it is a directive of the highest species of this 
 efficiency instrument to the first place. 
 
 Externality as an Aid in Directive 
 
 All kinds of externality are particularly useful in directive pro- 
 cesses but especial mention may be made of the freedom and scope 
 given to directive methods by using abstract externality in the form 
 of a broad view of things. 
 
DIRECTIVE 
 
 207 
 
 In particular many efficiency processes should be organized so as to 
 produce not only the result immediately called for but also a surplus, 
 often a continuous stream of results, and arrangements made to 
 direct this surplus to the apices of other efficiency processes. 
 
 Ideal Species 
 
 In general the entire body of the Efficients when organized to- 
 gether form the most powerful and comprehensive of all aids in 
 directive work. Or to state the matter in a still more general way 
 the ideal form of the instrument under consideration is the directive 
 of efficiental data in efficiental ways for efficiental ends. 
 
 Recapitulation of Chapter 
 
 To sum up the chapter, one of the most obvious methods of ob- 
 taining better results in any situation is that of directive action or 
 management. Simple as this method often seems, it nevertheless 
 needs careful analysis and study in order to realize even its main 
 efficiency possibilities. 
 
 Species of management may be classified according to the various 
 kinds of material moved, or according to the various agencies which 
 move objects, or with respect to the ways in which objects may be 
 moved, or according to the various results aimed at. Individual 
 mention may be made of such special forms as inaction, initiative, 
 and indirect management. 
 
 Directive action not only has such palpable uses as the utilization 
 of otherwise unused materials and the prevention of various kinds 
 of waste, but it also has the more fundamental value of leading to 
 the formation of groups, systems, and various other Efficients, and 
 hence to the efficiency results characteristic of each of these. In a 
 peculiar sense it thus leads to self-developing results and often to 
 transcendent fruitage. Each special kind of directive produces its 
 own peculiar efficiency results. Hence also directive finds a special 
 field of application in each department of life. 
 
 The same general principles which have been laid down in pre- 
 vious chapters as to the best methods of using other Efficients, ap- 
 ply also to directive. In addition, special attention is here called to 
 the importance of a careful study of action and inaction in any 
 field of operations, and also to the desirability of making con- 
 structive processes as dominant as possible over those which are 
 destructive. 
 
208 SOURCES OF EFFICIENCY 
 
 EXERCISE 12 
 
 State the class or classes of directive action to which each of the following 
 instances belongs : 
 
 1. Winding up a watch 4. The manufacture of shoes 
 
 2. Pruning a tree 5. The choice of one of two objects 
 
 3. Vaccination 6. Physical exercise 
 
 7. Use of lieutenants. 
 
 8. Exchange of goods with a foreign country. 
 
 9. Changing the direction of a moving object. 
 
 10. Directing sheep by directing their leader. 
 
 11. The use of a furnace with a thermostat attached. 
 
 \2. Introduction of the gipsy moth into the United States. 
 
 13. Making a woman's hat out of parts of old hats. 
 
 14. Damming of the Mississippi River and generation of electricity by 
 the water power thus made available. 
 
 State as many as you can of the different kinds of directive involved in 
 the work of a 
 
 15. Farmer 17. Editor of a paper 19. Manager of a factory 
 
 16. Teacher 18. Sculptor 20. President of the United States 
 
 Give two examples of each of the following species of directive action : 
 
 21. Imitation 26. Heterogeneous 31. Of high order 
 
 22. Prophetic 27. Negative 32. Indirect 
 
 23. Indefinite 28. Grouped 33. Substitution 
 
 24. Reciprocal 29. Multiplicatively grouped 34. Utilization 
 
 25. Homogeneous 30. Of low order 35. Exchange 
 
 36. Complex 
 
 37. Give a multiplicative series of methods of starting a fire. 
 
 38. State in what ways a mountain may, in effect, be removed by man. 
 
 39. Point out the elements of directive in the use of a tireless cooker 
 and the advantages which result. 
 
 40. Give an example of a process of directive which has been cumulatively 
 complex in its development. 
 
 41. State, as far as possible in efficiental terms, the advantageous results 
 of each of the cases of directive mentioned in Exs. 1-14. 
 
 Give an instance in which an important result of the following kind has 
 
 been obtained by the use of directive : 
 
 42. An economy of force 47. Of a diversity 
 
 43. An economy of time 48. The saving of life 
 
 44. A concentration of force 49. An externality 
 
 45. Formation of a group 50. A loss 
 
 46. Of a uniformity 51. Self-developing results 
 
 52. Point out the advantages and the disadvantages in carrying a number 
 of keys on one ring. 
 
 53. Give an example where intense heat is obtained by a directive process. 
 
 54. Also one where intense light is thus obtained. 
 
DIRECTIVE 
 
 209 
 
 55. Discuss the principles of directive involved in a use of a portable 
 saw mill. 
 
 56. Also in making and using an artesian well. 
 
 57. State the different kinds of directive action involved in transforming 
 an object. 
 
 58. Give an example in which the efficiency of a directive process is in- 
 creased by the use - of diversity. 
 
 59. By use of uniformity. 
 
 Give two examples in which directive action is restricted in itself or in 
 its results by limitations in : 
 
 60. Objects 61. Directors 
 
 62. Give some of the advantages which result from the use of artificial 
 light. 
 
 63. Give two examples where a directive process has been aided (or 
 might be improved) by the use of an improvised symbolism. 
 
 64. Give an example of a directive process which has been improved by 
 being made at least partly automatic. 
 
 65. State the advantages of having the reserve of supplies in a factory 
 kept up automatically by the use of a predetermined maximum and minimum. 
 
 66. Give an illustration of the value of partial or entire inaction with 
 reference to a given process. 
 
 67. Give an instance where action and inaction are combined advantage- 
 ously in alternate succession. 
 
 68. Discuss the advantages which result from the fact that man is now 
 able to transport live fish from any one part of the inhabited world to any 
 other part. 
 
 69. State the ways in which a wide knowledge of the state of the market 
 for any given article aids in the distribution and sale of the article. 
 
 70. Why is it often more advantageous to move a threshing machine to 
 wheat stacks rather than to move the stacks to the machine? Give two 
 other illustrations of efficiency obtained by the directive method here involved. 
 
 71. Discuss will power as an element of success. 
 
CHAPTER XII 
 KINEMATIC AND DYNAMIC 
 Illustrations 
 
 At the conference on Scientific Management held at Dartmouth 
 College in the year 191 1, an efficiency engineer stated that in a cer- 
 tain factory which he had been called on to inspect, he had found one 
 machine whose speed he was able to increase forty-four fold. In- 
 creasing the speed of a machine in this way evidently meant that 
 the capital invested in the machine and the wages of the workman 
 operating it were both made 44 times as productive as before and 
 meant also an increase in efficiency in the whole establishment in 
 other ways. 
 
 On another occasion an analytic examination of the work of a 
 bricklayer showed that the workman in laying a brick was making 
 18 distinct motions such as stooping down to pick up a brick, lifting 
 it, turning it over to examine it on all sides, etc. ; that this number 
 of motions might be reduced to 5 ; and that in this way the number 
 of bricks laid by the workman in one hour could thus be increased 
 from 120 to 350. In this case the motions made by a workman in a 
 given operation constituted a convenient symbol for the energy and 
 time expended by him, and a convenient means by which to study 
 and increase the degree of efficiency in his work. These illustrations 
 show how the study of motions as such may be an important source 
 of efficiency. 
 
 Again man in propelling a canoe by a paddle necessarily expends 
 considerable muscular energy. When for this muscular power some 
 prehistoric savage substituted wind energy applied by means of a 
 sail, he adopted an efficiency process of the first importance, viz. : the 
 utilization by man of the forces and motions in the external world. 
 For such utilization not only means an economy of human energy 
 and the employment in higher fields of the power thus saved, but 
 also greater velocity, larger and more concentrated masses of 
 energy, and power in more manageable form. The instance just 
 given illustrates the fact that the study of force as such, particularly 
 forces in the outside world, may be an important source of efficiency 
 to man. 
 
KINEMATIC AND DYNAMIC 21 1 
 
 General Statement 
 
 Hence it will be a prime source of efficiency temporarily to isolate 
 motion, speed, and force as a related group, to objectify them, and 
 to concentrate attention upon them with a view to developing them 
 to the utmost as factors in obtaining results. 
 
 At the outset it will be convenient to observe that motion for our 
 purpose means necessarily a regrouping in several ways ; that speed 
 means a concentration of motion with respect to time; and that 
 force is a useful externality or handle by which to control motion 
 and its results. It is difficult to discriminate a motion in all cases 
 from the force or forces connected with it. But in many instances it 
 will be an aid in obtaining the utmost efficiency from the categories in 
 hand, to treat as more or less pure or independent, those motions 
 where the forces involved are small or obscure, as well as those 
 which are logically separable from the forces producing them. 
 
 CLASSIFICATION OF MOTIONS 
 Classification of Objects which move 
 
 Motions may be classified by grouping them according to the 
 objects which move. Thus we may have motions of organic or 
 inorganic objects; of large, small, light, or heavy objects; of mater- 
 ial things ; or of ideal entities. Illustrations of the last class named 
 are the growth of a reputation, spread of an idea, or a motion like 
 that recognized in the phrase, quick as thought. 
 
 In this connection it is to be noted that all directed objects (see 
 the preceding chapter) are in a state of motion but that many other 
 motions are, for the present at least and in certain ways, best treated 
 as independent of any directing power. As examples of the latter 
 class we have the motions of the atoms in a molecule and of the 
 solar system through space, and a host of motions intermediate 
 between these two in some respect. 
 
 It should also be observed that every object moves in some way 
 or ways but not in all ways. Hence we have the general statement, 
 useful at least as a first approximation, that motion is the normal 
 state of the universe, and that any state of apparent rest is a case 
 of motions which cancel each in some respect. 
 
212 SOURCES OF EFFICIENCY 
 
 Classification of Forms of Motion 
 
 Motions may also be classified according to their forms or other 
 abstract individualizing qualities. In this respect the different 
 species of directive given in the preceding chapter are also different 
 cases of motion. But owing to the peculiarities of motion and force 
 as sources of efficiency when considered independently of human 
 originating power, certain of these species become of such peculiar 
 importance as to be worthy of special mention. To this list some 
 new species should also be added. 
 
 For instance particular mention may be made of wave or alter- 
 nating motion. This species is of such importance that it will be 
 treated at length in a separate chapter (see p. 230). 
 
 It is also important to note that spatially all motions may be 
 regarded as compounded of two fundamental species, viz. : motions 
 of translation and motions of rotation. 
 
 Attention should also be called to hidden or obscure motions. It 
 is sometimes of service to group such motions according to the 
 causes which make them invisible. Among these causes are small- 
 ness of the moving object, extreme slowness or quickness of the 
 motion involved, great distance of the object, intervening opaque 
 materials, and lack of color in, or the ideal nature of, the moving 
 object. 
 
 Groups of Motions 
 
 Motions may be classified in different ways with reference to the 
 group principle. Thus a resultant motion is a highly fused group of 
 motions. 
 
 Of especial importance are certain cases of multiplicatively 
 grouped motion. An instance is a motion obtained by gearing a set 
 of wheels so that the cogs on the rim of each wheel act upon the 
 cogs on the hub of the rest. Such a system may be used to produce 
 great velocity as in the apparatus used to measure the velocity of 
 light, or to produce slowness or uniformity as in the mechanism of 
 a clock. Another form of multiplicatively grouped motion is il- 
 lustrated in the swinging of a golf club, the body in this case being 
 treated as jointed from the toes up, each part rotating upon the 
 end of the part that precedes it in order. Still another species 
 under this general class is the combination of motions embodied in 
 the sun, planets, and satellites forming the solar system. 
 
KINEMATIC AND DYNAMIC 
 
 213 
 
 A case of multiplicatively grouped motion widely different from 
 the preceding is that of a propagation of some sort through any 
 genetic multiplicative group system as the transmission of a charac- 
 teristic through several generations of a person's descendants, or 
 that of the spread of a motion from the apex of any group system 
 throughout all its suborders, as when a piece of information is con- 
 veyed from the commanding general throughout an army. 
 
 Motions of High Order 
 
 For our purpose it is also important to notice that certain motions 
 are higher than others in what may be regarded as an order of 
 materials scale. Thus a motion may be of high order owing to its 
 position in a multiplicative group system of motion, an example being 
 the motion of the end of a golf club. Another important case is 
 motion of material of a high order even when the actual concrete 
 velocity is small. Thus with respect to the progress of the world, 
 the motion of Jesus as he toiled up Calvary was immeasurably more 
 swift than that of a driver in a Roman chariot race. 
 
 Complex Motions 
 
 The number of ways in which motions may be combined and 
 complexed is without limit. Instances are the motions involved in 
 a widespread storm, in a war, or in a period of human progress. 
 
 CLASSIFICATION OF FORCES 
 
 For our purpose it is useful to regard forces as grouped in three 
 different ways, viz. : 
 
 (1) According to the substances in which they are found or 
 contained or by which they are conveyed; 
 
 (2) According to the species of motion which they produce; 
 
 (3) With respect to other results produced by them. 
 
 Sources of Forces 
 
 Viewed in the first of these ways, particular groups of forces are 
 those obtained from wood, coal, oil, falling water, gas, winds, nitro- 
 glycerine, etc. In most of these cases the sun is the ultimate source 
 of energy. Also certain chemical materials as radium, are found 
 to be a prime source of energy. Viewing materials and substances 
 
214 SOURCES OF EFFICIENCY 
 
 in other ways we get other groups of forces, such as atomic, molecu- 
 lar, and mass forces ; or those termed physical, biological, mental, 
 spiritual, and social. Some of the highest and most important forces 
 reside in methods, especially in efficiency processes. 
 
 An important dual grouping of forces is that implied in the terms 
 organic and inorganic, organic forces being those which appear 
 only in connection with organic or so-called living matter, and inor- 
 ganic those which may also appear in connection with dead matter. 
 These classes have also been termed incarnate and uncarnate. 
 
 In this connection it is also well to draw a distinction between 
 forces which act apparently by direct contact of bodies and those 
 which, in appearance at least, act across empty space, examples of 
 the latter being gravitation, electricity, and magnetism. 
 
 Forces Characterized by Motions produced by them 
 
 On taking up the second method of characterizing forces, we 
 find that forms of motion produced by forces have already been de- 
 scribed. But often when forces and motions are considered together 
 in this way, individual species of force of especial importance arise. 
 An instance is the classification of winds as local, continental, or 
 planetary. 
 
 In this connection particular attention may also be called to the 
 multiplicative grouping of forces and to forces of various orders in 
 a multiplicative scale. 
 
 Forces Characterized by other Effects 
 
 In classifying forces primarily according to the results produced 
 by them (other than motions pure and simple) we have for example 
 forces of decay, repair, or growth ; attractive forces like gravitation, 
 chemical cohesion, and magnetism, and repulsive and radiating forces 
 such as light, heat, and magnetism. 
 
 Mention at this point should be made of negative and resistant 
 forces ; also of mere continuance forces such as inertia and momen- 
 tum. Closely connected with these ideas is a classification of forces 
 according to the degree of human control of which they are capable. 
 
 Forces Characterized by a Combination of Methods 
 
 For some purposes certain forces are best characterized by a 
 combination of the above principles of classification. Thus some 
 forces, as we usually discriminate them, are determined partly by the 
 
KINEMATIC AND DYNAMIC 215 
 
 material in which they are found incorporated, partly by the kinds 
 of motion to which they give rise, and in part by the more ultimate 
 results which they produce. Examples are sound, heat, light, elec- 
 tricity and magnetism, elasticity, and chemical affinity. More 
 abstract cases are the force of public opinion, of publicity, fashion, 
 supply and demand, etc. Of higher order still are the forces which 
 produce groups and the other Efficients, and also those which these 
 agents exert. The latter class we may term efficiental forces. The 
 force inherent in superior efficiency we shall find to be the most 
 powerful and inclusive of all. 
 
 It is also necessary to allow for subtle and even transcendental 
 forces as possible sources either of added efficiency or of limitation 
 and opposition. 
 
 Looked at in their historical development, especially if we include 
 abstract types, forces have been cumulatively complex from age to 
 age. 
 
 EFFICIENCY FUNCTIONS OF MOTIONS AND SPEED 
 
 In investigating the efficiency meanings and values of motion, we 
 consider three different cases or points of view. These are : 
 
 (1) The efficiency meaning of motion as such (i.e. when con- 
 sidered independently of forces) : 
 
 (2) The uses of motion in cases where the forces involved are 
 small, obscure, or beyond control; 
 
 (3) The efficiency function of motion when the related force is 
 considerable in amount, more or less evident, and under control. 
 
 Later the efficiency value of superior speed will be considered. 
 
 Efficiency Value of Mlotion in Itself 
 
 First, then, considering motion by itself, it is observed that a 
 moving point or object generates a group the elements of which are 
 the moving point or object in its various positions. The group thus 
 generated may take an extreme or infinite form as when a point 
 generates a line, or a line a surface, and so on. 
 
 It is to be noted that not only does a moving object generate a 
 group in the way mentioned but that it also, if its relations to objects 
 outside of its path be considered, gives rise to a continuity of new 
 multiplicative groupings and efficientizings. For instance, by trac- 
 ing progressive changes in organisms we get the various unities 
 which characterize the processes of evolution. 
 
216 SOURCES OF EFFICIENCY 
 
 Uses of Motions Related to Slight Forces 
 
 Where the related forces are inconsiderable, the following illus- 
 trations will serve to make clear some of the efficiency values of 
 motion. A single set of books kept in rapid circulation will take the 
 place of several sets each kept in a distinct library. By taking 
 advantage of the migration of birds a person is saved the labor of 
 travelling to different places in order to observe various species of 
 birds. A flower by utilizing the motion of the bee is saved the labor 
 of producing a large amount of pollen as a means to cross fertiliza- 
 tion. An astronomer in determining the distance of the sun, by 
 taking his station near the earth's equator and utilizing the rotation 
 of the earth on its axis, avoids the expense of measuring a large 
 arc of the earth's circumference and taking observations from each 
 end of the arc. A merchant who builds a store on a city corner 
 where many people are passing and repassing, is saved a large 
 amount of work and expense in looking up trade. 
 
 An important class of instances under this head is the motion 
 or growth of ideal or mental objects. An example is the method of 
 proof called superposition as used in geometry. A more general 
 and important case is that of the useful results obtained by the 
 more or less spontaneous motion of ideas among themselves as in 
 the processes of the imagination. 
 
 Motion in several of the above instances has the effect of giving 
 efficiency a new dimension. The -new dimension and also the dia- 
 lectic of advantages which sometimes results from it are illustrated 
 in the new powers conferred by aerial flight, particularly in war. 
 
 Uses of Motions Related to Considerable Forces 
 
 The uses which may be made of motions where the related forces 
 are considerable and more or less under control are illustrated in 
 the case of the bricklayer given on p. 210. In such cases not only 
 should the number of motions be considered, but also the duration, 
 amplitude, and often form of each. In general in such cases waste 
 motion is a symbol for waste energy. On the other hand graceful 
 motion means highly efficient action. A somewhat similar utiliza- 
 tion of motion as a symbol, is the recognition of a person by some 
 peculiarity of gesture or gait. A more important case is that of 
 reading the signs of the times, that is, grasping the future by means 
 of slight changes in progress at any given time. 
 
KINEMATIC AND DYNAMIC 
 
 217 
 
 Transcendent Values 
 
 The benefits conferred by motion are often unique and not other- 
 wise attainable. Thus the rotation of the planet Mars on its axis 
 enables us to observe the planet's entire surface, a fact which is* 
 more fully appreciated when we recall that the moon by keeping the 
 same face turned toward the earth, prevents us from ever seeing 
 more than one of its hemispheres. A more important case is that 
 where motion saves life. 
 
 Another class of the extreme or transcendental results of motion 
 is that whereby a motion or change beyond what is termed a critical 
 point produces a radical transformation in an object. An illustra- 
 tion is the fact that water becomes ice when its temperature passes 
 through the freezing point, or that positive quantity becomes nega- 
 tive by passing through the zero point. Other important cases are 
 the change of a solid into a liquid, or of a liquid into a gas. 
 
 Advantages of Speed 
 
 The advantages which often spring from increased velocity were 
 also illustrated in the opening paragraph of the chapter. In some 
 cases this element of additional speed adds what is in effect a new 
 dimension to efficiency. This is recognized in the pedagogic precept 
 first to learn to do a thing, then to learn to do it well, then to learn 
 to do it quickly. 
 
 This new dimension of efficiency may take certain special forms. 
 Thus superior speed in reaching Round Top at the battle of Gettys- 
 burg enabled the Northern army to win the battle. So in competi- 
 tive races of various kinds the man who wins by even an inch takes 
 the whole prize. This efficiency property of speed is recognized in 
 the proverb, the early bird gets the worm. The fortunes of the 
 Rothschild family were greatly advanced by the fact that their 
 London representative learned the result of the Battle of Waterloo 
 several hours earlier than any one else in the city. In like manner 
 the farmer who first brings his crop to maturity and the business 
 man who first learns the news that will affect the market, will each 
 profit thereby. 
 
 Superior speed at one time or in one respect may mean a whole 
 group of similar advantages. For instance the man who begins 
 work first on a given day may be able to begin every enterprise 
 
218 SOURCES OF EFFICIENCY 
 
 ahead of his competitors throughout the day. The same principle 
 applies to much larger periods of time. 
 
 An increase of velocity or a superiority in speed may also lead to 
 results apparently otherwise unattainable, or to results in some 
 respect immeasurable in value. Thus in time of flood in a valley, 
 increased speed may be a means of saving life. Also the rapidity 
 with which plant breeders attain results enables us to enjoy results 
 which the slower processes of nature could not achieve within our 
 lifetime. 
 
 Complex Fruitages 
 
 The above useful results of motion and speed are often complexed 
 in various ways. An instance is the circulation of the blood with the 
 many advantages to the organism which result, and the enhancement 
 of these advantages in those higher organisms where the circulation 
 is most rapid. 
 
 Increasing Value of Motion and Speed 
 
 A comprehensive grasp of the utilities in motion is obtained by 
 observing that the progressive development of various forms of life 
 and of human civilization as a whole have alike, as a rule, been 
 marked by an increasing use of motion in various forms, and by an 
 increasing speed in processes. The speed of the fish exceeds that 
 of the amoeba ; that of the bird -exceeds that of the fish ; and the 
 telegraph message moves more swiftly than the bird. The present 
 superior efficiency of certain processes of manufacture are due to the 
 fact that in the last ten years the average speed of machine work 
 has increased threefold in the United States and that of metal cut- 
 ting sevenfold where high-speed steel is used. On the other hand 
 lack of motion, or of velocity, or of utilization of motions, usually 
 means lack of power. Hence also it results that times of motions 
 and change are periods of exceptional opportunity for the capable 
 personality. 
 
 Limitations in the Utility of Motion and Speed 
 
 At the same time attention should be called to the fact that certain 
 dangers and losses are connected with the use of motion, or of in- 
 creased speed, in certain cases. Thus the danger in too much 
 motion is expressed in the proverb, a rolling stone gathers no moss. 
 
KINEMATIC AND DYNAMIC 219 
 
 The loss occasioned by an excessive dependence on objective motions 
 is illustrated by the limitations of a clam or oyster as compared with 
 the fish. 
 
 Similarly certain natural limitations often exist with respect to 
 speed, and any energy expended in trying to overcome these limita- 
 tions in direct ways will be wasted. Also often when it is possible 
 to increase speed, the attempt to do this will not pay, either because 
 of the large outlay of energy called for, or on account of the com- 
 pensating dangers and losses which result. Illustrations are the loss 
 of the steamship Titanic in April, 1912, or the evil physical and 
 moral effects of too high a speeding up of workmen in a factory, 
 or of too fast a pace in any life process. 
 
 Beyond the mere dangers of misuse of motions, certain inherent 
 defects are characteristic of motion as an independent phenomenon, 
 the chief of which is its frequent lack of tangible externality by 
 which it may be controlled. Hence arises the importance of force as 
 an auxiliary efficiency concept in connection with the use of motion. 
 
 EFFICIENCY FUNCTIONS OF FORCE 
 
 From the point of view which is fundamental in the present in- 
 vestigation, we find in force and in the objects in which forces are 
 stored or through which they act, efficiency properties of two princi- 
 pal kinds, viz. : 
 
 ( 1 ) Those properties which are an aid in the use of motion ; 
 
 (2) Those which belong more distinctively to force (or energy) 
 itself. 
 
 Force as a Source of Motion 
 
 In the first place, in treating motions by means of the objects in 
 which are stored the forces which produce motions, we utilize cer- 
 tain permanences which characterize these objects. Thus the force 
 stored in wood, oil, and coal does not vary appreciably in quantity 
 or form, however long these objects are stored. Hence arises the 
 possibility of transferring potentialities of motion (and its results) 
 widely in space and time. 
 
 This adds greatly to the scope of directive processes in space and 
 time, to the possibility of substituting a cheap source of motion 
 for a costly one, and to many other of the advantages of a large 
 externality. 
 
220 SOURCES OF EFFICIENCY 
 
 Also fuel and some of the other force-sources of motion are 
 capable of fine and exact subdivisions, and lead to certain important 
 delicacies and accuracies in motion. 
 
 These properties of the sources of motion also make it possible 
 to group multiplicatively and to systematize these sources and the 
 motions which they produce in extraordinary ways. 
 
 Values Peculiar to Forces 
 
 Force also has certain independent powers in producing the desira- 
 ble ends of efficiency processes as specified in Chapter IX. Thus 
 heat produces warmth, health, and hence, in a measure, life itself. 
 Light gives knowledge and externality in many ways, and has other 
 useful properties. Inertia often means certain permanences in 
 time, and similarly other negative forms of force have their peculiar 
 functions. The specific and more or less concrete uses of each kind 
 of force are described in books treating distinctively of them. 
 
 The general utility of objective forces as substitutes for more 
 costly forms of human energy was pointed out in the introductory 
 paragraphs of this chapter. 
 
 Transcendent Values 
 
 We should not fail to observe also that certain of the above values 
 in some circumstances may be transcendental or unique. Instances 
 are the utilization of night hours by the use of artificial light, or the 
 development of life by the aid of artificial heat in certain situations 
 where life could not exist otherwise. Other instances are certain 
 esthetic results, as when light in itself becomes a source of pleasure. 
 So various forces and motions may give rise to what is termed the 
 joy of living. 
 
 Values in terms of Human Progress 
 
 From another point of view we may realize the efficiency values of 
 force in the aggregate by observing that human civilization as it has 
 progressed has been marked by an increasing use of various forces. 
 Every great man has been full of power of some sort, and usually 
 mere physical fire and passion have been an element or aspect of 
 this. So every great race or nation has had great potential powers 
 of combat as well as of constructive power. 
 
KINEMATIC AND DYNAMIC 221 
 
 Limitations and Dangers 
 
 This part of the discussion should not be concluded without a con- 
 sideration of the fact that certain limitations and dangers are con- 
 nected with the use of force. Thus physical forces in general are 
 subject to the limitation which has been termed the dissipation of 
 energy. This means that forces when transformed tend to pass into 
 lower forms. Each particular form of force also has its own limita- 
 tions. 
 
 Certain dangers and losses are also connected with the use of 
 forces. Thus forces when used in too large or too small a way, or 
 when otherwise misdirected, may produce floods, droughts, con- 
 flagrations, blindness, or death. 
 
 As a whole, however, the mastery of forces in connection with 
 matter and substance tend to give a mechanical trigger control of 
 the universe, with a dialectic of resulting values. 
 
 EFFICIENCY ANALYSIS OF MOTION 
 
 In classifying motions and more especially in investigating the 
 efficiency functions of motion, it has been necessary to analyze the 
 idea of motion to a certain extent. Certain other remarks however 
 should be made on this matter in order to complete as far as possible 
 the determination of the fundamental sources of efficiency contained 
 in this concept. 
 
 Multiplicative Nature of Motion 
 
 The motion of an object implies certain diversities in the position 
 and relations of the object, along with a uniformity in the object 
 itself. This diversity and this uniformity are the primary sources of 
 the group nature of motion, and hence of most of its efficiencies. 
 
 From another point of view the multiplicative nature of motion 
 may be realized by observing that motion is a resultant of the ideas 
 of space and time. We shall find later that these concepts, from the 
 efficiency point of view, are primarily multiplicative in essence. 
 Hence it follows that motion must be essentially of the same charac- 
 ter. The formulas which are used to express the laws of motion in 
 terms of space and time are multiplicative in form and hence illus- 
 trate the principle under discussion. Examples of such formulas 
 are s = vt and s — x /z gt 2 . 
 
222 SOURCES OF EFFICIENCY 
 
 Unique Element in Motion 
 
 In motion as in other categories of efficiency, there is also present 
 a unique and irreducible element. In other words, after we have 
 analyzed the conception of motion as far as we can in terms of the 
 other Efficients and of conventional categories, something is left 
 which is incapable of further analysis. This element is the source of 
 useful results in ways not fully understood, and may at any time 
 become the source of still other results. 
 
 Definitions 
 
 It may be useful to sum up the preceding discussion of the nature 
 of motion in the form of an approximate definition. 
 
 Motion is a change of position accompanied by a continuous and 
 manifold re-multiplicative grouping of an object in relation to all 
 other objects in time and space. 
 
 Each special form of motion is also capable of its individual 
 analysis and efficiency description. Thus 
 
 Change is vague and formless motion; or motion determined 
 mainly by a difference in an object as viewed originally and after an 
 interval of time. 
 
 It is sometimes useful to regard a motion as a mere change, even 
 when the motion is fully understood. In this case change is the 
 prime group in the system of diversities constituting the motion. 
 
 Kinematic is a term by which it is convenient to denote the 
 abstract efficiental essence of motion and which it is possible to 
 clothe under given circumstances with the more concrete categories 
 which give rise to motion as conventionally understood. 
 
 EFFICIENCY ANALYSIS OF FORCE 
 
 The efficiency analysis of force, like that of motion, has been made 
 in large part in the course of the preceding discussion. 
 
 Multiplicative Nature and Uniqueness of Force 
 
 It may be added, however, that the multiplicative nature of force 
 or energy may be made more clear by a detailed study of the laws 
 which govern special forces. Thus the central forces, such as gravi- 
 tation, sound, magnetism, and light, are governed by what is known 
 as the law of inverse squares. According to this law, the intensity 
 
KINEMATIC AND DYNAMIC 
 
 223 
 
 of each of these forces varies inversely as the square of the dis- 
 tance from the center where the force originates. 
 
 Force like motion also contains a unique source of efficiency 
 which is constantly to be reckoned with. 
 
 Definitions 
 
 As an approximate definition we have the following: 
 
 Force is the aggregate of externalities which produce or prevent 
 motion, directly or indirectly. 
 
 Each specific form of force also contains its own specific sources 
 of efficiency and hence is capable of being described in efficiency 
 terms of its own. Thus 
 
 A cause is a force, or that which contains a force, considered as 
 preceding in time the motion associated with it. 
 
 Potential as a form of force means latent force. The term is 
 often used with reference to the possible generation, throughout a 
 given area, of force uniform in kind and degree. It is in this sense 
 that lines or surfaces of equal potential are spoken of. 
 
 Dynamic is a term by which it is convenient to denote the abstract 
 efficiental essence of force and which it is possible to clothe under 
 given circumstances with the more concrete categories which give 
 rise to force and energy as conventially understood. 
 
 METHOD FOR MOTIONS 
 
 In order to utilize motion to the utmost, it is important usually 
 not to regard it as mere vague or spasmodic change, but to realize it 
 as multiplicative in nature. 
 
 Variety and Extreme Forms of Motion 
 
 As with the other Efficients, this conception of the category in 
 hand aids us in realizing the great number of forms which it can 
 assume by the multiplicative combination of different objects, paths, 
 causes, and results. This conception also helps us to anticipate the 
 extreme forms which motion may assume, and in particular the 
 extraordinary velocities which may characterize it. For evidently 
 there is no appreciable limit to speed which may be generated by 
 even a finite number of levers each rotating upon the end of the 
 preceding. Hence it should occasion no surprise to find that the 
 
224 SOURCES OF EFFICIENCY 
 
 velocity of light is 186,000 miles per second, and we are even able to 
 deal with the statement that the velocity at which gravitation acts 
 must be at least 7,000,000 times that of light. 
 
 In all practical affairs it is well constantly to realize that things 
 not only hang together in groups, but that they also travel and 
 change in multiplicative ways, as by swings and rushes, which 
 present lightning strokes of both danger and opportunity. 
 
 In cases of difficulty and limitation it is often better to use crude 
 and vague motion rather than no motion at all. Certain instances 
 where this principle applies have been given in the chapter on direc- 
 tive action. A similar case is that of keeping up certain motions in a 
 merely formal way, while waiting for them to pass into more effec- 
 tive action. 
 
 Motion Study in Specific Cases 
 
 The importance of the specific study of each individual kind of 
 motion has already been pointed out. This applies to abstract or 
 ideal motions as well as concrete ones. Thus it is important to note 
 that at the present time the use of a new mechanical invention 
 spreads rapidly while a new ethical or political idea travels more 
 slowly. Much of the success of Napoleon was due to the fact that 
 he knew the velocity with which his armies could be made to travel 
 and he also knew the limits to this velocity. 
 
 In each department of life the detailed study of the motions 
 involved forms an important source of increasing efficiency. Men- 
 tion has already been made of the increased efficiency obtained in 
 bricklaying by diminishing the number of motions involved in the 
 laying of one brick. A similar study of almost any operation such 
 as husking an ear of corn or harnessing a horse may produce similar 
 results. A like opportunity for increasing efficiency is found in 
 combining and arranging buildings, rooms and parts of rooms so as 
 to reduce the size and number of motions of persons living and 
 working in these. 
 
 The relative importance of speed in different cases often merits 
 careful study. Thus great speed in firing a battle ship is of prime 
 importance, while it is of little or no value in calculating the date 
 of a distant eclipse of the moon. 
 
KINEMATIC AND DYNAMIC 
 
 225 
 
 Auxiliaries to Motions 
 
 Mention should also be made of the importance of using the best 
 possible auxiliaries in connection with motions, as in generating or 
 detecting very rapid or very slow motions. Symbolical and mechan- 
 ical means may also often be made effective aids in keeping a 
 machine running at its maximum speed efficiency. Thus "Mr. F. W. 
 Taylor has succeeded in establishing formulae sufficiently trust- 
 worthy for the production of slide rules by which it is possible to 
 determine in a few minutes the best speed and feed to use in ex- 
 ecuting any given piece of work in any given lathe and with any 
 given set of tools". With practice and experience similar semi- 
 mechanical methods may become more or less instinctive in the 
 individual life with respect to higher matters also. 
 
 METHOD FOR FORCES 
 
 Similarly, in order to utilize forces to the utmost, it is important 
 to regard them not as mere vague thrusts and pulls, but to under- 
 stand that they are multiplicative in their essential nature. 
 
 Variety and Extreme Forms of Forces 
 
 This conception enables us to realize their great number and 
 variety, their extreme forms, to grasp them in a shape ready for 
 use, and to apply them most effectively. Thus the steam railroad 
 would have been a practical fact much sooner if the extent of the 
 friction between a rail and the rim of a wheel had been understood. 
 The efficiency of the steam engine comes largely from the extreme 
 facility with which water vapor takes up large quantities of energy 
 and gives off the same by condensation. 
 
 Opposed Systems of Forces 
 
 In this connection it is important to realize that each case of 
 seeming rest or stability is merely a case of equilibrium between 
 balanced forces, and also that these balanced forces are multiplica- 
 tive in nature. Thus in the human body opposite sets of nerves hold 
 each other in check and the same is true of muscles. If one set 
 is rendered inactive, the other set will act often with great energy. 
 In general, the universe is in a state of approximate manifold 
 equilibrium between opposed multiplicative forces. Any change or 
 disturbance in one of two opposed sets of forces may result in sudden 
 
226 SOURCES OF EFFICIENCY 
 
 explosions or transformations. In other words all things are in 
 a state of triggerish opportunity or danger. 
 
 Study of Specific Forces 
 
 For this and other reasons the importance of making a specific 
 study of each individual kind of force is evident. In making 
 chemical syntheses, for instance, it is found that argon has too 
 small an affinity for other substances to be widely useful, that 
 fluorine has too great an affinity, and that the medium powers of 
 carbon in this respect cause it to be the most widely used of 
 substances. Similar special qualities are found to characterize all 
 forces. 
 
 Forces of High Order 
 
 Other things being equal it is best to use the force which is most 
 highly multiplicatively grouped in its nature or properties. For it is 
 evident that such a force can be adapted most readily to any given 
 end, such as delicacy or intensity of action. In such forces, a less 
 costly form of energy can most readily be substituted in part for 
 a more expensive form. 
 
 The advantage of using forces which govern, unlock, or control 
 other forces should constantly be kept in mind. It is also best wher- 
 ever possible to use abstract forces like pressure or influence instead 
 of brute, concrete forces. Competition is often an effective force 
 in producing results, but, as a rule, it is costly and of a low order, 
 processes of cooperation and direct grouping being in themselves 
 much higher. 
 
 In conclusion it is important to keep in mind that the highest 
 forces are those which spring from the use of the Efficients in some 
 form, and the highest motions are those which accompany such 
 forces. For instance the particular conception which a person has 
 of the summum bonum governs the life of that person, and the 
 world life is changed more profoundly by the views of society in 
 this respect than in any other way. 
 
 Hence the generation or utilization of efficiental force is one of the 
 highest sources of efficiency. 
 
 Summary of Chapter 
 
 To sum up, motion and increased speed are often the sources of 
 efficiency in various ways. The same is true of the utilization of 
 
KINEMATIC AND DYNAMIC 227 
 
 forces, whether these be human or external to man. Hence in the 
 science of obtaining results, both motion and force merit close study. 
 Motions are classified both with respect to their forms, and also with 
 respect to the objects which move. Similarly forces are classified 
 according to the substances in which they are contained, according 
 to the motions to which they give rise, or with respect to other 
 specific results produced by them. Also some forces are character- 
 ized by a combination of the above methods, examples being light, 
 heat, publicity, and highest of all, efficiental forces. 
 
 In studying the efficiency functions of motions, it is convenient, 
 first to investigate those of pure motion, then those of motions 
 where the force involved is slight, and finally those of motions 
 which are taken as representative of energy expended (as in brick- 
 laying). The values inherent in superior speed also merit particular 
 study. The fundamentally useful property in motion is that of 
 producing new groups, but this property often takes a multitude of 
 valuable special forms, some of them of transcendent value. Force 
 is useful as a source of motion and also in other special ways. 
 Hence human progress has ever been marked by an increase in 
 the amount and speed of motions, and in the utilization of forces. 
 
 In order to make the most effective use of motion, its essentially 
 multiplicative nature must be realized. Such a realization leads to 
 an appreciation of its many varieties and of the extreme forms 
 which some of these assume. Specific study of individual cases is 
 highly important. Every motion is associated with some object or 
 objects, hence the study of auxiliaries in connection with motions is 
 peculiarly fruitful in results. The same remarks apply to the use 
 of forces. In addition it should here be noted that apparent rest 
 is due to a balance of forces which, if understood, may often be 
 happily manipulated in whole or in part. Stress should always be 
 laid on efficiental motions and efficiental forces. 
 
 EXERCISE 13 
 
 1. Give an example of each of the principal kinds of motion. 
 
 2. Also of each of the principal kinds of force. 
 
 3. In a given factory a machine which is capable of making 200 revolu- 
 tions per minute is actually making only 50 revolutions per minute. State 
 the speed efficiency of the machine as a per cent. 
 
 4. A given factory contains four machines which are being run at 54, ^2, ^3, 
 
228 SOURCES OF EFFICIENCY 
 
 and Yz of their possible speeds respectively. If these machines work in 
 parallel fashion, find their average speed efficiency. If they run tandem, 
 find their resultant speed efficiency. 
 
 5. Three hours of labor by one man were once required to raise one 
 bushel of wheat. Within the past century this time has been reduced to 9 
 minutes. Express the degrees of relative efficiency involved. What are 
 the main sources of this increased efficiency? 
 
 6. In a given case the cost of floating 50,000 tons of coal from Pittsburgh 
 to New Orleans was $35,000. To send this coal by railroad would have cost 
 $150,000. State the degree of efficiency in the first process as compared with 
 the second. State the principle sources of this efficiency. 
 
 7. In moving a certain building the wages of the workmen employed 
 amounted to $18 per day. By using a team of horses at a cost of $3 per 
 day, the time occupied in moving the building could have been reduced from 
 six days to two. How much more efficient would the second method have 
 been than the first? 
 
 8. Point out the advantages with respect to speed and power in the use 
 of an autotruck as compared with a dray drawn by horses. 
 
 9. Give an example in which the superior speed of the automobile (as 
 compared with the horse and wagon) is a means of saving life. 
 
 Give an example of a unique or transcendent value 
 
 10. In motion 11. In superior speed 12. In force 13. In superior force 
 
 14. Give an example where a motion is a useful symbol of a force. 
 
 15. Give an example where a force (or the material object in which a force 
 is stored) is a useful handle by which to control a motion or another force. 
 
 16. Some of the air currents of the upper atmosphere travel with a velocity 
 of 100 miles per hour. If these could be utilized by an aeroplane in crossing 
 the Atlantic Ocean, what advantages would result? 
 
 17. Give an illustration of the power of publicity as a social force. 
 
 18. Give an example in which graceful motion is a sign of efficiency. 
 
 19. A laborer in husking one ear of corn was observed to be making eight 
 motions. If the same work could have been done with five motions, what 
 was the degree of efficiency in his work? 
 
 20. Make up and work a similar example concerning the process of hitch- 
 ing a horse. 
 
 21. Harnessing a horse 22. Washing a dish 
 
 23. Name four other processes of labor where the work involved might 
 be diminished by an analysis of the process into constituent motions. 
 
 24. Give an example in which momentum (or inertia) is made a source of 
 efficiency. 
 
 25. Point out some of the uses of friction. 
 
 26. Show how the dimensions of a force are increased by the use of the 
 hydraulic press. 
 
 27. Give an illustration of the "power of an idea". 
 
 28. Give an instance where it is more advantageous to use abstract than 
 concrete force. 
 
KINEMATIC AND DYNAMIC 229 
 
 29. Give three examples of the saving of human labor by the substitution 
 for it of the forces of nature. 
 
 30. Why is speed in firing a gun on a battleship more important than 
 speed in calculating an eclipse in an observatory. 
 
 31. Give an example where increased speed results in loss. 
 
 32. Give three examples of the misuse of natural forces. 
 
 33. State the advantages to a government of keeping the money issued 
 by it in rapid circulation. To a merchant, of turning over his capital rapidly. 
 
 34. State the advantages of being able, in certain cases, to send money by 
 telegraph instead of by mail. 
 
 35. State some of the advantages in business conducted by competition. 
 Also some of the disadvantages. 
 
 36. Write an account of the increased utilization of motion as civilization 
 has progressed. 
 
 37. Also of the use of increasingly high velocities. 
 
 38. Also of the increased use of forces of all kinds. 
 
CHAPTER XIII 
 RHYTHM 
 
 Illustrations 
 
 After studying the work of men engaged in loading pig iron on a 
 car, F. W. Taylor found that in order to load the maximum amount 
 in a day, a workman must be free from load 58 per cent of the 
 time. Hence in the Bethlehem Steel Works he required men doing 
 this kind of work to sit down and rest at intervals so as to bring 
 the part of the time when they were free from load up to the 58 
 per cent. This was an essential part of the method by which he 
 increased the amount of pig iron loaded per day by each man from 
 12^ tons to 47 tons. 
 
 Similarly a great artist often finds that he can produce results of 
 the highest order of excellence only by alternating long periods of 
 rest with relatively short periods of intense exertion. 
 
 Not only do men consciously use the rhythmic method of work in 
 order to gain added efficiency, but nature has also utilized the same 
 principle in various ways in building up efficiency organisms like 
 plants and animals. An example is the economy and power in the 
 assimilation of food gained by the rhythm which characterizes the 
 digestive process in man and the higher animals. The oscillating 
 method also is present in many forms in the inanimate world and 
 when rightly understood and utilized is a frequent source of effi- 
 ciency. Thus by noting the tidal rise and fall of the sea, the 
 navigator is able to pass over bars and to enter harbors otherwise 
 inaccessible. 
 
 General Statement 
 
 As a preliminary definition or description we may say that a 
 rhythm is the motion of an object in opposite directions in alternate 
 succession; or more generally it is the alternate appearance and 
 disappearance of an object or quality. The forces which produce 
 rhythms are frequently complex and more or less obscure. Hence 
 it is best usually to treat rhythms by means of the motions which 
 characterize them. 
 
 230 
 
RHYTHM 231 
 
 CLASSIFICATION 
 Objects Capable of Rhythmic Change 
 
 It is an aid in using rhythms effectively to classify them accord- 
 ing to the objects which move back and forth in the vibrations 
 involved. Thus we may have a rhythmic motion of a material 
 object, of a force, or of an idea. 
 
 In this connection it is well to note that every object or entity 
 is subject to rhythmic motion or change of some kind, but not of all 
 kinds. Thus the apparently immobile stone by the roadside is 
 composed of molecules each of which is in a state of constant 
 vibration. These vibrations themselves are subject to other rhyth- 
 mic changes such as those produced by the daily and annual changes 
 in temperature. All sounds made in the neighborhood also cause 
 the stone to pulsate in other ways. 
 
 An investigation of the matter has shown that a state of mental 
 attention is not uniform and continuous; on the contrary it is com- 
 posed of distinct pulses or beats. A similar alternation characterizes 
 each species of nervous and mental action, as perception, memory, 
 and emotion. 
 
 Extreme Cases 
 
 Likewise what appears at first sight to be a uniform motion or 
 an increasing or decreasing one, on examination is found to be 
 rhythmic in some way, as when it is part of a rhythmic motion of 
 great amplitude. Thus when a body falls from an elevated point 
 toward the earth, it seems to move in one direction only, and with 
 a constantly increasing velocity ; but if its motion were not inter- 
 rupted, the falling body, would pass through the earth and would 
 continue to vibrate back and forth past the earth's center. The axis 
 of the earth is continually shifting its position slightly in a complex 
 rhythmic way. 
 
 It is also to be carefully noted that the most abstract and complex 
 ideas and entities are subject to rhythmic change. Thus we have 
 rhythms of intensity, availability, efficiency, and of certain properties, 
 at least, of space and time. 
 
 Rhythms Classified according to Form 
 
 It is also useful to classify rhythms according to their various 
 forms. Thus rhythmic motions may be one, two, or three dimen- 
 sional. Examples of linear rhythms are the undulations in a rod, 
 
232 SOURCES OF EFFICIENCY 
 
 or wire, or those made by a point vibrating in a line past another 
 fixed point. Examples of areal rhythms are the wave motion in a 
 sounding board or in any surface. Illustrations of solid rhythms 
 are wave motions in any fluid as in the air, ocean, or ether. The 
 lines in which rhythms of one dimension act may be straight, 
 circular, or of any curved or irregular shape. An important case 
 is that which results from the combination of a circular motion 
 with a rectilinear motion, as in the motion of a point in the tire of 
 a moving wagon wheel. 
 
 Other Spatial Forms 
 
 Linear waves are of two principal kinds, viz. : ( i ) longitudinal 
 waves, or alternate condensations and rarefactions such as are made 
 in the air by a vibrating tuning fork or any sound wave; (2) trans- 
 verse waves, or vibrations at right angles to the line of progress 
 of the wave, such as are made by a stretched vibrating string, or 
 by light in the ether. 
 
 Various wave motions may also be grouped and classified accord- 
 ing to the lengths of the wave involved, their amplitude (i.e., 
 breadth), their geometric form, or velocity. 
 
 The motion of a solid object back and forth in a line like that 
 of a piston in a cylinder is termed reciprocating action. 
 
 Spherical wave motion is one which radiates in all directions 
 from a center in a solid space, as when sound travels in all direc- 
 tions from the object producing it. 
 
 In some rhythms the moving object is not changed internally. 
 An example is the earth as it rotates on its axis, or revolves about 
 the sun. In other cases the moving object does change internally. 
 Thus in wave motion in the ocean, as the wave moves forward, the 
 drops of water composing the wave change in their relative 
 position. 
 
 It is also well to observe that certain rhythms may be charac- 
 terized as increasing or decreasing in one or more respects as in the 
 length, amplitude, or velocity of successive waves. An important 
 special form under this general class is the infinite decreasing 
 rhythm. In some of these the whole space occupied is finite owing 
 to the fact that the undulations diminish in length; or the time 
 occupied by the motion is finite owing to the fact that successive 
 waves occupy less and less time ; or a rhythm with an infinite num- 
 ber of terms may be finite in both of these respects. 
 
RHYTHM 
 
 233 
 
 Numerical Forms 
 
 Rhythms may be characterized according to the category of num- 
 ber in different ways. The simplest of these is by the number of oscil- 
 lations involved in a given instance. A much more important stan- 
 dard is the number of objects which alternately become prominent 
 in a rhythmic motion. Thus the vibrating motion of a single object 
 like that of a piston in a cylinder constitutes a unitary rhythm. 
 The dominance in turn of two political parties, the alternate promi- 
 nence of expansion and contraction, or of intake and output, are 
 cases of dual rhythm. The cyclic changes of moisture through the 
 forms cloud, rain, river, ocean, cloud, constitute a case of quad- 
 ruple or fourfold rhythm. 
 
 Similarly when two or more simple or elemental rhythms are 
 combined to make a single resultant rhythm, this resultant may be 
 characterized by the number of its components. 
 
 Other Important Forms 
 
 With respect to time, rhythms may not only be termed temporary 
 or permanent, but may also be named according to the periods of 
 time in which a single alternation or a cycle of alternations is 
 completed. For example we have diurnal, weekly, monthly, or 
 annual rhythms. 
 
 With respect to the category of order (or direction) in many im- 
 portant rhythms certain subordinate parts may be regarded as 
 retrograde or back eddies. Examples are the method of leaping 
 ahead from one prominent point to another in a domain and return- 
 ing from time to time to fill in details, or the method of construc- 
 tion and repair, of using rules and exceptions, or of action and 
 reaction. 
 
 In relation to motion, special attention should be called to what 
 may be termed static rhythms. Examples are a series of land ridges 
 and depressions, or bands of alternate colors like the stripes of a 
 zebra. In some cases static rhythms are the result of some preced- 
 ing active rhythm, examples being the rings of annual growth in a 
 tree, a set of geological strata, or the series of moraines formed by 
 a glacier as it alternately advances and retreats. Also static rhythms 
 may give rise to active rhythms in various ways, an example being 
 the rhythm in mental cognition as the parts of a static rhythm are 
 viewed in succession. 
 
234 SOURCES OF EFFICIENCY 
 
 A highly developed and very important rhythm is that obtained 
 by arranging the chemical elements according to the periodic law. 
 Similarly it is often the source of certain kinds of efficiency to 
 arrange the elements of a multiplicative group system in a cyclic 
 linear order. 
 
 As to uniformity and diversity rhythms may be characterized as 
 continuous or discontinuous. Examples of the former species are 
 the motion of a wave in the ocean, or the alternate succession of day 
 and night. Examples of the latter are the periodic reappearances 
 of 17-year locusts, or the recurrence of eclipses. Also a rhythm 
 may be homogeneous (or heterogeneous), either as to the material 
 which moves, or with respect to the forms of the oscillations 
 involved. 
 
 Grouped Rhythms 
 
 Evidently also rhythms may be grouped multiplicatively in various 
 ways. One of these ways is to combine a number of rhythms to 
 form a resultant, then to make a resultant of resultants, and so on. 
 Or a given rhythm may give rise to a number of others, each of 
 which in turn produces still others, the process being repeated during 
 a series of stages. For instance the rhythmic motion of the earth 
 about the sun produces many derived rhythms such as the change 
 of seasons; each of these secondary rhythms gives rise to others 
 of the third order and so on. Similarly the alternation of day and 
 night gives rise to a whole system of derived rhythms. 
 
 Rhythms of High Order 
 
 Hence it follows that rhythms may be of different orders in 
 various ways, or according to different standards, the most important 
 of these standards being that of degrees of general efficiency. Thus 
 a rhythm may be of low order because it belongs to a low order in 
 a multiplicative group system, or because it is feeble or slow, or 
 owing to the fact that it is motion of a material or in a medium 
 of low order. An instance of the latter is the alternation in the 
 moods of an insane person. On the other hand illustrations of 
 rhythms of a high order are the alternate use of the abstract and 
 concrete in education ; of individualism and collectivism in sociology ; 
 of liberalism and conservatism in politics ; of appearance and reality, 
 or of the relative and absolute in philosophy. Other important cases 
 are those where certain Efficients, or parts of Efficients, are used 
 
RHYTHM 235 
 
 in turn recurrently. Thus it may be the source of great efficiency 
 to use a unit and multiplier in alternate succession, the product of 
 each step being the unit to which the next multiplier is applied. 
 Other important cases are the alternate use of algebraic and graphic 
 symbolisms, whether in mathematical work, in art, or in life in 
 general ; of externality and remultiplicative grouping, these taking 
 the form, for instance, of reading and meditation, or of travel and 
 study, or of expansion and reorganization of any kind; of analysis 
 and synthesis, as in chemistry ; of idealism and realism. 
 
 It will be found later that perhaps the most fundamental and 
 comprehensive case of all is the use, in cyclic succession, of phe- 
 nomena, categories, and the Efficients. 
 
 Natural and Artificial Rhythms 
 
 It is also important to discriminate between the two leading 
 classes of rhythms due to the presence or absence of the directive 
 principle. These are: 
 
 (1) Natural rhythms or those which exist independently of man's 
 volition, as for instance the alternation of day and night, or the 
 beating of the human heart; 
 
 (2) Artificial rhythms or those constructed by man more or less 
 intentionally, as the alternate use of humor and pathos in a novel, 
 or the rhythmic recurrence of the classical and romantic movements 
 in a field of art. 
 
 It will be found that each of these two classes has its own 
 strongly marked efficiency functions. This follows from the fact 
 that the causes and sources of artificial rhythms are in large measure 
 under man's control, while natural rhythms must in large measure 
 be dealt with as we find them. 
 
 It is to be noted in this connection that certain rhythms may be 
 regarded as semi-natural or semi-artificial. For instance we have 
 rhythms like the swinging of a pendulum which, after being initiated 
 by man, continue to act for a considerable period without his aid. 
 Also the rhythmic acts of one individual often serve as objective 
 or natural rhythms to another person. 
 
 Complex Rhythms 
 
 It is useful also to remember that the above species of rhythms 
 may be compounded and complexed in various ways. Illustrations 
 
236 SOURCES OF EFFICIENCY 
 
 are the network of alternations which constitute the work of a farm 
 during a year, or the combination of rhythms involved in a musical 
 symphony. 
 
 EFFICIENCY FUNCTIONS OF NATURAL RHYTHMS 
 
 Since a rhythm is a form of motion and also involves forces from 
 certain points of view, it follows that the efficiency functions of 
 motions and forces as presented in the preceding chapter hold also 
 for rhythms to a certain extent. However the rhythm, owing to its 
 individual characteristics, is also the source of efficiency in ways 
 peculiar to itself. 
 
 In discussing the latter class of uses it will be an aid to observe 
 the distinction between natural and artificial rhythms. We shall 
 consider first the efficiency uses of natural rhythms including under 
 this head the uses of artificial rhythms when the latter are viewed 
 objectively or apart from their originators. 
 
 Illustration of Uses of a Natural Rhythm 
 
 Owing to the somewhat complex nature of a rhythm, the efficiency 
 functions of any specific rhythm are usually manifold and more or 
 less interwoven. Thus a tide which enables a navigator to carry 
 his ship over a bar is a special accumulation of water which man 
 utilizes by the means of the directive principle. The advantage 
 in this case may also be immeasurable in that it might be impossible 
 to get the ship over the bar in any other way when pursued by a war 
 vessel. Also if the navigator instead of hiring a tugboat uses the 
 tide to carry his ship up a river, he applies the force principle of 
 efficiency in the shape of substitution of a cheap force for a costly 
 one as explained in the preceding chapter. This also constitutes 
 another application of the directive principle. 
 
 The interval of time between successive tidal crests also constitutes 
 an important natural unit, which is not subject to man's control and 
 is therefore not liable to capricious change. Owing to the per- 
 manency of the causes producing tides this unit has an enormous 
 multiplier giving rise to a multiplicative group system, which com- 
 prehends all tides the world over and which is also unlimited in 
 time. The approximate uniformity in the depth of tides at any 
 given place, together with the slight rhythm of changes in this depth, 
 gives another cross multiplicative group systematization of tides. 
 
RHYTHM 
 
 237 
 
 The result is a general system of water changes which constitutes a 
 wide field for the employment of the directive principle in adding 
 efficiency to the processes of commerce. 
 
 The units, uniformities, and multiplicative group systems involved 
 in the daily rhythm of day and night and the change of seasons are 
 even less subject to change and more comprehensive than those 
 connected with the tides, and hence enable us to plan and direct our 
 activities even more widely and vitally. 
 
 Reuse in connection with Rhythms 
 
 It is to be noted also that the uniformity which characterizes the 
 wave elements in a given natural rhythm, opens the way to reuse of 
 our knowledge of one of these oscillation periods in connection 
 with all the rest in the given rhythm. 
 
 Also the similarity between the general wave structure in one 
 rhythm with that in other rhythmic systems enables us to apply 
 to the rest what we learn concerning any one of them. Thus the 
 general principles of wave motion, as for instance the laws which 
 govern reflection of waves or their concentration, when once learned 
 can be reused in mastering the properties of each particular form of 
 such motion, as sound, heat, light, and electro-magnetic waves. This 
 method is particularly useful in learning the action of invisible waves 
 by observing the properties of those which are visible. It was by 
 this means that Herz arrived at the properties of electro-magnetic 
 waves and opened the way for wireless telegraphy. 
 
 Additional Illustrations 
 
 Another domain of useful applications of natural rhythms is 
 illustrated by the fact that counting the number of rings of annual 
 growth (a static rhythm) on a tree stump enables us to determine 
 the age of a tree, and get knowledge which perhaps we could not 
 obtain in any other way. Similarly an examination of a series of 
 terminal moraines, or of a series of geological strata, gives us impor- 
 tant knowledge of the past history of the earth, perhaps of the present 
 position of valuable deposits as of coal and iron, and thus enables 
 us to shape our directive action more effectively. 
 
 A study of tidal action enabled George H. Darwin to determine 
 the past history of the earth in relation to the moon. 
 
 The arrangement of the chemical elements in the periodic system 
 made it possible for Mendeleveff to predict the existence of chemi- 
 
238 SOURCES OF EFFICIENCY 
 
 cal elements as yet unknown and also to foretell certain of their 
 properties. It has also aided men in searching for and finding 
 these. Among the elements thus discovered were gallium, scandium, 
 and germanium. So afterward in the year 1894, when Ramsay had 
 discovered argon, a gas distinctively different from the chemical 
 elements previously known, "the periodic law immediately suggested 
 the existence of a number of elements" allied to it. A search was 
 made for these and the result was the quick discovery of neon, 
 krypton, and xenon. 
 
 By the observation of the long continued vibration of a pendulum 
 we obtain our most accurate determination of the force of gravita- 
 tion. The combination of two rhythms in such a way that the ele- 
 vations in one correspond to the depressions in the other often 
 forms the most convenient way of obtaining a stable or uniform 
 result. An example is that of obtaining a uniform income by invest- 
 ing partly in the stock of a company which produces iron, and 
 partly in another company which buys iron and uses it as raw 
 material. 
 
 A knowledge of the law of action and reaction, on the one hand 
 prevents excessive optimism in times of prosperity, and on the 
 other hand prevents depression in times of disaster. 
 
 The various efficiency attributes of many rhythms as of sound, 
 light, color, flight of birds, dancing, make them sources of pleasure 
 and efficiency beyond the possibility of complete analysis at present. 
 
 USES OF ARTIFICIAL RHYTHMS 
 A Source of Groups and New Power 
 
 The fundamental reason which has led man to form and use 
 rhythms is the fact that in such rhythms he obtains groups at less 
 cost than in other available ways and also at times he overcomes 
 limitations otherwise insuperable. This principle was illustrated in 
 the opening paragraphs of the chapter. 
 
 The element of repetition which characterizes a rhythm brings 
 with it an inevitable reuse of the groupage which is the efficiency 
 essence of each wave or undulation in the rhythm. The result is not 
 only the direct efficiencies which characterize reuse, but also other 
 auxiliary efficiencies such as are usually included under such terms 
 as increased ease and mastery. These involve certain physiological, 
 nervous, and mental economies, externalities, motion, force, and 
 various self-developing efficiencies. 
 
RHYTHM 
 
 239 
 
 Illustrations of Efficiental Values 
 
 Particular forms of artificial rhythmic actions are often accom- 
 panied by characteristic groups of efficiencies. In the motion of a 
 piston in a cylinder, there is reuse of the walls of the cylinder. In 
 all cases of reciprocating action, some similar form of reuse is 
 present. If a number of persons alternate in the use of an object, 
 as a pump, the efficiency of the pump receives a large multiplier, at 
 times with the immeasurable advantage of saving human life. When 
 Stonewall Jackson made long marches and won battles by causing 
 his men to lie down and rest at the end of each hour of marching, 
 he used repeatedly the prime groups in the physical powers of his 
 soldiers. So when a man pursues different occupations alternately, 
 he reuses his prime groups of body and mind (and thus obtains 
 a more or less continuous use of them), his more sensitive and 
 specialized faculties being enabled to rest and recuperate in turn. 
 
 The back eddy method of progress, that is, the method of leaping 
 ahead and then returning to correct errors and to perfect details, has 
 the advantages which arise from the use of externality and from the 
 treatment of prime groups first in a large domain of material. To 
 take a specific instance, the most efficient method of political 
 progress is to proceed by certain definite steps and to pause after 
 each step till the reorganization called for by that step has been 
 completed. 
 
 The alternate use of two contrasted objects or methods often 
 brings efficiency in the form of a repeated use of a reciprocal unit 
 and multiplier. This form of efficiency is illustrated in the alternate 
 use of the concrete and abstract in education, or of the object and 
 symbol, of the local and universal; or in the use of humor and 
 pathos in a speech or in any literary narrative. 
 
 Negative Values 
 
 Certain negative values often accompany the use of artificial 
 rhythms. For instance by the alternate conference of power on 
 different political parties, important governmental evils are fre- 
 quently removed or kept from taking deep root, or are even pre- 
 vented from appearing at all. 
 
 Transcendent Fruitages 
 
 The results obtained by the use of artificial rhythms are often 
 transcendent and unique. For instance by the use of the rhythmic 
 
240 
 
 SOURCES OF EFFICIENCY 
 
 method a person is frequently able to overcome an otherwise 
 insuperable difficulty, or to achieve otherwise unattainable results. 
 An illustration is the breaking down of an obstacle by rhythmically 
 repeated blows. A more abstract case is the solution of a mathe- 
 matical or other problem which would otherwise be insoluble, by 
 the use of successive like steps. A more subtle case is that of keeping 
 an approximately straight track, as in driving a bicycle, by slight 
 deviations alternately to the right and left, that is, by the alternate 
 use of what may be regarded as positive and negative externality. 
 
 Complex Values 
 
 The above efficiency values may also occur in various complex 
 forms. A comparatively simple case is that of a preacher who 
 finds that he obtains better results by preaching a highly developed 
 sermon occasionally than by attempting to make all of his discourses 
 masterpieces. He thus not only uses his own powers with rhythmic 
 effectiveness, but he sets up certain useful rhythms of self-activity 
 and interest in his auditors. A rotation of crops by an agriculturist 
 gives greater uniformity in income, and in the number of laborers 
 employed, prevents the accumulation of crop pests, opens the way to 
 economies in fertilizers, and has many other advantages. More 
 complex still are the benefits obtained from a rhythmic variety of 
 activity in the higher thought and culture life. 
 
 Limitations and Drawbacks 
 
 It is to be noted however that certain limitations and compensa- 
 tions are often connected with the use of rhythms. Thus while 
 one political party is in power, the members of the other party are 
 frequently idle or not working to their full capacity. Also a change 
 from one party to another may produce costly breaks and interrup- 
 tions in efficiency processes. 
 
 Human Progress Marked by More and Higher Rhythms 
 
 In the aggregate, however, in most fields, the advantages in the 
 use of rhythms vastly predominate over their drawbacks. Hence 
 it is not surprising to find that human progress has been marked 
 by an increasing use of both natural and artificial rhythms, and of 
 rhythms which take ever more comprehensive and vitally effective 
 forms. An example of a recently developed and highly effective 
 
RHYTHM 
 
 241 
 
 form of objective rhythm is the use of electro-magnetic waves in 
 wireless telegraphy, and of the propeller in aerial navigation. In- 
 stances of more ideal rhythms whose use has developed with ad- 
 vancing civilization, are the alternate employment of liberal and 
 conservative movements in various lines, and the method of leaping 
 ahead and returning to complete each step. 
 
 EFFICIENCY ANALYSIS OF RHYTHM 
 
 As with the study of the other Efficients, so here it will be an 
 advantage to make some investigation of the sources of efficiency 
 in rhythms apart from the partial presentation of the matter neces- 
 sarily given in stating the efficiency functions of rhythms. 
 
 Multiplicative and Limitation Elements 
 
 The group or multiplicative principle is present in rhythms not 
 only in ways already indicated but also in certain other ways as 
 with respect to the principle of limitation. Thus in the vibrations of 
 a tuning fork, as a prong bends away from its natural position the 
 resistance increases in a multiplicative way 'till a point is reached 
 where the momentum of the prong is overcome and the motion is 
 reversed; the velocity in the opposite direction then increases in a 
 multiplicative way till it again encounters a multiplying resistance, 
 and so alternately. In the action of a geyser, in the oscillations in 
 the supply and demand of an article of trade, in successive waves 
 of insect pests, and their enemies, the same general law is found 
 at work. 
 
 Externalities present in Rhythms 
 
 The group in some of its developed efficiental forms is also 
 present in rhythms. For instance owing to the limitations inherent 
 in wave action, a space exists between two successive waves or their 
 crests which forms a natural externality to these waves and also a 
 place where other externalities may be applied. Another inherent 
 source of efficiency in a rhythm is the fact that a rhythm by mere 
 continued action produces an externality homogeneous with the 
 original data, and one to which the multiplicative group and order 
 of material principles may be readily applied. 
 
 Other noteworthy elements of efficiency in this respect are the 
 space and time categories which are combined in a rhythm. The 
 
242 SOURCES OF EFFICIENCY 
 
 space category for instance opens the way for a multiplicative 
 group treatment by introducing the idea of the deviation from a 
 line (or standard) alternately in opposite directions. 
 
 Imperfectly Understood Sources of Efficiency 
 
 Rhythms often contain certain dimly understood and perhaps 
 transcendent sources of efficiency. For instance it has been found 
 that light acting intermittently on vegetation will, under some circum- 
 stances, produce more rapid effects than light acting continuously. 
 But the reasons for such a result are not fully known. In the appli- 
 cation of sewage to filter beds, intermissions covering 18 hours out 
 of every 24 are found to be necessary. By the use of the alternating 
 electric current power may be transmitted for long distances where 
 such conveyance would not be practicable by the use of the con- 
 tinuous current. 
 
 Different Aspects 
 
 It should be stated that in classifying and using rhythms an 
 element of relativity is often prominent. Thus what is a rhythm 
 from one point of view is a mere collection of uniformities and dif- 
 ferences in another aspect. An example is a series of glacial ter- 
 minal moraines. Similarly a cyclic repetition of a certain group of 
 elements may often be regarded as a linear multiplicative group ; 
 also a federal multiplicative group when made over into a linear 
 form becomes a rhythm. An element of relativity is also present 
 among different species of rhythm. For what is one species from 
 one standpoint, may be another species when viewed differently. 
 
 A preliminary definition of the rhythm was given on p. 230. In 
 the light of the further analytical examination which has just been 
 made a rhythm may be described as a special form of multiplicative 
 group system resulting from the operation of the multiplicative prin- 
 ciple in a field of great limitation. 
 
 METHODS OF APPLICATION 
 
 Multiplicative Principle an Aid in Many Ways 
 
 In order to make the most efficient possible use of rhythms, it is 
 important to realize their many groupish or multiplicative elements 
 and aspects and to apply these aggressively. Thus the multiplica- 
 tive principle enables us to anticipate the large number of existent 
 
RHYTHM 
 
 243 
 
 or possible rhythms ; to realize their propagative nature ; to grasp 
 them in systems ; and to detect, or be prepared for, the appearance 
 of obscure rhythms of extreme forms, such as a tidal wave, in any 
 time or place. 
 
 Rhythms in Difficult Cases 
 
 It is important also to realize that in a situation of difficulty it is 
 often better to use a crude rhythm rather than no rhythm or other 
 more developed Efficient. Thus the atomic theory of matter repre- 
 sents (or includes) certain useful ways of regarding the constitution 
 of matter; the ether hypothesis includes other of these useful 
 methods. It would be highly advantageous to combine these two 
 views into a single more fundamental one. As this cannot be done 
 at present, men of science often use the two hypotheses in alternate 
 succession, and obtain many useful results in this way. 
 
 Adaptation to Special Situations 
 
 Again it is often a matter of careful consideration to determine 
 what particular form of rhythm to use in a given case, or whether 
 indeed to use a rhythm or some other Efficient. For example at 
 times it may be best to let a panic of a fashion run its course and 
 to wait for a natural reaction, instead of trying to check the move- 
 ment at once or trying to substitute some other process. In like 
 manner it is important to know when it is best to submit to a natural 
 rhythm, as that of day and night, and when to supersede it by an 
 artificial rhythm consisting of periods of intense work alternating 
 with periods of rest determined by special circumstances. Thus the 
 rhythm followed by a person doing manual labor would usually 
 be very different from that employed by a great artist. In this 
 connection as well as with reference to other considerations it is 
 important to study the more or less technical properties of certain 
 natural rhythms, as for instance, those of some physical forces, or 
 those which characterize certain processes of physiology, psychology, 
 and sociology. 
 
 Preference to Rhythms of High Order 
 
 Where a choice among various rhythms is possible, it is of course 
 desirable to use that one which is highest in the scale of efficiency. 
 Thus in certain forms of the steam engine much has been gained by 
 
244 SOURCES OF EFFICIENCY 
 
 substituting a rotary for a reciprocating motion. Similarly the rotary 
 snow plow is more efficient than one which acts by direct thrusts 
 and recessions. One of the most profound and therefore useful 
 rhythms is the alternation of directive with laissez faire methods. 
 
 An important method of elevating a rhythm in the scale of effi- 
 ciency is to develop or master it till it becomes as automatic as 
 possible, alike in its main action, its adjustments in details, and in 
 its ability to give way to other more efficient processes. 
 
 Standard Forms and Systems 
 
 With rhythms as with other Efficients, it is often an aid to select 
 certain standard forms, and to arrange and master these few stan- 
 dard forms as a multiplicative group system. It will be an advantage 
 wherever possible to give the preference to these standard forms 
 and often to utilize them by variant reuse instead of inventing alto- 
 gether new forms. 
 
 Externality often an Aid 
 
 Externality has important uses in aiding us to discover, create, and 
 operate rhythms. One rhythm may be a help to others in this respect. 
 An example is the well known value of song in the operation of 
 both subjective and objective rhythms. 
 
 It is desirable in many cases to use calculus methods in treating 
 rhythms ; that is, methods that are largely symbolic and mechanical 
 and yet give the results of rationality. An instance is the analysis of 
 a rotary motion into two linear rhythms at right angles to each other, 
 only one of the two components in many cases being effective. An- 
 other instance is the compounding of two linear rhythms to obtain 
 a circular rhythm. A more general instance is the use of the instru- 
 ment called the harmonic analyzer. 
 
 In the mastery of rhythms many special methods beside the direct 
 use of rhythms are available. Thus one's leisure may often be 
 profitably utilized by watching the rhythmic motions involved in 
 weather changes, as in noting the daily motions of storm centers 
 and anticyclones. Practice of this sort aids in grasping the 
 equally large but slower and more subtle rhythmic alternations of 
 taste and thought in the world life. 
 
RHYTHM 245 
 
 Ideal Species 
 
 It is an important aid in obtaining the largest results from the use 
 of rhythms to conceive of an ideal form of this Efficient and to apply 
 this form under all possible circumstances. This ideal in its general 
 form consists of the rhythmic motion or alternate use of the Effi- 
 cients in efficiental ways for efficiental ends. It is also important 
 for each person to study his limitations and opportunities and to give 
 this ideal a special form adapted to his circumstances. This individ- 
 ual species will usually be found to be some particular form of the 
 processes of leaping ahead by use of the best material at hand, no 
 matter how fragmentary and imperfect this may be, and returning 
 occasionally ; in other words, a making of all of life into a compre- 
 hensive rhythm of externality and re-multiplicative grouping. 
 
 Summary of Chapter 
 
 By way of summary for this chapter, we may say that the alter- 
 nation of rest with work is essential to the most efficient labor. 
 This is an illustration of the many forms of rhythm each of which 
 has its own peculiar uses. Rhythms may be classified according to 
 the objects in them which change in pulsating ways, or according to 
 the special forms of these changes. An important distinction is that 
 between natural and artificial rhythms. Special mention may also 
 be made of active and static rhythms. 
 
 A rhythm means a repetition, and it also often means condensations 
 in the forms of waves. Hence, in a double way it means the for- 
 mation of groups, and of group systems, accompanied by the useful 
 properties characteristic of these Efficients, such as reuse, and often 
 the attainment of results otherwise inaccesible. It is useful to con- 
 sider separately the valuable functions of natural and artificial 
 rhythms. Special mention is to be made of the value of the back- 
 eddy method of progress; that is, of the method of leaping ahead 
 and then returning periodically to perfect one's work. Human 
 progress has been marked by increasing use of rhythms, especially 
 of those of the highest type. 
 
 The rhythmic method is particularly useful in difficult situations. 
 Special study should be given to hidden and deceptive forms of 
 rhythm, and care should be taken to use the highest possible form 
 in each particular case. The highest form of all is an efficiental 
 rhythm reduced to an automatic and self -developing form. 
 
246 SOURCES OF EFFICIENCY 
 
 EXERCISE 14 
 
 State the class or classes to which each of the following rhythms belongs : 
 i. Breathing. 
 
 2. Democracy, aristocracy, and monarchy when dominant in a country in 
 cyclic succession. 
 
 3. Motion of a bird's wing. 
 
 4. Running around a closed track repeatedly. 
 
 5. Daily change of temperature of a typhoid patient. 
 
 6. Variations in the length of a solar day. 
 
 7. Successive returns of the same comet. 
 
 8. A sound which gradually dies away and then disappears. 
 
 9. The daily and annual changes in the color of prawns. 
 
 10. The so-called line of beauty. 
 
 11. The vertebral column. 
 
 12. Alternations of good and bad times. 
 
 13. The alternate use of induction' and deduction. 
 
 Give an example of rhythmic change of 
 
 14. Distance 17. Velocity 20. Price 
 
 15. Temperature 18. Fashion 21. Value 
 
 16. Density 19. Thought 
 
 22. Give an example of each of the principal kinds of rhythms. 
 
 23. Give two examples to show what is meant by the amplitude of a 
 rhythm. 
 
 24. State, as far as you can, the amplitudes involved in Exs. 1-10. 
 
 25. Mention the various rhythms 1 involved in the process of walking. What 
 additional rhythms are involved in dancing? 
 
 26. Give some of the rhythms which result from the beating of the 
 human heart. 
 
 27. Give two examples of rhythmic motions which are so rapid as to be 
 invisible. 
 
 28. Give two examples of rhythmic motions which are difficult to perceive 
 for some other reason. 
 
 29. The average annual profits on a certain farm when wheat alone was 
 raised were $4000. Later when rotation of crops was practiced the profits 
 averaged $5500 per year. Compute the degrees of relative efficiency involved. 
 
 30. When sailors pull on a rope they usually heave rhythmically and in 
 unison. Why is this? 
 
 31. State the uses or advantages connected with each of the cases mentioned 
 in Exs. 1-4. 
 
 32. Give an example of a rhythmic change in some processes of trade. 
 S3. Mention a natural unit derived from a rhythmic motion. 
 
 34. Give a case where a knowledge of the law of action and reaction is 
 useful. 
 
 35. Give two examples where an equilibrium or other uniformity is obtained 
 by the use of an alternation across a mean. 
 
RHYTHM 
 
 247 
 
 36. Give an example of a uniformity obtained by the combination of two 
 rhythms. 
 
 37. Name some book in which humor and pathos are made to alternate 
 effectively. 
 
 38. Also one in which humor alternates with some element of strength 
 other than pathos. 
 
 39. Give a case where the use of a rhythmic action gives a result otherwise 
 unattainable. 
 
 40. State the advantages of repeatedly forgetting and relearning some 
 subject. Also state the disadvantages. 
 
 41. Show how a rhythm often opens the way to reuse. Give illustrations. 
 
 42. Discuss the advantages and disadvantages of party government. 
 
 43. Why is it that when clearing in the daytime, after a storm, the sky 
 is alternately overcast and clear? 
 
 44. Mention a case where it is advantageous to use directive and laissez- 
 faire methods alternately. 
 
 EXERCISE 15 
 Review 
 
 1. A yellow wall paper of a given kind reflects 42 per cent of the light 
 falling on it, and a red wall paper 16 per cent. Express the relative light effi- 
 ciency of these two kinds of paper. 
 
 2. Newton stated that he had accomplished what he did because he stood 
 on the shoulders of giants. What principles of efficiency are implied in this 
 statement? 
 
 3. In a certain city the average cost of delivering a ton of coal by motor 
 truck is 18 cents, and by horse and wagon is 40 cents. Compute the degrees 
 of relative efficiency involved. What are the main sources of superior effi- 
 ciency in the first of the two methods used? 
 
 4. What principles of efficiency are involved in nipping an evil in the bud? 
 
 5. Why was it appropriate for Homer to speak of articulate speech as 
 "winged words"? 
 
 6. Name the various uses which man makes of the tides? 
 What is the prime Efficient involved here? 
 
 7. What efficiency principles are involved in the statement "The pen is 
 mightier than the sword"? 
 
 8. It costs $314 to send 24,000 pounds of glass a given distance as freight 
 at the 100 pound rate and only $168 by the carload rate although in the latter 
 case the glass must be paid for as if it weighed 30,000 pounds. State the 
 degree of efficiency involved and the source of this efficiency. 
 
 9. What Efficient is illustrated in the aphorism, "An ounce of prevention is 
 worth a pound of cure"? 
 
 10. A man who was digging 6 tons of iron ore by hand, later by a steam 
 shovel was able to dig 200 tons per day. State the degree of labor efficiency 
 involved and the sources of the increased efficiency. 
 
248 SOURCES OF EFFICIENCY 
 
 11. A physician before he used antitoxin lost 82 per cent of his patients 
 sick of diphtheria. After he used antitoxin he lost only 8 per cent. Compute 
 the degree of the relative efficiencies here involved. State the efnciental 
 sources of the increased efficiency. 
 
 12. What Efficients are involved in the circulation of the blood in the 
 human body ? State some of the advantages which result from this circulation ? 
 
 13. State the elements' of difference between a rotary motion and a recipro- 
 cating action. Discuss the relative advantages of each of these in snow plows. 
 Also in steam engines. 
 
 14. What Efficients are implied in the statement "Thou hast ordered all 
 things in measure and number and weight". 
 
 15. Compute the numerical value of 8976 X 579 — 8976 X 577 by per- 
 forming the multiplications before the substraction involved. Also calculate 
 the value of the expression by first substracting 577 from 579. Estimate 
 the efficiency of the second process as compared with the first. 
 
 16. Discuss the ordering of objects or acts in time as a source of 
 efficiency. 
 
 17. Also discuss the orderly arrangement of objects in space as a source 
 of efficiency. 
 
 18. Discuss the combining of order in time and order in space as a source 
 of efficiency. 
 
CHAPTER XIV 
 DIALECTIC 
 Illustrations 
 
 In the year 1856 a young chemist named W. H. Perkin was at 
 work in London on the problem of the artificial synthesis of quinine. 
 He did not succeed in compounding quinine, but in the course of his 
 manipulations he accidently produced mauve, the first of the aniline 
 dyes. This discovery not only led to the whole artificial dye indus- 
 try, but to many other important results of which no one had any 
 conception at the time. As some one has said, "Who would have 
 dreamed that the discovery of the first aniline dye by Perkin should 
 be an essential link in the development of modern bacteriology and 
 therefore in the crusade against tuberculosis and other infectious dis- 
 eases?" Similarly when Sir William Crookes attempted to obtain 
 a more accurate determination of the atomic weight of the chemical 
 element thallium, he did not have the remotest idea that his work 
 would result in the discovery of Roentgen rays, or radium, and in the 
 realization in some particulars of the dream of the medieval alchem- 
 ists as to the transmutation of metals. Columbus failed to find a 
 short route to Asia, but he made the far more important and un- 
 expected discovery of a new world whose beneficial influence on 
 the old world is only beginning. Nothing is more blighting and 
 narrowing than the love of gold for its own sake, yet the search 
 for gold has been the leading factor in the exploration of the world 
 and in the civilization of distant and barbarous regions. 
 
 In business the application of any one kind of efficiency usually 
 brings some additional unexpected useful results. Thus increased 
 order and system bring increased speed and many other benefits. 
 Rural free delivery of the mail has compelled the improvement of 
 country roads, which in many sections has led to the consolidation 
 of country schools and to many other wholly unforeseen improve- 
 ments in rural life. 
 
 In higher fields the greatest thinkers tell us that as a rule their 
 best ideas come to them, not when deliberately and consciously 
 worked for, but in some unforeseen, sudden, and isolated way. 
 
 249 
 
250 SOURCES OF EFFICIENCY 
 
 General Statement 
 
 The principle of efficiency illustrated in the above instances is that 
 of the unexpected appearance or augmentation of useful results, 
 owing to some unrealized development of the group or multiplicative 
 category. This principle of efficiency we term dialectic. This source 
 of efficiency has been frequently alluded to in a more or less casual 
 way in the preceding pages, but we now propose to concentrate at- 
 tention upon it for a time and to investigate it systematically. In 
 one sense this is a study of by-products, but it is to be remembered 
 that the by-product results here under consideration may be much 
 more important than the result directly aimed at, and may develop 
 over long stretches of time. 
 
 Dialectic in Different Fields of Material 
 
 Various dialectic processes may be grouped and classified accord- 
 ing to the material given at the start; or, to express the matter in 
 another way, according to the fields in which the different processes 
 operate. 
 
 One of these fields is the world of inorganic matter. Thus a 
 chemical element may unexpectedly assume a new allotropic or 
 crystalline form, or even, as indicated above, be transmuted into 
 another element. Veins of gold, or deposits of other useful material, 
 are often found in strange positions or develop in unforeseen ways. 
 Inorganic matter is transformed, into living matter, and physical 
 forces into biological and mental ones. Also forces seem at times 
 to take on the properties of matter, and vice versa. 
 
 Living organisms evolve in surprising ways, an example being the 
 development of the bird from the reptile. So at any time, under the 
 hand of the plant breeder a strikingly new and useful species of 
 vegetable life is liable to appear. Similarly a dialectic transforma- 
 tion may take place in a part of an organism, an example being the 
 development of the skin into such diverse forms as the teeth and 
 the crystalline lens of the eye, or that of hair into the horns of cattle. 
 
 In the mental world we have the various peculiar instincts or 
 highly specialized psychic processes in animals, and in man the 
 strange and unforeseen ways in which perceptions or words often 
 pass into actions, conscious and voluntary acts into unconscious and 
 involuntary ones, and the sudden and unexplained appearance of 
 ideas often of the first order of importance. 
 
DIALECTIC 251 
 
 Social processes are so complex that they are especially fitted as 
 a field for the operation of dialectic. Instances vary from the capri- 
 cious moods and actions of a mob to the extraordinary results which 
 have sprung from the labors of statesmen like the founders of the 
 American nation, of whom it is said that "they builded better than 
 they knew". Probably no one of the American revolutionary states- 
 men dreamed that their work would result in the conversion of 
 China into a republic within 150 years. 
 
 In the ethical world the principle in hand is illustrated by the 
 attainment of happiness while simply seeking to do one's duty; and 
 in religion, by the extraordinary phenomena which often attend 
 conversion. 
 
 In the domain of abstract thought, we have the development of an 
 idea of space into something that is spaceless, or of time into the 
 timeless, or, as illustrated by the progress of modern scientific 
 thought, of materialism into a form of idealism. In like manner 
 idealism may give rise to materialism. The sudden development of 
 one Efficient into a special form of some other Efficient has been 
 frequently illustrated in the preceding pages. The general dialectic 
 power of symbolism for instance has been discussed on pp. 177-178. 
 
 In concluding this part of the presentation it may be remarked 
 that almost every important invention or idea has occurred to the 
 discoverer in some small or special form and has afterward not 
 only been generalized, but has found many unanticipated fields of 
 usefulness. The man who first made a wheel could not have dreamed 
 of its use as a part of a dynamo, nor could Plato or Aristotle have 
 anticipated many of the uses of the terms idea and category invented 
 by them respectively. 
 
 Classification according to Form 
 
 In characterizing dialectic processes according to their forms, 
 and more particularly according to spatial and quantitative cate- 
 gories, many of the terms used for classification purposes in pre- 
 ceding chapters may be applied. Thus self-developing processes 
 may be narrow, comprehensive, or universal ; one, two, or three 
 dimensional. A dialectic may work from within outward, or vice 
 versa. 
 
 As to number, such a process may comprise a single event such as 
 the discovery of the Fraunhofer lines, or it may be composed of 
 many events occurring simultaneously or unfolding in succession. 
 
252 SOURCES OF EFFICIENCY 
 
 An illustration of the latter species is the application of the spectro- 
 scope to one unforeseen field after another. Also a dialectic process 
 may be dual, triple, or n-fold in the sense that it is composed of 
 two, three, or n strands of action. An important case of two- 
 stranded dialectic is a process which consists of both a movement 
 forward to new results, and one backward to a deeper grasp of 
 sources and origins. For example, the Roentgen rays have both had 
 many unexpected useful applications in the field of medicine and also, 
 by working in the opposite direction, have thrown new light on the 
 atomic structure of matter. In a similar manner a new idea as to 
 business management when introduced into an establishment, may 
 lead on the one hand to a reorganization of the business internally, 
 and on the other to an extension of external trade. 
 
 An important case of temporal dialectic is that in which sur- 
 prising results follow from being in a given place first. Thus the 
 Puritans by arriving in New England first dominated its civilization 
 to an extraordinary degree, and like results have followed from the 
 fact that their descendants first settled many parts of the western 
 United States. 
 
 A process of reciprocal dialectic is one in which two elements 
 act and react on each other, often in rhythmic fashion, thus pro- 
 ducing many unexpected results. An example is the way in which 
 abstract science and practical engineering have each developed the 
 other. A still broader instance is Jhe reciprocal influence of the new 
 and old worlds on each other in the development of civilization. 
 
 A somewhat similar form of dialectic is that which may be termed 
 polar. In this the existence of one strong form of efficiency tends to 
 bring into being or to develop its opposite or complement. Thus in 
 business the fact that one member of a firm is sanguine and daring 
 may make another member cautious and conservative. Similarly a 
 materialistic movement is sure to beget some form of idealism, often 
 a very extravagant one. Polar dialectics may also be triple or mani- 
 fold in form. Thus strong personalities often appear in groups of 
 three, an example being the group of statesmen consisting of Web- 
 ster, Clay, and Calhoun. A larger group is that composed of the 
 great men prominent at the time of the American Revolution. Often 
 one strong personality develops several others, each of which is 
 strikingly different from the others in some respect. Instances 
 are Napoleon and his marshals, and Lincoln and many of the great 
 men associated with him. 
 
DIALECTIC 
 
 253 
 
 An important special case of dynamic dialectic is that which may 
 be termed inductive influence. An illustration is the expansive and 
 unifying effect upon one's ideas which often accompanies a walk 
 under the open sky after a day's work at the desk. More compre- 
 hensive instances are the results of living and working near great 
 men, or surrounded by great books, in particular those containing 
 efficiental material of high order of any kind. 
 
 Efficiental Forms 
 
 It goes without saying that dialectic processes may occur in groups 
 and also in multiplicative group systems. As an example of the 
 latter we have the extensive system of results which followed from 
 the assumption of the erect position by man in his early development. 
 Among these, in one direction, we have the differentiation between 
 hands and feet, and the evolution of the opposable thumb. In an- 
 other direction we have the grasp of a larger visual externality with 
 its many efficiental consequences. 
 
 Processes of dialectic may be of different orders, either because 
 they operate in fields of material which are essentially of different 
 orders, or because they operate with different degrees of efficiency. 
 An important case of dialectic of higher order is dialectic of dialec- 
 tic. For instance when one form of evolution develops into a higher 
 form, as brute evolution into that which is rational, we have the 
 evolution of evolution, or evolution of the second order. Similarly 
 we may have dialectic of dialectic. 
 
 With respect to externality, dialectic processes may be character- 
 ized by the amount of indirectness in them. In this connection we 
 also have what may be termed matrix dialectic. This arises by 
 virtue of the fact that if any process goes on in a given domain, some 
 corresponding process must proceed outside of the domain. Thus in 
 tying up a bundle, or forming a group of any kind, we unconsciously 
 make the rest of the universe into a corresponding group. 
 
 An important instance of complex dialectic is the cumulative devel- 
 opment of extraordinary results which has accompanied the succes- 
 sion of fundamental inventions such as articulate speech, or fire. 
 
 EFFICIENCY FUNCTIONS OF DIALECTIC 
 
 Many of the efficiency properties and results of dialectic pro- 
 cesses have been indicated in connection with the preceding discus- 
 
254 SOURCES OF EFFICIENCY 
 
 sions and illustrations. Others of them have been mentioned more 
 or less incidentally in earlier chapters. It will be an advantage 
 however at this point to make a more full and systematic statement 
 of the matter. 
 
 Economies produced by Dialectic 
 
 In the first place, as a dialectic process often gives an extra result 
 without extra effort it is the source of noteworthy economies. For 
 instance when the lens was invented and used as a burning glass 
 and it was afterward found that it could be used to remedy defec- 
 tive vision, the latter useful result was obtained practically without 
 cost. This element of economy is greatly emphasized by the fact 
 that the result obtained is frequently so different in quality from 
 the anticipated and customary result, that the amount of effort re- 
 quired to hit upon it would have been enormous. Hence dialectic 
 often means force and rationality acting independently of man, and 
 serving as substitutes for human work of all orders. 
 
 A Source of Power 
 
 A dialectic process frequently advances not only without our aid, 
 but seemingly in spite of insuperable difficulties or opposing forces. 
 In this and in other ways it may be regarded as producing direct 
 results, rather than as a mere economy. 
 
 The gain involved often in effect constitutes the creation of a new 
 type or object. An instance is the evolution of the eye from the skin, 
 or the bird from the reptile. Hellriegel when studying the nutrition 
 of leguminous plants in the year 1886, made the unexpected dis- 
 covery that the roots of leguminous plants fixate nitrogen. The 
 result essentially amounted to the creation of new processes of effi- 
 ciency in agriculture. In the field of abstract work, as in mathemati- 
 cal investigations, this creative function is even more apparent. 
 
 An important special form of this result is the conversion of the 
 harmful into the useful, or of defeat into victory. The Colorado 
 potato beetle at first greatly diminished the potato crop in certain 
 sections of the country, but in the end, by causing agriculturists to 
 study improved methods of potato culture, led to crops two or three 
 times as large as those obtained before the appearance of the beetle. 
 Similarly the San Jose scale has proved a blessing in disguise to 
 the fruit grower. 
 
DIALECTIC 
 
 255 
 
 Efficiental Results 
 
 Dialectic processes also produce efficiency results by giving rise 
 to new and unexpected diversities and uniformities, and consequently 
 to the fruits of these instruments. As to diversities, the word 
 dialectic means literally a laying apart, that is, the development of 
 new forms of diversity. A comprehensive illustration is what is 
 called the divergence of species in the process of evolution. As 
 examples of uniformity results we have the unexpected likenesses 
 in efficiental essence which often appear in radically different do- 
 mains as in language, mathematics, and different branches of science. 
 Another kind of a result is that obtained when a few glimpses frame 
 themselves together in a continuous whole. The multiplicative prin- 
 ciple often shows an unexpected power to check and control its 
 own exuberance and thus to produce uniformity in the guise of 
 relative unity and system. This result often means not only a 
 corrective of extravagance and error, but often a production of the 
 efficiency values of so-called reality, or the discovery, or creation 
 out of the relative and incidental, of an efficiency absolute (that is, 
 of that which has all of the efficiency properties of the so-called 
 absolute). A specific instance is that in which the observation and 
 practice of the relatively useful leads to a recognition of an absolute 
 in morals (the categorical imperative). 
 
 When a systematic (or multiplicatively grouped) arrangement of 
 objects is made in one way, the result is often found to contain other 
 unexpected cross systems of multiplicative groups. Thus objects 
 when arranged rectangularly like the squares in a checkerboard or 
 hills in a cornfield may be regarded as grouped systematically in a 
 vast number of ways beside the original rectangular one. So a prob- 
 lem in mathematics (or elsewhere) that can be solved in one way may 
 usually be solved in many other ways. In fact in any multiplicatively 
 grouped system any element may be taken as the primal apex, and the 
 whole multiplicatively grouped with respect to this apex. 
 
 Also in practical affairs, where many difficulties are present, effec- 
 tive system and order are often possible only because we are able 
 to leave many matters of secondary importance to take care of them- 
 selves. In this case dialectic adjustment takes the form primarily of 
 cancellation and elimination. 
 
 In a process of evolution the elimination of types between certain 
 standard forms may give rise to a multiplicative ordering of ma- 
 
256 SOURCES OF EFFICIENCY 
 
 terials. This occurs also when the materials and processes in a 
 business are standardized. An example is the differentiation of 
 seagoing vessels into certain well denned types. The same develop- 
 ment is evident in automobiles and railroad trains. 
 
 A dialectic process often produces a multiplicative series in a more 
 aggressive way as by the development of a higher type than any given 
 at the start, and afterward of other progressively higher types. The 
 evolution of plant and animal forms of life in the past history of the 
 world is an example of this. 
 
 A process of dialectic may give rise to various other Efficients 
 beside those which have been mentioned. Thus a new and im- 
 portant externality may be obtained either in some unforeseen direct 
 way, or by a working back to causes or origins, or by a generation 
 of or linking up with parallel procedures. Similarly a dialectic 
 process often begets an important rhythm, as that of alternating steps 
 of analysis and synthesis. A dialectic also may unexpectedly pass 
 into or produce another and often more efficient dialectic. An ex- 
 treme case is the dialectic of dialectic mentioned on p. 253. 
 
 Negative and Complex Values 
 
 Dialectic also has certain negative values or uses. Its corrective 
 power mentioned above is one of these. Others are its power to 
 reveal weakness and limitation. A still more important property in 
 this connection is illustrated by the fact that certain evils, perhaps 
 all evils in the long run, are self-destructive. 
 
 The complex values of dialectic assume many forms. One of 
 the most important of these is its function of making clear the best 
 ways in which to use the Efficients in combination. These complexes 
 of its uses and results also appear in striking form in many places 
 in human progress. It is to be noted also that these complex func- 
 tions become more prominent as the world advances. For the more 
 the group and multiplicative principles are recognized and employed, 
 the more numerous and important will be their unexpected mani- 
 festations and fruitages. 
 
 Limitations and Drawbacks 
 
 It is not to be overlooked that dialectic as an instrument of effi- 
 ciency has certain drawbacks and limitations. 
 
 Some of these are inherent in its nature. Thus it is often slow 
 
DIALECTIC 257 
 
 and acts in a blind and costly way. Usually it is not flexible and 
 readily manageable. 
 
 Again it frequently acts in a destructive instead of constructive 
 way. Thus a mistake or evil may multiply itself in an unexpected 
 manner. A scratch may produce death. Even that which is good 
 in itself, owing to the presence of other unsuspected evils or limi- 
 tations, may become a source of harm. An example is the injurious 
 results which have followed from the introduction of rabbits 
 into Australia. In business and in life in general, one must be 
 constantly on the lookout for some unexpected accident or other 
 extraordinary unfavorable development, and if possible have abun- 
 dant means ready to meet such emergencies. 
 
 EFFICIENCY ANALYSIS 
 Result of the Multiplicative Principle 
 
 The primary cause which gives rise to dialectic as an efficiency 
 instrument is the unrealized prodigality of results in a multiplicative 
 process. For example 2 100 when multiplied out gives a number so 
 large that counting at the rate of 100 per minute it would take a 
 billion billion years to count all the units included in the number. 
 In other words the ramifications of the multiplicative principle are 
 so broad and comprehensive, that frequently no one at the outset of a 
 given application of it can grasp them all in detail. 
 
 This holds often even with respect to a single group. The extent 
 of the group may be so great as to be only in part realized, or the 
 developments of other groups may mask or hide the given group 
 in part or entirely, for the time being. An understanding of this 
 makes it clear why a mere change of position or of point of view 
 often produces such vast consequences. These unrealized cluster- 
 ings and hangings together of objects, may take special group 
 forms, as those of imperfectly grasped reuse, units and multipliers, 
 externality, etc. Thus George Westinghouse when he invented 
 high pressure gas mains did not realize that he had discovered 
 a process whose essence he could use later in transmitting electricity 
 at high pressure. When a certain differential equation was first 
 formed and solved, its author did not anticipate that this solution 
 when applied to the Atlantic cable would result in making this 
 cable a practical success. Owing to the common efficiental essence 
 in a number of seemingly different acts, or in a number of depart- 
 ments, in learning to do one thing we often unconsciously learn to 
 
258 SOURCES OF EFFICIENCY 
 
 do a vast number of other things. The often unnoticed uniformity in 
 the size of algebraic symbols is the source of many of their dialec- 
 tic properties . The outcome of a dialectic process often takes a 
 rhythmic and in part paradoxical form. When typesetting machin- 
 ery was invented it at first diminished the number of compositors 
 employed, but later had the unexpected result of increasing this 
 number. If the matter had been viewed in a broad way this result 
 might have been anticipated at the start. An economical use of one's 
 powers often results in dialectic results owing to the fact that part of 
 a person's energy is left free to be employed in any high field which 
 he may choose. 
 
 If the manifoldnesses involved in a single group are difficult to 
 realize, much more difficult is it to grasp all the meanings and uses 
 involved in a whole system of groups. This was illustrated for 
 rectangular arrays of elements on p. 255. And vastly more difficult 
 will it be to comprehend all the ramifications and intersections of 
 several systems of groups. Thus modern bacteriology is due to a 
 number of factors each unfolding in multiplicative style. The first 
 is Pasteur's study of ferments, including a use of diversity in 
 various forms, of various externalities, of directive, and other Effi- 
 cients. The second was Perkin's discovery of aniline dyes ; the third 
 was the improvements in the microscope itself, due to a number of 
 causes such as the invention of Jena glass. Other more general 
 factors might be specified. 
 
 Element of Spontaneous Force 
 
 Another primal element of efficiency in dialectic is a certain 
 apparently spontaneous force or energy which characterizes such 
 processes. This force may be more or less concrete like many of 
 those involved in ordinary physical growth, or it may be abstract 
 and efficiental in nature. As an example of the latter force or 
 energy, we have the fact often noted that when a group has been 
 once formed it tends to increase in size, the reason being that laws 
 of increased efficiency in a measure compel such a result. The force 
 in a dialectic process may also be due in part to the action of 
 unconscious subjective powers in a person or persons associated 
 with the process. These various forces may also have a highly 
 multiplicative structure which also is imperfectly realized. Hence, 
 for instance, the surprising results which often follow from merely 
 making a start in any enterprise, as for example, the spontaneous 
 
 
DIALECTIC 
 
 259 
 
 flow of words and ideas which follows the mere taking of one's pen 
 in hand. Some kind of difficulty or obstacle often stimulates this 
 subjective multiplicative apparatus into action. This perhaps is 
 the cause of the fact that a haze or gauze when thrown on a beauti- 
 ful object, often increases the charm of the object. In its most 
 general and aggressive form this subjective factor in dialectic is a 
 generalization of Kant's doctrine of subjective categories. 
 
 The above various factors are often combined in a process of dia- 
 lectic. Thus when a business like that, for instance, of the manu- 
 facture of glass is once established in a given place, it will often 
 grow surprisingly, even though the place has no special adaptation to 
 the business. 
 
 In modern life the number of multiplicative processes simulta- 
 neously at work in the social, educational, and business worlds, and 
 in private individual lives, is so great that surprising results are 
 constantly appearing. 
 
 Element of Limitation 
 
 In order fully to account for processes of dialectic, an element 
 of limitation must be taken into the account. This element appears in 
 two principal forms, viz. : our inability to grasp all the ramifica- 
 tions of a multiplicative process and in the obstructions or difficulties 
 which make a process more or less necessary, and hold it in check 
 throughout its progress. 
 
 Unique Element 
 
 In dialectic, as in each other Efficient, there is also present a 
 unique and characteristic source of power. After we have carried 
 as far as we can our analysis of the instrument in hand, an irredu- 
 cible something is left over. 
 
 It may be well also to call attention to the respects in which 
 dialectic differs from efficiency processes in general. These are the 
 element of unexpectedness in its results, the obscurity of many of 
 its elements, the native force and energy which carry it forward, 
 and its rationality apart from human interference. 
 
 Above all it is to be borne in mind that dialectic is not mere 
 vague haphazard change in which some useful spot is occasionally 
 observed, but that it is a multiplicative process imperfectly appre- 
 hended and hence, by careful study and some management, capable 
 of producing increasingly important results. 
 
2 6o SOURCES OF EFFICIENCY 
 
 Definitions 
 
 As an approximate definition we may take the following : 
 
 Dialectic is an efficiency process in which results come of them- 
 selves, in whole or part, and are therefore altogether, or in some 
 respect, unanticipated. 
 
 It may be well also to define a few similar terms. 
 
 Development is a vague and general species of dialectic. It may 
 produce results which are either higher or lower than the data, or 
 which are mixed in character. 
 
 Progress means a somewhat more definite series of changes than 
 development and leads to plainly useful results. 
 
 Evolution is a dialectic process in which limitation is prominent, 
 the steps are small, the process slow, but the change is toward 
 what is higher. 
 
 METHOD OF APPLICATION 
 
 Multiplicative Principle an Aid in Various Ways 
 
 A realization of the multiplicative nature of dialectic is an aid 
 in many ways toward the full utilization of this instrument of 
 efficiency. For instance it facilitates a grasp of the great number of 
 results which may be obtained from this source, the extreme forms 
 of some of them, and the explosive suddenness with which results 
 may appear. 
 
 It also facilitates the arranging different forms of dialectic in an 
 order of materials scale and thus aids in applying to a given domain 
 of material that form of dialectic which is best fitted to this field. 
 Thus in certain difficult cases only the crudest form of dialectic can 
 be used. Instances are the use of mere motion, as in shaking a 
 fluid or agitating a situation, and waiting to see what results will 
 follow ; or the use of the mere juxtaposition or separation of the two 
 objects. An important general case is the Baconian method of group- 
 ing facts according to their likenesses or differences, and waiting for 
 general laws to appear among the spatial groups thus formed. Bacon 
 himself would be astounded at the results which have already been 
 obtained by his method. Dialectic by induction (see p. 253) may 
 also be useful as an initial method in a difficult case. 
 
 Uses of Crude Dialectic 
 
 A less crude form of dialectic is that of making a start toward a 
 given end, and using light and power as these appear. In its 
 
DIALECTIC 261 
 
 more advanced form this process consists in the rhythmic use of suc- 
 cessive externalities and re-multiplicative groupings, and the utili- 
 zation of the dialectic results which appear at each stage of the 
 process. 
 
 In a difficult case it is often well to avail oneself of dialectic 
 in the double form often called compromise. A compromise in effect 
 frequently consists in allowing two or more methods or processes to 
 develop till one of them becomes clearly more efficient than the 
 other, or some new method more effective than either appears on 
 the scene. 
 
 Preference to Dialectic of High Order 
 
 The aim should be in all cases to make the dialectic used of as 
 high an order as possible. Beside the dialectic processes of high 
 order of efficiency described on p. 253, special mention may here be 
 made of that process which consists essentially of perfecting the 
 prime groups of a given domain or piece of work to the utmost, and 
 leaving the rest of the process largely to dialectic development. 
 Another important species is that which emphasizes the self correc- 
 tive power in multiplicative processes, and thus makes it possible to 
 use aggressive methods in an imperfectly known field. Special 
 emphasis should also be laid on the ideal form described on p. 263. 
 
 Standard Varieties 
 
 With dialectic as with the other Efficients it is important when a 
 good unit form has been found to reuse that species to the utmost; 
 or, to express the matter in another form, to give it as large a 
 multiplier as possible. An illustration is the generalization of a 
 principle or method by using the dialectic habit which leads us, 
 when we have thought of the numbers one, two, three, also to think 
 of any number however large. Thus having observed that anti- 
 toxin aids in the cure of diphtheria in a few cases, the query arises 
 in our mind whether it may not be an aid in all cases. This process 
 may often be repeated to advantage in many different fields. A 
 similar use may be made of the letters of the alphabet taken in 
 order. Other standard cases are the dialectic which come from the 
 use of the comparative method (that is, manifold homogeneous 
 externalities) in scientific and historical investigations, or from the 
 method of transformations. An extreme form of the latter is that 
 
262 SOURCES OF EFFICIENCY 
 
 of expressing any given process in terms of any given Efficient, or, 
 expressing each Efficient in terms of the other. Having mastered 
 a few standard forms of dialectic it is often an advantage to arrange 
 these as a multiplicative group system, as an aid in using them 
 either directly or by variant reuse. 
 
 Relation, to Other Efficients 
 
 Added efficiency in the utilization of dialectic is often obtained by 
 studying the relations of this agent to each of the Efficients. For 
 instance, it has been observed that, as the result of dialectic, a sud- 
 den, explosive disaster or opportunity is liable to occur at any time. 
 Hence the importance of having on hand some margin, reserve, or 
 other externality is apparent. This externality should, if possible, 
 be of such a kind that it can be utilized in other ways in case the 
 accident allowed for does not occur. Thus it is well to allow a 
 margin of time in starting for a train, and, in case no unforeseen 
 contingency arises to consume this margin, to spend the unoccupied 
 time in reading. The same principle applies to vastly wider and 
 higher fields. 
 
 It is especially important to know where to use directive and dia- 
 lectic in relation to each other. Often, as already indicated, effi- 
 ciency is obtained by using the two instruments in alternative 
 succession, or in some other mottled way. Frequently the directive 
 part of an operation should consist of the mere selection and launch- 
 ing of the proper dialectic process. 
 
 In general, after any efficiental process has been worked out 
 consciously, an added element of power and efficiency can often 
 be conferred upon it by developing it till it acts in more or less 
 dialectic fashion. 
 
 Special conventional forms of dialectic, such as growth, evolu- 
 tion, and development, are utilized most effectively when viewed 
 explicitly as species of dialectic, that is, as essentially multiplica- 
 tive in nature. 
 
 Ideal Species 
 
 From the point of view under consideration in this book the ideal 
 form of dialectic is that which proceeds from efficiental material, and 
 acts in efficiental ways to produce efficiental results. To look at the 
 matter in more detail, we can conceive of the Efficients as so per- 
 
DIALECTIC 263 
 
 fected that they will of themselves attack every point of need 
 or opportunity with manifold power, speed, and adaptation. In other 
 words the process would possess the highest mechanistic and ration- 
 alistic properties in combination. The fact that processes of dia- 
 lectic in actual operation fall so far short of this ideal, shows that 
 some principle of a limitation is at work, and it is this principle 
 which we shall next investigate. 
 
 Recapitulation of Chapter 
 
 As a summary of this chapter we may say that when working for 
 a given end, a person is often surprised by the appearance of some 
 valuable result which had not been anticipated. Often this unfore- 
 seen fruitage exceeds in value the end consciously aimed at. The 
 principle of efficiency here involved is termed dialectic. It acts in 
 all fields, from those which are material and inorganic, to those 
 which are most abstract and ideal. The species of dialectic may also 
 be usefully classified according to the various forms in which they 
 occur. Special mention may be made of the kinds termed recipro- 
 cal, polar, and inductive. 
 
 Since the process of dialectic acts in hidden, unforseen ways, the 
 results obtained from it may often be regarded as obtained abso- 
 lutely without cost. Hence dialectic is a peculiarly effective source 
 of economy and new power. Frequently a process of this kind 
 gives rise to one or more of the Efficients with their corresponding 
 fruitages. Dialectic also in special ways and to a peculiar degree 
 supplies an element of charm and even of romance to kinds of 
 work which might otherwise be limited in interest. 
 
 Since dialectic is primarily due to the multiplicative principle 
 acting in one or more unobserved ways, in order to be able to 
 utilize this source of efficiency to the utmost, a person must obtain 
 some grasp of the great profusion of results which may arise from 
 the action of the multiplicative principle in even one form, and 
 hence of the vastly greater number of results arising when two or 
 more species of it act in combination. This will make plain that 
 no one can anticipate all the forms which dialectic may assume. In 
 cases of great difficulty, after initiating elementary efficiency pro- 
 cesses, much may be left to dialectic self-development aided by 
 occasional efficiental regulation. In general, also, it is highly im- 
 portant to study and utilize the relations of dialectic to the other 
 Efficients. 
 
264 SOURCES OF EFFICIENCY 
 
 EXERCISE 16 
 
 1. Give an example of each of the principal forms of dialectic. 
 
 2. Reinforced concrete was first invented in modern times by a French 
 gardener in making reservoirs for water. Give some unexpected results. 
 
 3. Name some of the by-products now obtained in the manufacture of 
 steel. 
 
 4. In the refinement of oil. 
 
 5. State the dialectic of uses of a telephone directory. 
 
 Give an example where the result of a dialectic process is 
 
 6. A multiplicative group system. 
 
 7. A uniformity. 8. A diversity 9. An externality 
 
 10. Name some of the unexpected evil results which have followed the 
 invention of printing. 
 
 11. Give an instance of your own of loss produced by dialectic. 
 
 12. Give an example of a dialectic process resulting from a positional 
 relation. 
 
 13. Name some of the dialectic results which have followed from Napoleon's 
 wars upon Germany. 
 
 14. State some of the unforeseen advantages which may come to a 
 business man from keeping a considerable reserve of cash. 
 
 15. To any person from having a reserve of physical vigor. 
 
 16. Give an example where the use of system or organization has brought 
 unexpected 'efficiency results. 
 
 17. As a blacksmith hammers he often sings and as he sings he hammers 
 with greater energy and precision. Discuss the dialectic involved. 
 
 18. Why is it that if one member of a family expends his energies largely 
 in processes of thought, some other member is likely to become a person of 
 action. 
 
 19. Discuss the dialectic results of a notebook kept by a business man. 
 
 20. By a literary man. 
 
 21. Methods of wrong doing are often self destructive in unexpected ways. 
 Give an example of this species of negative dialectic. 
 
 22. If a primitive man in building a camp fire happened to place a lump of 
 iron ore among the stones about the fire and thus discovered the metal iron, 
 what principle of efficiency was involved? 
 
 23. Discuss the rhythmic dialectic relations of fire and iron in their histori- 
 cal development. 
 
 24. Mere formal imitation of a process often ends in an intelligent grasp of 
 the same. What Efficient is here involved? 
 
 25. Give an instance where it is advantageous to use the directive and 
 dialectic methods in alternate succession. 
 
 26. Give an example of a difficult case where only- crude dialectic can be 
 employed. 
 
CHAPTER XV 
 
 LIMITATION 
 Illustrations 
 
 In the eighteenth century the invention in England of machine 
 and factory methods of weaving cloth and manufacturing other 
 articles caused a considerable part of the rural population to move 
 to the towns and cities for the sake of the higher wages there 
 obtainable. The result was a scarcity of agricultural laborers. 
 This compelled the landowners to study means of meeting the de- 
 ficiency, the outcome being certain improved methods of agriculture, 
 the most important of which, perhaps was the systematic use of 
 the horse with adapted implements. In this way not only was the 
 deficiency in hand labor made up but additional results were ob- 
 tained which have ever since given England the leadership in agri- 
 cultural efficiency. 
 
 No living person can run ioo yards in less than 9^ seconds, and 
 probably this record will never be excelled by more than a fraction 
 of a second. A knowledge of facts like this may be made the source 
 of important efficiencies. Thus in the loading and firing of a 12-inch 
 gun in the United States navy, by careful study it has been found 
 that the shortest times in which the various operations involved 
 can be performed are in seconds, as follows: }i, 3^, 4^5, }i, 2^5. 
 By organizing the work of gun practice in accordance with these 
 facts the firing efficiency of the fleet has been increased several hun- 
 dred per cent. The heat obtained by burning a pound of coal is lim- 
 ited to a certain amount. In whatever ways physical energy may be 
 transformed, it can never be increased or decreased. These facts 
 have enabled engineers to determine the amount of waste energies in 
 steam engines and, by diminishing this waste, to increase the effi- 
 ciency of such engines threefold. 
 
 General Statement 
 
 The above instances illustrate the fact that the efficiency of pro- 
 cesses is subject to various limitations. Some of these limitations 
 are insuperable in the sense that they cannot be directly overcome. 
 
 265 
 
266 SOURCES OF EFFICIENCY 
 
 But a knowledge even of these insuperable restrictions is often an 
 aid to efficiency in certain ways, as in the negative way of prevent- 
 ing a waste of energy in striving to overcome these deficiencies by 
 direct methods. In other cases by devising means by which to over- 
 come a given limitation or part of a limitation, we not only suc- 
 ceed in diminishing or removing the deficiency, but may obtain 
 additional results or increases in efficiency. In other words one of 
 the most important kinds of efficiency is the negative efficiency which 
 consists of the removal of waste, loss, error, and limitations of cer- 
 tain kinds. This negative efficiency is often accompanied by a 
 dialectic of positive efficiency. Casual references to these facts have 
 been made in the preceding chapters. We shall now isolate this 
 principle of limitation in a measure, and concentrate attention upon 
 it, in order as far as possible to avoid the losses and increase the 
 efficiencies connected with it. 
 
 CLASSIFICATION 
 Limitations in Various Objects 
 
 Considered with reference to the category of efficiency every object 
 is limited in many ways. For example every given kind of matter 
 is limited as to the amount of it which is accessible to man. Two 
 bodies of matter (as matter is ordinarily understood) cannot occupy 
 the same space at the same time. Matter cannot be created or 
 destroyed. Each particular kind of matter also has its characteristic 
 limitations with respect to density, combustibility, fusibility, and to 
 magnetic, electric, luminous, and other physical properties. Hence 
 each kind of matter is restricted in efficiency power, and in its 
 efficiental functions as in the kinds of reuse, groupability, and direc- 
 tive it is capable of, or can aid in. 
 
 In like manner the force of energy of any kind that is accessible 
 to us is limited in amount. Transformations of energy are 
 hemmed in in various ways. For instance, when the energy in coal 
 is converted into motion by the use of the steam engine, nine-tenths 
 of this energy is lost. Innumerable attempts have been made to 
 find a way of converting coal directly into electricity, but all have 
 been failures. A more general limitation in this respect is what is 
 termed dissipation of energy, or, to use a more popular expression, 
 the impossibility of perpetual motion. The efficiency of many 
 processes is greatly restricted by the fact that only a certain amount 
 
LIMITATION 267 
 
 of energy can be stored in a given bulk of fuel, or in the core of an 
 electro-magnet, or in a storage battery. Also physical energy, like 
 matter, can neither be created or destroyed. 
 
 Living organisms are subject both to the limitations of the matter 
 and energy composing them, and to other limitations peculiar to 
 themselves as living objects. Thus protoplasm is limited as to the 
 speed with which it can assimilate sunshine and food, the amount 
 of each which it can absorb, and the ways in which it can trans- 
 form what it absorbs. Hence organisms are limited as to the size 
 which they can attain and their various efficiency properties. These 
 facts are recognized in such proverbs as "You can't get blood out of 
 a turnip", and the query "Can a leopard change his spots?" The 
 limitations in the efficiency properties of vegetation are illustrated by 
 the fact that after the saccharine matter in the sugar beet reaches 
 about 18 per cent of the entire beet, further increase is apparently 
 impossible owing to the fact that the ordinary vegetative processes 
 in the beet break down when more sugar is present. Man, the most 
 efficient of organisms, is limited in the speed with which he can walk, 
 run, or perform any act, in his ability to replace a lost member, to in- 
 crease his bodily height or his length of life. In fact every specific 
 quality of living organisms is hemmed in by, and in one aspect means 
 restrictions of various sorts. 
 
 Similarly psychic powers are limited in man and to a much greater 
 extent in other organisms. Thus in the human mind we find many 
 limitations with respect to perception, memory, imagination, reason, 
 volition, and emotion. For instance the number of distinct objects 
 which one can hold in his field of vision at one time is limited to 
 five or six. The limitations in the reasoning and imaginative powers 
 of the ordinary man are made evident by comparing him with the 
 genius. Perhaps the most important psychic limitations for our 
 purposes are man's circumscribed powers of conceiving and using 
 groups and other fundamental efficiency instruments. Probably most 
 other psychic limitations may be in large measure reduced to or 
 expressed in terms of these more primary limitations. 
 
 The kinds of limitations which have been mentioned thus far are 
 necessarily present in some form in the social, political, religious, 
 industrial, educational, artistic, and similar worlds. Each of these 
 fields also has its specific limitations. For example each particular 
 form of government has its own inherent defects. The same re- 
 
268 SOURCES OF EFFICIENCY 
 
 mark applies to each individual kind of music, or musical instrument. 
 The time required for a given educational process cannot be dimin- 
 ished beyond a certain point. 
 
 Limitations in Abstract Fields 
 
 Important cases of inhibition are also found in more abstract 
 fields. Thus space as we ordinarily understand the term, is re- 
 stricted in the number of its dimensions and in many of its proper- 
 ties. For example only one straight line can pass through two given 
 points, and a triangle cannot have the sum of two of its sides 
 less than the third side. The circle cannot be squared by the use 
 of the straight edge and compasses. 
 
 Similarly numbers have their characteristic limitations. Prime 
 numbers cannot be factored, and two plus two cannot equal five. 
 
 Time, in the conventional meaning of the term, is limited to a 
 single dimension, and also with respect to certain forms of control. 
 Thus we cannot recall the past so as to live it over again and change 
 its content. 
 
 Closely related to this are certain restrictions of order. To quote 
 a familiar illustration, we cannot unfry an Qgg. So the inverse of a 
 process is often more difficult than the direct form. An example is 
 the process of the division of numbers as compared with that of 
 multiplication. In some cases the inverse is easier than the direct 
 process; for instance, a house can be burned down more readily 
 than it can be built. 
 
 Limitations in speed are often of primary importance in an 
 efficiency process. 
 
 Every species of quality has its characteristic limitations or cir- 
 cumscriptions. A soil that is fitted to raise one kind of crop is 
 by that very fact unfitted to raise certain other kinds of produce. 
 Gases are unfitted to perform certain of the functions of solids and 
 vice versa. In fact the expression "it has the defects of its quali- 
 ties" is a common proverb. A man who is especially qualified for one 
 kind of work is often by that very fact unfitted for another kind. 
 
 Similarly each of the primary instruments of efficiency has its 
 own special limitations or defects, many of which correspond to 
 characteristic useful properties. These have been discussed in 
 more or less detail in the preceding chapters. 
 
LIMITATION 269 
 
 Forms of Limitation 
 
 Thus far we have grouped limitations according to the materials 
 or objects in which they occur. It is also useful to classify them 
 according to certain characteristic forms. 
 
 Thus, with respect to the categories of space and quantity, re- 
 strictions may be large or small ; may be scattered or compact ; 
 and may occupy various positions, the most important being an 
 apexal or commanding one. 
 
 As to the category of force, the most important distinction is that 
 between passive and active limitations. Among the former are 
 those which take the forms of resistance or inertia. Among the 
 latter are those which manifest themselves aggressively and which 
 often assume such individual forms as disease, wickedness, insanity, 
 or, in general, what is termed evil. 
 
 Aggressive limitations are often closely associated either with 
 some form of actual personality as with individuals who are igno- 
 rant or wicked, or with personality used in a more or less symbolic 
 sense, as when we speak of imps, goblins, devils, the father of 
 lies, the beast, or the evil one. 
 
 Also with respect to personality limitations may be classified as 
 subjective or objective. 
 
 It may also be well to note at this point that limitations often 
 occur in a reciprocal form. For example in certain states of mind 
 feeling and perception (or reasoning) restrict each other. More 
 generally, specificality and generality (i.e., intension and extension) 
 have reciprocally inhibitive powers. 
 
 Grouped Limitations 
 
 Limitations also occur in certain combined or grouped forms. 
 For example several limitations combine to prevent the perfecting of 
 the telescope lens, among these being chromatic aberration, spheri- 
 cal aberration, variations in the density and the chemical properties 
 of a piece of glass, and instability in temperature. More familiar in- 
 stances are the groups of limitation found in any one person, or form 
 of government. 
 
 A given limitation is often the resultant of a number of compo- 
 nent or contributing restrictions. Thus the limitation in the rapidity 
 with which a man can run a given distance is determined by the 
 limitations in his height, in heart, muscle, and nerve action, and in 
 his power to store and to give out energy rapidly. 
 
270 SOURCES OF EFFICIENCY 
 
 Similarly limitations often occur as multiplicatively grouped aggre- 
 gates. For examples the limitation in the intensity of sunlight gives 
 rise to a whole system of other limitations, such as those in the 
 size of crops, in the closeness of human associations, and the rate 
 of human progress. Each of these in turn produces its own distinct 
 set of restrictions. Or viewed by the method of analysis the limi- 
 tation in the number of bushels of wheat which can be grown on one 
 acre of land is due to the diffused nature of sunshine, the limited 
 powers of matter, force, and protoplasm, and defects in human 
 knowledge and directive action. Again the limitation in the power 
 of sunshine is the resultant of a number of more elemental limita- 
 tions such as those in the nearness of the sun, in the temperature 
 of the sun's surface, and in the angle at which the sun's rays fall 
 on the earth. Similarly each of these restrictions could be resolved 
 into a group of constituents. A still larger multiplicative group 
 system of limitations could be obtained by analyzing the slowness of 
 human progress into its causes. 
 
 Scales of Limitation 
 
 As a result it follows that limitations may often be arranged in 
 an order of materials scale. A limitation may be of a high order 
 owing to the fact that it occupies an apexal position in a multipli- 
 cative group system of limitations, an example being a limitation in 
 human knowledge ; or owing to .the fact that it is a limitation in 
 some material or object of a high order. Thus a serious lack of 
 some kind in the president of the United States may check the 
 development of the whole nation. 
 
 Relative and Absolute Limitations 
 
 The most important distinction in this connection is that between 
 relative and absolute limitations. Some restrictions seem to be 
 ultimate and beyond human control, while others are only superficial, 
 contingent, or apparent. Examples of the absolute species are 
 human inability to raise the dead to life, or the logical limitation in 
 the number of sides of a triangle. Examples of the relative are 
 limitations in human efficiency due to certain preventable diseases, 
 as yellow fever or malaria. 
 
 An important form of relative limitation is that which exists only 
 with reference to certain other limitations. Thus in a factory it 
 may be possible to run a given machine with much greater rapidity 
 
LIMITATION 271 
 
 than is actually used, but it may not pay to do so owing to the 
 limitations in the speed of other processes in the establishment. Gold 
 exists in vast quantities in sea water, but it does not pay to extract 
 it at present owing to the greater efficiency of other methods of 
 obtaining this metal, and also, perhaps, to the limitations in our 
 knowledge of the best way to extract this gold. The interior heat 
 of the earth cannot at present be profitably utilized by man owing 
 to the fact that tunnels to reach this heat, and make it practically 
 available would cost at least $25,000,000. But at some later stage in 
 the world's history it may be profitable to make even this expenditure. 
 In allowing for limitations in connection with efficiency processes, 
 it is important to remember that restrictions of various kinds may be 
 compounded and complexed in many intricate ways. Among the 
 most important cases of complex limitation are those which are 
 cumulative in form. As an illustration we have the limitations 
 which accumulate progressively in the successive fields of matter, 
 force, life, mind, society, and education. 
 
 EFFICIENCY RELATIONS OF LIMITATION 
 
 It will be an aid to efficiency in important ways to observe certain 
 facts with reference to the nature of limitation. 
 
 Limitations are Multiplicative 
 
 In the first place it is important to realize that various limitations, 
 in the vast majority of cases, are not scattered, discordant, or acci- 
 dental in their relations, but on the contrary are connected in multi- 
 plicative systems. For instance there exist certain vital and primary 
 limitations, such as ignorance, each of which includes many second- 
 ary and derived cases. 
 
 It follows that limitation is not primarily a lumpish, blind, and 
 inert something, but that it is normally active and aggressive, and that 
 different forms of it often combine to act in sudden and overwhelm- 
 ing ways. An example is the loss of the steamship Titanic in the 
 year 1912. 
 
 Sources of Efficiency in Limitations 
 
 In naming and treating a given case as primarily a case of limita- 
 tion, a certain human element is often present. This often proves a 
 serious hindrance in the efficient treatment of such cases, though in 
 
2.^2 SOURCES OF EFFICIENCY 
 
 some it is a help. The thorn on the rose having pricked us, we 
 regard the thorn as a drawback or limitation to the beauty of the 
 rose, without stopping to consider the utility of the thorn as a pro- 
 tection to the rose under certain circumstances, and its consequent 
 value in the general scheme of things. So in general limitation 
 from the broader point of view is often entirely, always perhaps in 
 part, mere diversity, our unpleasant feeling concerning it coming 
 largely from narrow personal associations. In certain other aspects 
 limitation is that which helps form units and even the Efficients them- 
 selves. Friction and inertia are often disagreeable, but they enable 
 us to walk, to weave materials together as cloth, and to make many 
 other groups and multiplicative groups. 
 
 In connection with the fact that limitation is in some respects 
 diversity viewed in a certain personal way, the nearness of these two 
 sides of the matter should be noted. From this it follows that 
 wherever a so-called limitation, or even evil appears, some utility 
 must be very close at hand. The defects of qualities and qualities 
 themselves are in immediate contact. Often also the greater the 
 limitation the greater the potential efficiency associated with it. The 
 fact that Faraday lacked an extensive knowledge of technical mathe- 
 matics left his mind free to take certain large and fundamental 
 steps and, in effect, invent a new theory of the matter and ether, 
 and discover among other things the principle of the dynamo. 
 Graham Bell knew just enough qf electricity to enable him to take 
 the bold step which an expert electrician would have hesitated to 
 take and which resulted in the making of the telephone. 
 
 EFFICIENCY METHODS OF TREATING LIMITATION 
 
 Externality the Best General Method 
 
 It has already been stated that the best general method of treating 
 cases of limitation is by the use of externality; that is, by taking a 
 larger view of things, so as readily to perceive such efficiency 
 aspects of co-called limitations as diversity, units and their multi- 
 pliers, groups, or more generally the fundamentally multiplicative 
 nature of limitation and its relation to the multiplicative scheme of 
 things. However, just as there is a whole scale of degrees of limita- 
 tion, so there is a scale of degrees and kinds of externality which to 
 apply, with a variety of special forms of efficiency as a result. 
 
LIMITATION 
 
 2?3 
 
 Treatment of Difficult Cases 
 
 In the first case, some forms of limitation are so fundamental and 
 stubborn that only remote and indirect externalities can be applied 
 to them as a means of remedying and overcoming them, and perhaps 
 obtaining other more positive efficiency results. A ton of coal once 
 burned cannot be burned again. But if the energy obtained by burn- 
 ing the coal be stored in some permanently useful shape, as in a 
 manufactured machine, or as ideas worked out while the thinker is 
 sustained by heat given off during the combustion, the energy in the 
 coal may be reused and the coal in a manner be said to be recon- 
 sumed. Life may be prolonged indefinitely in the sense that the 
 mind can forecast and in a measure anticipate many of the experi- 
 ences of the future. Often the externality applicable to the class 
 of restrictions under consideration takes the form of mere patience. 
 
 A knowledge of limitations also has important efficiency uses 
 even when we do not attempt to overcome the given restrictions. If 
 the given prohibitions are fundamental and insuperable along certain 
 channels, we are saved the losses of various kinds which must follow 
 an attempt to overcome limitations in such ways. Thus a knowledge 
 that the circle cannot be squared by the use of the ruler and com- 
 passes, saves us the loss of time and energy involved in attempting 
 thus to square it. In this case the externality involved is that of a 
 large view of the aims and ends of action and of the means of 
 attaining these aims, and the use of a totally new channel in reach- 
 ing a large measure of positive non-equivalence. 
 
 Some Limitations a Direct Source of Efficiency 
 
 The limitations surrounding an object or domain are often better 
 known or easier to grasp than the object itself, and hence form a 
 convenient externality by which to deal with the object or subject 
 in hand. Thus it is often easier to understand and deal with a man 
 by observing what he is not or by his mistakes than by his direct 
 qualities. Of a similar efficient nature are the proofs by exclusion as 
 used in logic or mathematics. Similarly it is a well known fact that 
 in the human body a set of nerves of a given kind is held in check by 
 another set, and that often the best way to stimulate a man is tem- 
 porarily to paralyze the inhibiting nerves to some degree. Or in 
 general the most advantageous way of making a person or domain 
 efficient may be merely to sever a set of restraining bonds. It is 
 
274 SOURCES OF EFFICIENCY 
 
 evident that this use of negative externality may be built up in 
 multiplicative group fashion. 
 
 So in general all increases of efficiency, in one aspect, are obtained 
 by a removal of waste, ignorance, or other limitation ; that is, all 
 positive efficiency has a negative aspect. This negative aspect is 
 often the more accessible and manageable of the two. 
 
 A Cause of Dialectic 
 
 Of somewhat similar nature are those instances where a lack of 
 one desirable quality leads to the development of other and often 
 more desirable ones. An illustration is the case of a woman who, 
 owing to a deficiency in physical beauty, is led to the development in 
 high degree of mental powers and a spirit of service. Often the 
 wide and deep externality thus called into play leads to an impor- 
 tant dialectic of results. For example the fact that our organs of 
 speech can make only a limited number of distinct sounds has com- 
 pelled men to reuse these organs in various ways, as in various order 
 groups, thus producing the group system of articulate speech. This 
 smallness of the number of primal units of speech has led to other 
 efficiencies such as the invention of the phonetic alphabet, the 
 typewriting machine, the Morse and other like alphabets with their 
 many applications. So the limitation in the amount of available 
 gold in the world has resulted in the wide use of symbols such as 
 paper money and checks to represent this gold and as a consequence 
 to great economics and efficiencies in commercial processes. Simi- 
 larly a difficulty or defect often calls into action latent efficiency 
 powers either in an individual or a social organization. An example 
 is the effect produced in Germany by the conquests of Napoleon. 
 
 We next consider cases of limitation which may be remedied in 
 some indirect way and often thus, from one point of view, made the 
 source of higher efficiencies. An example is limitation in human 
 vision as overcome by the lens. It is to be observed that the first 
 use of the lens in the telescope to overcome deficiencies due to dis- 
 tance has brought with it a dialectic of results illustrated by the use 
 of the lens in the microscope, and of the latter in the investigation 
 of malaria, tuberculosis, and like diseases. 
 
 Applications of Externality 
 
 The externalities applied in such cases frequently takes many im- 
 portant special forms. Often a wide survey of material reveals 
 
LIMITATION 
 
 275 
 
 certain spots where a difficulty disappears, and light or power which 
 can be reused in important ways becomes prominent. Thus both 
 Darwin and Wallace by travelling and observing widely chanced 
 upon facts which clearly indicated the variation of species, and which 
 when fully interpreted gave the theory of evolution. Similarly a 
 wide grouping of facts by the Baconian method, although applied 
 first to the removal of difficulties, has often ultimately led to scien- 
 tific discoveries and inventions of direct value. 
 
 Another way in which it is often advantageous to use externality 
 is to allow an evil or limitation to develop its own consequences, and 
 thus bring its own cure in whole or part. This process is often 
 efficient by virtue of the fact that it arouses the attention, and 
 utilizes the hitherto inert powers of a large number of more or less 
 unoccupied persons. As has already been pointed out, it is often a 
 source of efficiency to allow this method to take the form of alter- 
 nate dialectic and directive. 
 
 Personifying evils and limitations (that is, annexing the extern- 
 ality of personality to them), as when we speak of the works of 
 imps, goblins, and devils, often forms an effective method of sum- 
 ming up and making vivid the tendency and results of a given evil, 
 and of arousing powers which will overcome it. This method 
 however has compensating drawbacks. 
 
 Overcoming Limitations in Groups 
 
 A much more important principle in this connection is that of 
 taking such a comprehensive view of matters as to be able to remove 
 limitations and evils in groups, as by overcoming some deep-seated 
 limitation which is the source of many more superficial ones. An 
 example is the removal of many forms of disease, much poverty, 
 ignorance, vice, and unhappiness in a city by improving its sanitary 
 condition and by the education of its children. 
 
 Often, in overcoming limitations in groups, many forms of 
 externality are used together which, beside overcoming the given 
 limitations, bring added positive efficiency results. The Krupp firm 
 in making cannon have to overcome limitations in the properties of 
 iron, in the physical powers of workmen, and in human knowledge. 
 In doing this work they employ coal and various physical forces, 
 manifold machinery, and the largest physical and chemical labora- 
 tory in the world. But by so doing they have not only achieved 
 
276 SOURCES OF EFFICIENCY 
 
 their immediate purpose, but have also discovered many mechaincal 
 principles and scientific facts widely useful in the arts and trades. 
 
 Adapted Treatment of Limitation 
 
 Some species of limitation may be regarded as relative, in the 
 sense that it pays under some circumstances to submit to them for 
 the time being, and under others to try to overcome them; that is, 
 at some times to apply only a remote and indirect externality, and 
 at others a direct one. For instance in some parts of the world and 
 in some ways it is a source of efficiency to overcome the limitations 
 of peat as a fuel, and in others it does not pay to use peat in this 
 way. The English system of weights and measures in itself has 
 great defects as compared with the metric system. But it has the 
 important property that its very deficiencies make it homogeneous 
 with the great majority of efficiency methods in use the world 
 over. Hence its mastery furnishes a convenient unit to reuse in 
 connection with other processes. The same remark applies to the 
 systems of spelling and pronunciation which characterize the English 
 language. Perhaps the great practical power of the English and 
 American peoples may be due, in a measure, to their training in these 
 and similar disciplines. At the same time the English speaking man 
 of science in his private work does not hesitate to set aside the 
 English system of weights and measures for the more convenient 
 metric system. 
 
 Similarly the wise man recognizes and submits to his personal 
 limitations in selecting a field of life work. At the same time, under 
 many special circumstances he tries to overcome these limitations as 
 far as possible. A wider illustration of this principle is the whole- 
 some moderation which was characteristic of the Greeks in all their 
 process of life, and by which they were able to attain such vast and 
 permanent results. So, in general, sacrifice and restraint, in some 
 respects, are necessary to broad and vital efficiency processes of any 
 sort. 
 
 Value of Exact Knowledge 
 
 At this point becomes especially evident the value of the exact 
 knowledge, quantitative as far as possible, of the various species and 
 forms of limitations. Vast amounts of such knowledge are found in 
 various technical treatises on the different sciences and arts. Each 
 
LIMITATION 277 
 
 man in his particular field can often determine other more special 
 and detailed limitation facts as to his work. Thus Mr. F. W. 
 Taylor in his investigations which led to the system of efficiency 
 which he calls scientific management, has found that work in certain 
 shops is most efficient when each planner or overseer has under him 
 not more than three men on the average, and that a shovel load 
 for a common laborer should not exceed 21 pounds. In general if 
 the boundary facts are known in any line or department of human 
 knowledge or action, it is possible to construct with confidence the 
 largest available or practical multiplicative group or order of mater- 
 ials system in that domain, with a view to varying from this by 
 marginal reuse from time to time according to circumstances. 
 
 In this connection it is also well to note that in every situation a 
 residuum of work by somebody is always necessary, and that it 
 often does not pay to try to remove all of removable limitation, 
 but that better results are obtained by working partly in other 
 lines. Similarly instead of working with great rapidity in a single 
 line, it often pays better to work at a more moderate rate in several 
 directions. 
 
 From the preceding discussion it is evident that, in discriminating 
 between cases of limitation and also for general purposes, it is an 
 important source of efficiency to keep in mind the multiplicative 
 nature of limitation. This facilitates an appreciation of the many 
 forms which limitation may assume, the extreme nature of some of 
 these, the grasp of them as a tabulated whole, and the marginal reuse 
 and more general group methods of treating them. 
 
 Two Opposed Systems 
 
 Hence the best way to treat limitation as a whole is to consider it, 
 not in an isolated fashion, but in connection with the general system 
 of efficiency and surplusage, and to regard the two principles (of 
 gain and limitation) as two opposed multiplicative systems ; not to 
 neglect or ignore parts of the two systems which seem to cancel 
 each other, but to regard the two opposed systems as always existent 
 and in action. Thus in psychology the process of forgetting is not 
 to be regarded as a mere erasure of mental data, but as due to the 
 encroachment of one multiplicative mental grouping upon another. 
 The same ultimate two-systemed conception of things is found in a 
 crude form in the doctrine of total depravity along with that of divine 
 
278 SOURCES OF EFFICIENCY 
 
 grace in certain theologies. In all cases however in dealing with two 
 opposed systems the positive or useful system is to be regarded as 
 dominant over the negative one. 
 
 This general combination concept often takes various special 
 forms. Thus it is frequently an advantage to conceive of it in the 
 form of a rhythm in which the main action is that of positive multi- 
 plication, while the negative part consists of mere back eddies. The 
 advantage in this method of viewing the matter is that it facilitates 
 the application of dialectic in taking care of the limitations 
 involved. 
 
 Other Uses of the Two Opposed Systems 
 
 Similarly the more general conception of two opposed multiplica- 
 tive systems brings important efHciental values. For it provides an 
 endless store of diversities and varied reciprocal externalities to 
 be utilized in efficiency processes. In Germany where, at the present 
 time, in many respects, scientific efficiency has reached its highest 
 
 development, it is estimated that only — — part of the sun force 
 
 which falls on a cultivated field is collected in a useful form by the 
 crops produced. When we consider the great array of efficiency 
 processes which are here applied, we realize the vast extent and 
 power of the limitations at work. We get a more comprehensive 
 view of these when we consider that the world as a whole is moving 
 forward only at a snail's pace with back eddies some of them tens of 
 centuries long. We may thus realize to some extent the enormous 
 results which it is possible to attain by a mere negating of limitation 
 as well as the extent of more positive opportunities. In this connec- 
 tion it may also be noted that the greatness of a difficulty, or even 
 defeat, often is a measure of the greatness of the related opportunity. 
 The double multiplicative view of limitation both prevents a raw and 
 unlimited optimism and inculcates a sane, wholesome, and discrirrj- 
 inating optimism. 
 
 The most important general result which follows from conceiving 
 the world as two opposite multiplicative systems lies in the fact that 
 the separation thus involved enables us to conceive of an ideal goal 
 of human endeavor, or, to express the matter in a more general 
 form, to conceive of a summum bonum of all processes. For when 
 considered apart from limitation, the positive surplusage treated in 
 
LIMITATION 
 
 279 
 
 Chapter IX becomes unlimited in amount and quality for each per- 
 son and entity; or in other words each person and conscious entity 
 would have a near and instant and unlimited wealth and ecstasy. 
 
 Summary of Chapter 
 
 To sum up the chapter, a fundamental but somewhat indirect 
 source of efficiency is that of studying the limitations of a given 
 process, determining whether these limitations are fundamental or 
 superficial, and devising means to overcome them as far as possi- 
 ble. It is advantageous to classify limitations both according to 
 the objects or fields in which they are found, and also according 
 to the forms which they assume. Special mention may be made of 
 the species of limitation respectively termed active, passive, abso- 
 lute, relative, grouped, or complex, since a knowledge of each of 
 these is an important special source of power. It is also important 
 to realize whether each given limitation is personal and subjective, 
 or objective. It is also at times an aid to new results to understand 
 that a limitation is essentially a diversity, and hence may be made 
 the source of those fruitages which are characteristic of diversities. 
 
 The principle of externality supplies the best method both for 
 the accurate determination of limitations, and also for the advan- 
 tageous treatment of them. It is evident also that various adapted 
 species of externality should be applied to difficult kinds of limita- 
 tion. Hence the value of thorough and exact knowledge in every 
 field of operation. The most general and useful conception in 
 dealing with any large domain of material is that of efficiency and 
 limitation acting in the domain as two comprehensive and opposed 
 multiplicative systems. 
 
 EXERCISE 17 
 
 1. Give an example of each of the principal kinds of limitation. 
 
 2. The limitation of the speed of a railroad train is the resultant of what 
 component limitations ? 
 
 3. It is said that the clay which underlies the city of Philadelphia contains 
 over $125,000,000 worth of gold. State some of the reasons why this gold 
 cannot be utilized. 
 
 4. It is estimated that one ton of radium would drive a 15,000 ton ship 
 for thirty years at a speed of 15 knots per hour. Why is not radium used for 
 propelling steamships? 
 
280 SOURCES OF EFFICIENCY 
 
 5- State three cases in which friction is a limitation to human activity, 
 and also three in which it is an aid. 
 
 6. Name some noted man the limitations of whose childhood have helped 
 make him great. 
 
 7. Show that the limited amount of food in the world has had the effect 
 of making the forms of animal life on the earth more efficient. 
 
 8. Give an illustration of the difference between a real and an apparent 
 limitation. 
 
 9. Show how the phrase "defects of its qualities" is illustrated by the 
 properties of water. 
 
 10. Of iron 11. Of electricity 12. Of money 
 
 13. Give a case where the limitations of an object are easier to recognize 
 and to use than the object itself. 
 
 14. If the efficiency of man's body when used as a machine is 21 per cent 
 and that of a small steam engine is 3 per cent, compare the two efficiencies. 
 What means are there of overcoming the limitations involved in each 
 ease? 
 
 15. If a large steam engine is 10 per cent efficient, while a small one is 1.5 
 per cent efficient, state the degrees of relative 'efficiency involved, and also the 
 sources of greater efficiency in the large engine. 
 
 16. If a steam engine is 10 per cent efficient and a gas engine Yz efficient, 
 compare the efficiencies involved, and state in efficiental terms some of the 
 sources of the difference. 
 
 17. Compare the relative advantages and disadvantages in having a building 
 erected by contract and by day's labor. 
 
 18. State some of the causes which limit the amount of income from a safe 
 investment. 
 
 19. A soil that is suitable for the raising of sweet potatoes is not fitted for 
 raising tobacco and wheat. Give a similar illustration of your own. 
 
 20. Every musical instrument is said to have some characteristic limitation. 
 Name these as far as you can. 
 
 21. Heat expands metal. Give an example where this property is useful. 
 Another where it is a disadvantage. 
 
 22. Why is it that the tides, as sources of mechanical power, are not gen- 
 erally available for human use? Answer the same for the waves of the ocean. 
 
 23. Give an example of an efficiency blessing appearing in the disguise of a 
 limitation. 
 
 24. Give an example where the use of an externality not only overcomes a 
 given limitation but is also a source of positive efficiency. 
 
 25. Give an illustration of the fact that a wide survey of material often 
 reveals a place or places where a given limitation disappears. 
 
 26. Give an example where the exact knowledge of limitations has led to 
 their more efficient treatment. 
 
 27. Give an example of a group of limitations or evils which have been 
 overcome by destroying their common root. 
 
CHAPTER XVI 
 ERROR AND PARADOX 
 Removal of Waste and Error as a Source of Efficiency 
 
 In the preceding chapter it was stated that every efficiency process 
 from the ideal point of view is a mere removal or undoing of limita- 
 tion or unnecessary loss ; that is, every efficiency process has a nega- 
 tive as well as a positive aspect. It was also pointed out that, in 
 obtaining increased efficiency in a given domain, it is often an advan- 
 tage to pay primary attention to this negative aspect which consists 
 of the removal of limitation. This principle is of particular impor- 
 tance with respect to certain special kinds of limitation. One of 
 these is that species of limitation where some element of personality 
 is involved, as, for instance, in cases of ignorance and error. The 
 removal of these is often an especially valuable means of creating 
 or improving efficiency. One reason for this is that a mistake is 
 something below the general level of current social efficiency, and 
 the manifold adjacent social externality supplies abundant aids of 
 various kinds in remedying the given source of loss. This applies 
 for instance to a person of intemperate habits who lives in a highly 
 moral community, or to a glass manufacturer who is melting his 
 glass in pots while his neighbors use large tanks for the purpose. 
 Another reason why particular attention to the prevention and cor- 
 rection of mistakes is a fruitful source of efficiency, is the fact that 
 direct efficiency often means merely added luxury and hence some- 
 thing which may be dispensed with, while a mistake may mean ruin 
 and the loss of all essentials. Hence awareness of error and loss 
 is frequently far more stimulating and productive of the use of all 
 possible factors and aids in obtaining results, than is the mere concep- 
 tion of new and additional sources of profit. 
 
 Further Advantages 
 
 For certain special reasons also, measures taken to prevent or to 
 correct errors are often the source of peculiarly powerful dialectical 
 (i.e. extra and unexpected) efficiencies. For in case of error we 
 are concerned with the double fact that, objectively, the multiplica- 
 
 281 
 
282 SOURCES OF EFFICIENCY 
 
 tive principle is giving results so profuse that they cannot be fully- 
 grasped, and also that, subjectively, certain powers are at work in 
 like manner, such as the directive faculty or the mental powers in 
 general. Hence error is best regarded in general as the multiplica- 
 tive principle acting in a special doubly errant way, or, in other 
 words, as double misgrouping of some kind. Socrates was persecuted 
 and put to death because he was falsely classed with the selfish 
 destroyers of the national customs. Selfishness is mainly due to the 
 lack of externality and hence is a form of misgrouping. Errors in 
 the use of words and figures are simpler cases of misgrouping. 
 Hence the fundamental means of preventing and correcting errors 
 is the acquirement of a thorough knowledge of the group principle 
 in all of its aspects, including, in particular, an aggressive use of 
 various kinds of externality. It is also to be remembered that these 
 methods often lead to a new and vital dialectic. As an illustration 
 we have the fact that a man who overcomes the habit of drunken- 
 ness must usually acquire some ideal, or religious principles, or even 
 a new and profound philosophy of life, giving many aggressive 
 efficiencies over and above the mere correction of a bad habit. In 
 order to obtain a quick detection and correction of error and waste, 
 a business man often devises some special method of keeping ac- 
 counts, one, for instance, by which any element of his business can 
 be summarized and balanced at the end of each day. This method 
 not only brings the quick correction of errors, often in groups, but 
 the knowledge thus obtained often leads to the development of new 
 and positive efficiencies. Similarly the syllogistic method of exam- 
 ining a course of reasoning in order to detect possible fallacies, 
 frequently leads to a searching analysis of data which, in the end, 
 begets a more fundamental and efficient multiplicative grouping of a 
 given domain. 
 
 General Method of Investigating Error 
 
 As error always occurs in the process of striving after results, 
 in illustrating the different species of error it will be useful fre- 
 quently to point out the efficiency principles which are distorted or 
 misused in a given case. For if a given principle is found to be 
 misused in many different cases, a more correct use of this principle 
 will lead to the detection, correction, and prevention of errors in 
 groups, with a corresponding intensification of dialectic results. 
 
ERROR AND PARADOX 283 
 
 In order to condense the treatment as far as possible special at- 
 tention will be paid to those extreme and persistent sources of error, 
 the mastery of which confers a grasp of many lesser and more 
 superficial ones. 
 
 CLASSIFICATION 
 Different Fields of Error 
 
 The domain of material in which a given error has been made 
 to some extent determines the source of the given error, and also 
 the form which the error takes. Hence in classifying errors accord- 
 ing to material or content, we shall also to a certain extent be classify- 
 ing them according to source and form. 
 
 Important errors have been made with respect to inorganic objects, 
 and the correction of these mistakes has been the source of far-reach- 
 ing efficiencies. For instance for a long time it was regarded as 
 impossible that the addition of a fraction of one per cent of carbon 
 to a mass of iron would of itself convert the iron into steel. The 
 correction of this error has led to vast improvements in the manu- 
 facture of steel. A similar mistake was that concerning the resist- 
 ance which air makes to projectiles. It is to be noted that the root 
 of these errors was a failure to grasp the extreme results which 
 follow from the multiplicative properties of matter. Other like 
 paradoxical truths which have been or may become the sources of 
 efficiency are the fact that water is more dense than either of its 
 constituent gases, oxygen and hydrogen; that solder has a lower 
 melting point than either of its components, lead and tin ; that the 
 process of tempering hardens steel and softens copper ; and that the 
 diamond chemically is pure carbon. 
 
 Similarly we have paradoxical properties and corresponding 
 errors concerning forces. Illustrations are the fact that wate'r will 
 wear away a stone ; that river courses are often more permanent 
 than mountains ; and that gravitation is the feeblest of known forces. 
 Surprise and error concerning these statements arise from a failure 
 to realize that the action of water in the above instances is a re- 
 peated one, and hence has a dimension not possessed by the 
 cohesive force which holds a solid object together; and gravitation, 
 as we are familiar with it, also has its source in enormously larger 
 bodies than the other forces with which we are familiar. Lime 
 binds sandy soils and loosens compact clay soils. It is an important 
 
284 SOURCES OF EFFICIENCY 
 
 source of agricultural efficiency to take advantage of these two 
 apparently contradictory properties. 
 
 In the domain of living organisms, a hybrid plant is sometimes 
 more immune to disease than either parent species. A scratch at 
 one time may be barely felt; at another it may produce death, the 
 action in the first being additive, in the latter multiplicative. The 
 extract from the thyroid gland in the human body is necessary to 
 life, yet when injected directly into the veins it kills like lightning. 
 The pancreatic fluid forms sugar in the intestine and destroys it in 
 the blood. In an army it has often been observed that some frail 
 looking clerk from a city store often can outmarch a husky young 
 giant from a farm, the difference being due to the fact that the 
 nervous energy characteristic of the former type of physique is of a 
 higher order than the muscular energy prominent in the latter. 
 
 As a transition from the biological to the mental field we may 
 take the case of two children born of the same parents but differ- 
 ing as much in mental capacity as, for instance, did Joseph and 
 Napoleon Bonaparte. A possible explanation is that in the one child 
 a set of factors may act together in an additive manner, or even 
 cancel each other in a measure; while in the other child but slightly 
 different factors act upon each other in multiplicative and progressive 
 ways. Cases more detailed in nature are the fact that a nerve im- 
 pulse will travel in less time from the tip of the finger than from 
 the elbow to the brain; or that one minute's advice from an expert 
 at a cost of $100 is cheaper than an hour's free advice from an 
 ignoramus. 
 
 Error in More Abstract Fields 
 
 One of the most important forms of cognitive error is that of 
 regarding the outside appearance as corresponding to or more im- 
 portant than, the inner reality. This error may be regarded as 
 essentially a mistake with reference to the relation of the upper 
 and lower parts of an order of materials scale, or as a misuse of 
 symbolisms with respect to the object represented. A similar case 
 is a mistake as to the relations of words and the actual intention of 
 a speaker, or any distortion of the meaning of any act, word, or 
 appearance. Memory, imagination, and reasoning are forms of 
 reuse and multiplicative grouping, hence errors in them are essentially 
 cases of misgrouping of some kind. Owing to their abstract nature 
 
ERROR AND PARADOX 285 
 
 and to that of the groups involved, efficiencies of high order are 
 possible in their treatment. Mention may also be here made of the 
 paradox that the more one knows, the less one knows. The study 
 of the illusions produced by a sleight-of-hand performer or so-called 
 magician, is often instructive because the solution of a trick of this 
 kind frequently reveals in explicit form the proximate efficiental 
 cause of the error involved. Thus some of these illusions are due 
 to the unrealized fact that the hand of the performer can move 
 more rapidly than the eye can follow, or to a failure to realize the 
 infinite number of surfaces that go to make up a solid (as in the flag 
 trick), or to appreciate the vast number of externalities which may 
 be employed in such performances (as externalities above, below, 
 behind the stage, or in other persons), or the limitations in the 
 scope of one's attentive consciousness (misgrouping). So, in gen- 
 eral, various illusions may be shown to be due, at least proximately, 
 to mis-efficientizing of some sort, and this knowledge may lead to 
 the efficient avoidance or correction of error, often with many dialec- 
 tic results. 
 
 Social and Religious Errors 
 
 By a cumulative combination of the preceding sources of mistakes, 
 as well as for independent reasons, history, politics, and sociology 
 are full of errors and paradoxes. Thus the greatest political crimes 
 have been committed in the name of liberty. Civil and religious wars 
 have been the most bloody and cruel. 
 
 Similarly the field of ethics is full of errors of the most vital sort, 
 the dominant cause being the same extreme lack of externality. 
 Examples are the error of living for the immediate present, and 
 hence in prodigal and wasteful fashion, or in working consciously 
 or unconsciously for narrow selfish ends. Other cases are the fre- 
 quent inconsistency between knowledge and action. Still other 
 instances are the errors connected with the paradoxical fact that 
 intelligent selfishness leads to altruism. 
 
 In like manner the whole field of religion and theology is full of 
 error due to misgrouping of the vast entities involved. Instances 
 are the mistake of regarding some particular type of infinite extern- 
 ality as the only possible one ; or of regarding some special method 
 of approaching and utilizing infinite externality as the only one 
 allowable. Also each form of conventional religion contains princi- 
 
286 SOURCES OF EFFICIENCY 
 
 pies which, in certain respects, at least, are paradoxical and the 
 occasion of many errors. For error as a rule is proportional to 
 power, and "unexpected sources of error lurk in every complicated 
 process". 
 
 When errors occur primarily with reference to certain categories, 
 it is often advantageous to characterize and group them with respect 
 to these categories, even though the various instances might also be 
 classified according to the more concrete materials in which they 
 occur. 
 
 Misconceptions as to Dimensions 
 
 Thus among the groups formed with reference to the various 
 categories of space, are errors as to size, form, or position. Among 
 the most subtle, and also the most important as sources of waste and 
 hence of corrective efficiency, are those with respect to dimensions. 
 Thus the fact that it is harder to keep money than to make it is 
 explained by the fact that a higher dimension of time is involved in 
 the former case than in the latter. A machine or a bridge which is a 
 success in the model, when built on the large scale demanded by 
 actual practice often fails, and indeed may not sustain its own weight, 
 the error involved being due to the fact that the weight of an object 
 increases as the cube of its linear dimensions, while its strength 
 increases only as the square. Lightning strikes at a single point 
 while the thunder which accompanies it is heard over a wide area. 
 The unconscious assumption that the danger from lightning extends 
 over the area throughout which the sound is heard is the source of 
 the extreme terror often produced by a thunder storm. Similarly 
 many other kinds of cowardice may be cured by a realization of the 
 narrow and local nature of the evil which is feared. Likewise it is 
 often of the highest importance to comprehend the fact that good is 
 higher in the dimensions of its efficiency than evil; for while a 
 method of doing good is indefinitely reusable and multiplicative, any 
 form of robbery or wrongdoing can be repeated only a few times 
 before it becomes self-destructive. 
 
 Some Famous Paradoxes and Errors Explained 
 
 To complete the discussion of the principle in hand, it may be 
 well to note that in the dimensional principle which is under consider- 
 ation, we find the explanation of Pascal's paradoxes concerning the 
 
ERROR AND PARADOX 287 
 
 smallness and greatness of man. For man is small in his additive 
 relations but great in his multiplicative essence and powers. A 
 similar explanation holds for Kant's antinomies ; for the universe, 
 for instance, is small (or finite) when the multiplicative principle is 
 used to condense it, and large (or infinite) when the same principle 
 is used to expand it. A special application of the fact that the 
 world is small owing to its multiplicative nature is found in the 
 fact that a traveller in any given place on the earth, usually finds 
 himself near some acquaintance, or at least near some acquaintance 
 of an acquaintance. A somewhat different application is the fact 
 that when processes are fully understood a very few steps will 
 carry us from the data of common life to their most abstruse and 
 technical development. An example is the way in which gunpowder 
 is made in Jules Verne's Mysterious Island, by a shipwrecked man 
 deprived of the ordinary materials supplied by civilized life. 
 
 Of somewhat similar nature are errors with respect to the ratio 
 between cause and effect, or in the various proportions of objects. 
 Illustrations are the mistake that the length of a man's jump will be 
 in proportion to the length of his running start, or that growth and 
 strength will correspond to the amount of food consumed. Another 
 important error of this class is a disproportion between the means 
 employed by a person and his power to use those means. 
 
 The fallacy of the undistributed middle, in which one word is 
 unconsciously used in two or different senses, is an example of error 
 with regard to number and symbols. Illustrations of the numerical 
 paradoxes which are frequently connected with errors are the state- 
 ments that the greatest things are both simple and complex, and that 
 the universe is both unitary and multitudinous. 
 
 Temporal Errors 
 
 Besides ordinary errors as to time, we have its paradoxical 
 properties such as are implied in the statements that life is short 
 yet long ; that all things are old yet new. Similarly errors occur with 
 respect to order. These often take extreme resistant forms, while 
 an understanding of them gives a deeper grouping of the facts of 
 life with new and higher efficiencies in dealing with these facts. 
 Thus in the history of the human race we find that contrary to the 
 common supposition the use of ornaments such as bracelets, neck- 
 laces, and rouge, preceded that of clothing, and that animals were 
 
288 SOURCES OF EFFICIENCY 
 
 first tamed to serve as pets rather than to serve for sources of food. 
 This is an illustration of the fact that ideal efficiency is more primal 
 than concrete utility. What was originally the bottom of a valley 
 has in many cases become a mountain top. Similarly we have a 
 general paradox as to order expressed in the statement, the first 
 shall be last and the last first. 
 
 An important error as to velocity is indicated by the proverb 
 "More haste, less speed". With respect to quality, we have that 
 which confuses size with quality, as bigness with greatness. 
 
 A still more vital and inclusive classification of cases of error is 
 obtained by grouping these according to the various Efficients which 
 are primarily misapprehended or misused in the different instances. 
 
 Errors as to Uniformities and Diversities 
 
 In particular since the principles of uniformity and diversity are 
 of primary importance in making groups and hence in forming the 
 other Efficients, the correction of errors in regard to uniformity and 
 diversity constitutes a conspicuous method of obtaining negative and 
 dialectic efficiency. For instance the failure to realize that the 
 surface of an iron rail, though apparently smooth, is rough enough 
 to have great frictional properties, hindered the early development 
 of railroads. For in the absence of this conception engineers thought 
 that the rail and the wheel running on it must be cogged and must 
 operate in rack and pinion fashion. 
 
 Besides such common violations of uniformity as inaccuracy or 
 want of certitude, misconception as to uniformities often take the 
 costly form frequently denominated "hasty generalizations". This 
 consists in jumping to the conclusion that what is true of certain 
 members of a class is true of all members of the class. For in- 
 stance since most black and peaty soils are fertile some farmers 
 have concluded that all such soils are rich and productive, whereas 
 such soils in places along the Mississippi River, for example, are so 
 deficient in potash as to be practically barren. 
 
 More paradoxical properties of uniformities and diversities about 
 which errors are often made are illustrated by the fact that fre- 
 quently the greater the number or extent of a uniformity the greater 
 the diversities connected with it, and vice versa. The latter of 
 these cases is illustrated by the properties of a book, which is essen- 
 
ERROR AND PARADOX 289 
 
 tially composed of separate leaves, as compared with the ancient 
 manuscript roll. In this connection may also be mentioned 
 Napoleon's maxim, that nothing is so certain to happen as the 
 improbable. 
 
 Errors as to Groups 
 
 A hasty generalization may also be regarded as a group made 
 unduly large. In like manner groups may be made too small or 
 otherwise misused. The misuse of the unit and multiplier principle- 
 is illustrated by the case of a person who is swindled as a result of 
 taking some bait that has been held out, or by the practice on the part 
 of some of magnifying the errors of other people and using them, 
 as pretexts and handles by which to obtain unworthy advantages. 
 
 Errors in regard to multiplicative groups are of many kinds. 
 Among the most important is that of neglecting or failing to see 
 the importance of the general multiplicative structure of a domain. 
 Examples are the failure to realize that a well organized team of 
 moderately able players is often stronger than an all star team not so 
 well organized ; or that the physical texture of a soil is more impor- 
 tant than its chemical constituents. Another instance is that of 
 mistaking a case of tandem for one of parallel elements of efficiency, 
 or vice versa. 
 
 Among the most costly errors are those with respect to the rela- 
 tive importance of factors of efficiency in a given multiplicative or 
 order of materials scale. Among those factors which are often 
 mistakenly inverted are brain and brawn, blessedness and happiness, 
 quantity and quality. An error of this kind often takes the form of 
 consuming or expending the framework of life or character, as if it 
 were something temporary or incidental. 
 
 Errors as to Externality 
 
 Errors in regard to externality are of great importance. Instances 
 are egotism and selfishness in their various forms, or the use of one 
 method of obtaining results to the exclusion of other methods. In 
 striving for results it is of especial importance to remember that 
 what is efficiency from a narrow point of view may be the grossest 
 waste when viewed in a larger way, and that on the other hand 
 what is seeming waste may be real economy and efficiency. In par- 
 ticular efficiency for narrow or selfish ends in the long run is not 
 
290 SOURCES OF EFFICIENCY 
 
 efficiency at all, but relative waste. Similarly as a rule the best 
 and quickest route to extreme technical efficiency lies through a 
 manifold grounding in fundamental theoretical principles. Ex- 
 pressed in more paradoxical form the above principle becomes pro- 
 verbs like, "Luxury is economy", or "The longest way round is the 
 shortest way home". 
 
 Errors as to Other Efficients 
 
 Errors in regard to symbols are numerous and often vitally im- 
 portant because of the wide gap which usually exists between an 
 object and the symbol representing it. Such errors are also costly 
 owing to the highly abstract and efficiental nature of most symbols. 
 Both of these causes open the way to aggressive and wilful abuses 
 such as falsehood, swindling, and forgery. The extreme forms which 
 verbal errors may take are illustrated by the fact that an entire 
 legal document may be invalidated by the omission of a comma. 
 Whole classes of symbolic errors are indicated by such words as 
 misspelled, misread, misname, miscalculate, misrepresent, and other 
 words beginning with the syllable mis. 
 
 A great variety of errors also appear in connection with the 
 Efficient which we have termed directive. Large classes of such 
 errors are indicated by words like mistake, misplace, misdirect, 
 misuse, misapply, misguide, mismanage, as well as by many words 
 formed differently. 
 
 Similarly numerous errors occur in the application of each of 
 the other Efficients. These may take general forms, such as the 
 over use or under use of any one Efficient, or the use of a wrong 
 species or of a faulty combination of Efficients, or they may take 
 more individual and specific forms. Important errors which relate 
 to all processes are those concerning the relative values of the re- 
 sults of different processes. 
 
 Forms of Errors 
 
 Errors may also be classified according to the various categories 
 of form. Thus important cases occur which may be characterized 
 by one or more of the following adjectives: large, small, pervasive, 
 cumulative, conscious, unconscious, resultant, manifold, reciprocal, 
 temporary, permanent, passive, aggressive, primary, secondary, 
 simple, complex, rhythmic. An example of a resultant error is one 
 
ERROR AND PARADOX 
 
 291 
 
 composed of mistakes as to the size, shape, color, and duration of 
 any object, or the combination of errors which led to the loss of the 
 steamship Titanic in April, 1912; of passive errors, are those due 
 to inertia, or imitation; of active errors, are the spendthrift habit 
 or aggressive wrongdoing of any kind. 
 
 Scales of Error 
 
 Errors high in a multiplicative scale are naturally of prime impor- 
 tance. An error may be of high order either because it occurs with 
 respect to some material of high order, as with respect to some 
 fundamental principle of efficiency, or with reference to any Effi- 
 cient. Also an error which leads to or includes a number of other 
 errors is of high order. An example is selfishness or wilful ignor- 
 ance about the laws of health. A like place is held by an error with 
 respect to the nature and methods of correcting errors. 
 
 It is to be noted in this connection that the correction of any 
 fundamental mistake includes the correction of a host of subsidiary 
 errors, with a dialectic of other useful results. 
 
 Transcendent Errors 
 
 Certain errors are so extreme as to be difficult even of proximate 
 explanation and hence may be termed transcendent. The tendency 
 which persons feel to throw themselves from the top of a precipice, 
 and to which an individual occasionally yields even with the cer- 
 tainty of losing his life, has been explained as due to the fascina- 
 tion produced by the thought "of the momentous consequences that 
 would result from such a comparatively simple act". Nevertheless 
 it is difficult to realize how disproportion of this kind could work 
 such a spell that a person would sacrifice his life in order to have 
 this surplusage experience. Of even more extreme nature however 
 are certain cases of moral wrongdoing when the doer is fully aware 
 of the deadly nature of the results of evil and of the beneficial out- 
 come of what is good. 
 
 Paradoxes 
 
 In this connection special mention may be made of the paradox. 
 The paradox is essentially a contradiction between outer appearance 
 and inner reality, but one of so stubborn a nature that it persists in 
 the mind even after it has been explained. Illustrations are the fact 
 
292 SOURCES OF EFFICIENCY 
 
 that in winter "as the days begin to lengthen, the cold begins to 
 strengthen" ; or the ethical principle that it is more blessed to give 
 than to receive; or the spiritual fact that he would gain his life 
 must lose it. These paradoxes are all capable of explanation in 
 terms of the Efficients. Thus receiving is a single or unitary act, 
 while the right kind of giving is continuous and multiplicative in 
 nature, and hence is of a higher order of efficiency; hence the con- 
 trast in this case is between the unit and the multiple or product. 
 Similarly the concrete life must be lost in order that the abstract 
 and comprehensive life may be won, an application being thus made 
 of principles of externality and orders of material. 
 
 Similarly the human will is measurably free in the field of the 
 efficiency abstract, but is relatively restrained in the concrete world. 
 Nevertheless owing to the momentum or dynamic of certain crude 
 psychic habits the feeling of contradiction persists to some extent 
 ofter the explanation has been made. The study of paradoxes 
 however is often particularly useful in that their explanation often 
 brings out into peculiarly clear light the essential nature of many 
 fundamental errors and the most efficient methods of preventing, 
 correcting, or even utilizing these. Such a study also by remov- 
 ing difficulties opens the way to more extensive multiplicative group- 
 ings of errors than would otherwise be possible, and hence to greatly 
 enlarged efficiencies. 
 
 Makers of Errors Classified 
 
 It is often useful to classify errors according to the agencies 
 which make given mistakes. The principal classes of errators are : 
 
 (i ) Individual persons, or certain faculties or parts of a personality 
 such as the memory or imagination. 
 
 (2) Small groups of persons, as families. 
 
 (3) Societies or nations, or even humanity as a whole. 
 
 It will be noticed that the number of agents (that is, the size 
 of the acting group) involved in these three cases increases 
 progressively. 
 
 Complex Errors 
 
 The different species of error and paradox which have been men- 
 tioned in the preceding pages may be combined in various ways. 
 A number of illustrations of complex mistakes have already been 
 
ERROR AND PARADOX 293 
 
 given, but a still more complex case is found in the various errors 
 which have acted as a continuous and often cumulative stream in 
 human history, and which together with other limitations have held 
 human efficiency in so many respects within narrow limits. 
 
 An illustration of paradox combined with error is the fact that 
 Faraday, although he discovered the principle of the dynamo, classed 
 the electro-magnetic engine with mesmerism and perpetual motion, 
 and called them all "ill weeds which cannot be extirpated". A 
 similar instance is the fact that Charles Darwin was publicly repri- 
 manded in the Shrewsbury school for setting up a laboratory for 
 scientific experiment. 
 
 These instances illustrate both the great difficulty in detecting and 
 preventing complex or compound errors, and also the large efficiency 
 results which may often be obtained by so doing. 
 
 NATURE AND EFFICIENCY RELATIONS OF ERROR 
 
 The nature and sources of error, or at least the best way of regard- 
 ing these matters for efficiency purposes, have of necessity been 
 indicated in large measure in the part of the chapter which pre- 
 cedes. It will be useful however to state some of these properties 
 more systematically and to call attention to certain additional ones. 
 
 Dual Nature of Error 
 
 Every case of error may be regarded as dual in nature; that is, 
 as containing 
 
 ( 1 ) a more or less ultimate element, viz. : the fundamental prin- 
 ciple of limitation acting through personality; 
 
 (2) a relative or approximate element, viz.: that of the misuse 
 in some way of an Efficient or of a combination of Efficients. The 
 useful properties connected with the first of these elements have 
 been stated in the preceding chapter and need not here be repeated. 
 
 Multiplicative Element in Error 
 
 With respect to the second of these two elements, the realization 
 of error as due to, or at least accompanied by, the multiplicative 
 principle facilitates an appreciation of the enormous number of 
 ways in which error may arise, and of the explosively destructive 
 consequences of many mistakes ; aids in the recognition and admis- 
 sion of one's own mistakes, and in the treatment of those of others, 
 charitably and in other efficient ways. 
 
294 SOURCES OF EFFICIENCY 
 
 Advantages in Efficiental View of Error 
 
 Thus, for example, the above conception makes clear in striking yet 
 safe ways that what is often regarded as pure folly or malice may 
 contain much that is good and usable. As has been remarked in 
 another connection, the dominant motive in a bullying schoolboy is 
 pleasure in the exercise of his directive faculty, the nature of the 
 effect on others being entirely secondary. The use of these powers 
 may frequently be freed from error and directed into useful channels. 
 The same analysis applies to many of the tyrannies and other errors 
 of older persons. Or, in general, the efficiental view of error and 
 wrongdoing often separates and sets free certain Efficients and 
 allows and stimulates them to act aggressively and effectively. 
 
 In this connection it is well to note that error is often in proportion 
 to power; that it is the man of energy and constructive capacity who 
 makes mistakes. In other words, where there is much waste there is 
 much to save and utilize. 
 
 The above multiplicative view of error also makes clear the need 
 and value of treating error by manifold checks and tests and by 
 inclusive group methods. It also indicates the rich dialectic results 
 which are likely to follow such methods of treatment, and stimulates 
 one to apply such processes. 
 
 Advantageous Use of Error and Waste 
 
 As has been stated in another place, in certain circumstances, 
 especially when hemmed in by certain limitations which for the 
 present seem insuperable, the elimination of waste is the most 
 available source of additional efficiency. Often also error and 
 waste are the most conspicuous signs of possible new positive 
 efficiencies, and the most manageable routes by which to attain 
 these. Also in competitive work a large element of success consists 
 in merely taking advantage of the mistakes of others. Napoleon 
 Bonaparte, for example, obtained many of his greatest victories in 
 this way. This method of procedure in obtaining efficiency is entirely 
 legitimate when the mistakes of evildoers are utilized as a means of 
 overthrowing such people, or the errors of any class of persons are 
 employed as a means of benefiting them. The mistakes made by 
 other people may often also without impropriety be regarded as 
 experiments made for our benefit without cost to us. 
 
 Similarly if the multiplicative elements which are in conflict in a 
 
ERROR AND PARADOX 
 
 295 
 
 paradox be realized, by this very means these elements are set free 
 to act independently, yet in a certain measure with mutual helpful- 
 ness since they stimulate each other to develop in different fields while 
 still maintaining useful relations. The efficiental explanation of 
 paradoxes also, as has been remarked, clears the field of obstacles and 
 thus opens the way to deeper unities and freer action. 
 
 Era of Progress often preceded by Period of Error 
 
 After the above study of the relation of error and paradox to 
 efficiency, it is not surprising to find that almost every important 
 epoch of human progress has been preceded by a stage of error and 
 need, the more or less efficiental treatment of which has led to the 
 subsequent period of progress. Thus we have the age of the 
 Sophists before Socrates, and the period of decadent Greek and 
 Roman morality before Christ. Similarly the destructive Hume 
 preceded the constructive Kant. At various times eras of political 
 oppression have been followed by periods of freedom and progress. 
 The principal ways in which error and evil tend to produce reaction 
 and new efficiencies have been indicated in the preceding pages. 
 
 METHODS OF EFFICIENT TREATMENT 
 
 Many principles and details with respect to the most efficient 
 methods of treating error are contained in, or follow obviously from 
 the preceding discussion. It will be useful however to make certain 
 additional statements as to this matter and to present the whole topic 
 in a more systematic form. 
 
 Multiplicative Principle an Aid in Various Ways 
 
 The multiplicative principle not only aids us in realizing the great 
 number of ways in which errors may arise, but also the extreme forms 
 which errors and their consequences may take. Hence it also sug- 
 gests the importance of using wherever possible a variety of checks 
 and cross multiplicative groupings in preventing, correcting, or utili- 
 zing errors in a given domain of material; and it also makes clear 
 the numerous tests which are usually available. Examples of checks 
 in the forms of cross multiplicative groups are the double entry in 
 bookkeeping and the initiative and referendum in government. 
 
 One of the methods by which the proprietor of a large business 
 often secures efficiency in its management, is that of dividing the 
 
296 SOURCES OF EFFICIENCY 
 
 business into sections or departments, and requiring daily reports of 
 the cost and profit of each department. Any waste or error in any 
 one section is thus quickly revealed and remedied. This constitutes 
 a highly important application of the group method in the treatment 
 of error, and one which frequently gives rise to new, aggressive, 
 and often dialectical efficiencies. 
 
 Application of Principle of Diversity 
 
 The principle of diversity is often a valuable auxiliary in this 
 connection. Thus if a page of proof be corrected first entirely with 
 respect to the spelling, then with respect to the punctuation, and so on 
 for other individual elements, a more thorough correction and utili- 
 zation of error will be obtained than if all the sources of error be 
 treated simultaneously. 
 
 Manifold Treatment of Highest Material 
 
 This multiplicity of safeguards is of especial importance with 
 respect to material which in any given case stands highest in the 
 scale of importance. Thus the traveller should frequently check up 
 his money and at all times should vigilantly protect it from loss or 
 error. So the wide awake business man carefully notes the char- 
 acter of each document to which he affixes his signature. Every wise 
 man in like manner will jealously guard certain first principles of 
 life and action to see that they are not impaired or encroached upon. 
 
 Similarly, cases of especially difficult error, persistent fallacies, 
 paradoxes, and mysteries call for the use of extreme and manifold 
 externality and cross treatment. With sufficient externality a clue 
 to each tangle usually somewhere comes to the surface. 
 
 Application of Unit and Multiplier 
 
 The unit and multiplier principle is often of great service in the 
 treatment of error. For instance its use often prevents the exag- 
 geration of a difficulty and the dismay, discouragement, and other evil 
 results which would follow. When applied in the form of experiment 
 it frequently is a means of avoiding loss of time and resources, and 
 sometimes, either directly or indirectly, leads to the solution of a 
 difficulty. In cases of doubt the erroneous nature of a principle may 
 often be detected by developing the consequences of such a principle 
 by the unit and multiplier method. When used in the step by step 
 
ERROR AND PARADOX 297 
 
 form of the Greek logic, this method often prevents or corrects 
 theoretic errors, or unravels abstract difficulties. When utilized as 
 a means of realizing the consequences of an act or principle, it 
 serves to arouse the attention and to stimulate to action in safe- 
 guarding against mistakes. 
 
 Application of Other Efficients 
 
 The principle of reuse may also be of service in this connection. 
 An instance is the reuse which one makes of the experience of others 
 in the matter of mistakes and difficulties. A person utilizes this 
 principle when consulting a specialist in a given line. 
 
 It is often important to remember that it does not pay to try to 
 prevent all error and waste from this source, but rather that it is 
 frequently best to proceed by the most available efficiency methods 
 and from time to time to correct as far as possible such errors, and 
 provide for such wastes as may have arisen. Similarly it may be 
 advisable at times to allow the results of the errors of others to accu- 
 mulate till in time they, in a measure, check themselves. This in 
 effect constituties a use of the rhythmic method in the backeddy and 
 often dialectic form. 
 
 In another aspect this method consists of giving the leading place to 
 the creation of aggressive efficiency, and a secondary place to the 
 prevention of all errors. It pays better to try to have a large surplus 
 on hand with which to pay for some errors, rather than to try to 
 avoid all mistakes. This is especially true in the more inventive and 
 creative elements of life and action. 
 
 Study of Special Pitfalls 
 
 It is well to remember also that each special field of work or 
 life has its own particular pitfalls or characteristic sources of error 
 and consequent waste. Hence it is important carefully to study the 
 mistakes which are made, or are likely to be made, in any 
 given domain; to ascertain their sources as far as possible; and to 
 treat them in systematic ways. At this point is evident the value 
 of as complete a knowledge as possible of the facts and principles of 
 the various branches of science. Similarly it behooves each person 
 to make a study of the mistakes which are characteristic of his per- 
 sonality, and which therefore he is most likely to make. 
 
298 SOURCES OF EFFICIENCY 
 
 Other General Principles for Treatment of Error 
 
 In the treatment of paradoxes it is desirable to keep in mind the 
 fact that some powerful source of efficiency is usually close to, or is 
 contained in, each apparent contradiction of this kind ; and that it is 
 important to use as extensively as possible each source of efficiency 
 involved in such contradictions, no matter how opposed to each other 
 some of these sources may seem to be at times. Thus the fact that 
 lime when applied to soils both binds a loose soil and loosens a 
 compact one shows the wide and manifold value of this chemical 
 element in agriculture. 
 
 In all cases the power of externality to convert a mistake into a 
 source of ultimate advantage is to be noted. In fact it is not too 
 extreme a statement to say that, with few exceptions, no matter what 
 error one commits, if one has or acquires large enough externality 
 one may convert such error into something advantageous. In the 
 rhythmic series involved all depends on the degree of ultimate 
 externality. 
 
 In general it is important to remember that the entire body of the 
 Efficients is the most effective agent available, both in detecting 
 errors and in treating them in the most useful way. 
 
 Synopsis of Chapter 
 
 An especially important form of limitation is the active, personal 
 one termed error. The peculiar gravity of this species of limitation 
 arises from the fundamental place and function of personality in 
 all efficiency processes. Also the correction of error and removal 
 of waste often form a peculiarly easy way of improving a process. 
 Errors may be conveniently classified according to the objects to 
 which they relate, according to the personalities making mistakes, 
 or with respect to the forms which errors assume. Of prime im- 
 portance are those in regard to the fundamental qualities of objects, 
 to spatial dimensions, to uniformities and diversities, to groups or 
 other Efficients. A paradox is an error which persistently recurs 
 after it has been explained. 
 
 It is of the first importance to realize that every error contains 
 both an ultimate and an approximate or contingent element, and 
 that the latter of these consists essentially in some mistake with 
 reference to the multiplicative principle, and more particularly with 
 reference to one or more of the Efficients. Often by realizing errors 
 
ERROR AND PARADOX 299 
 
 in this way they may be avoided or corrected in large groups. 
 Hence, in general, the best way to avoid, correct, and, in some 
 cases, to utilize errors is by a thorough study and careful appli- 
 cation of the multiplicative principle in its various forms. 
 
 EXERCISE 18 
 
 1. State and explain some costly mistake due to a misunderstanding of 
 the dimensions involved in the material considered. (See p. 286.) 
 
 2. Give two instances of hasty generalizations with disastrous conse- 
 quences. Show how these errors might have been avoided by efficiental means. 
 
 Give an example of 
 
 3. A fallacy 5. An idol of the tribe 
 
 4. An idol of the den 6. An idol of the forum 
 
 7. Of the other principal kinds of error. 
 
 8. At an expenditure of $300,000 a city so diminished the leaks and wastes 
 in its water system that an expenditure of $3,600,000 in order to increase its 
 water supply was avoided. State the degree of efficiency involved. Describe 
 possible dialectic efficiencies which might follow. 
 
 9. Give an illustration of your own of increased efficiency obtained by the 
 elimination of waste instead of by an enlargement of plant. 
 
 10. If in a given country the annual loss from forest fires is $50,000,000 
 and an annual expenditure of $5,000,000 will prevent half of this loss, state 
 the degree of efficiency of the expenditure. 
 
 11. Give an instance of your own where the correction (or prevention) 
 of an error has had dialectic efficiency results. 
 
 Explain each of the following paradoxes : 
 
 12. Hot and cold applications to a part of the human body often produce the 
 same effect. 
 
 13. Genius and insanity are closely related. 
 
 14. At the seashore, the hotter the sun's rays the cooler the sea breeze. 
 
 15. A cool sea breeze means warm surf bathing. 
 
 16. Give an error that is dual 17. Manifold 18. Of high order 
 
 19. State the species of error implied in the statement "all is not gold that 
 glitters". 
 
 20. Give two examples of optical illusions with explanations of the same. 
 Show how these explanations may be made the basis of aggressive efficiencies. 
 
 21. How is it possible that some rivers at certain seasons of the year flow 
 up stream? 
 
 22. Why should the river Nile be smaller near its mouth? 
 
 23. Why is it that that which looks most easy to do, as the playing of a 
 violin by an expert, is often most difficult? 
 
 24. Give two examples of paradoxes with explanations of the same in 
 terms of the principles of this book. 
 
 How might these explanations be made sources of efficiency? 
 
300 SOURCES OF EFFICIENCY 
 
 25. Why is it that, in some respects, the best way to see the country is to 
 go to the city? 
 
 26. Give an example of an error arising from confusing quantity with 
 quality. 
 
 27. Why is it that many pensons think of Palestine as larger than New- 
 foundland or Peru? 
 
 28. Give an example of a mistake due to inertia or momentum. 
 
 29. State and explain the principles of efficiency involved in the statement 
 that the serpent, though it has no limbs can "outclimb the monkey, outswim 
 the fish, outleap the jerboa, and, suddenly loosening the coils of its crouching 
 spiral, it can spring into the air and seize the bird on the wing". 
 
 30. Why is it that a person is often the most solitary when in a crowd? 
 
 31. Give an example of an error which consists essentially of regarding a 
 multiplicative process or relation as merely additive? 
 
 32. Give an instance where, instead of trying to prevent all error and waste 
 greater net efficiency is obtained by employing in aggressive ways the energy 
 that would be thus spent. In this connection what is the meaning of the 
 business man's profit and loss account? 
 
 Give an instance 
 
 33. Where the use of externality has been the means of detecting error 
 or loss. 
 
 34. Where the use of externality has prevented error or waste. 
 
 35. Where the use of cross multiplicative groups detects or prevents error. 
 
 36. Where the use of the unit and multiplier principle has prevented waste. 
 
 37. Why are the simplest things often the hardest to understand? 
 
 38. What efficiental term would be used in describing an error concerning 
 errors? 
 
CHAPTER XVII 
 
 COMBINATIONS OF EFFICIENTS 
 SUMMARY 
 
 Illustrations of Combinations of Efficients 
 
 When man supports himself by hunting and fishing, he uses 
 food which is of a high nutritive value, but one which is relatively 
 scarce. Hence in the hunting and fishing stage of civilization man 
 necessarily lived in a somewhat isolated manner. When men who 
 have tried to support themselves in this way have multiplied in 
 numbers, it has become necessary for them, in the end, to subsist 
 more and more on vegetable products. Such food is of a relatively 
 low order, but it has the property that by externality and by the 
 cooperation of the producers it may be made very abundant. Hence 
 its preparation in time came to be accompanied by an elaborate 
 social organization with many unexpected resultant advantages such 
 as a high degree of mental development and of the arts and sciences 
 which accompany such development. The complex social organiza- 
 tion of certain kinds of insects, as of some species of ants, and their 
 great relative intelligence find a like explanation. Originally ants 
 were meat eaters and like spiders lived approximately solitary lives. 
 The stages may be traced by which, as their food changed, first to 
 the mixed form and then to a vegetable basis, their social organiza- 
 tion and general intelligence also developed. These cases are illus- 
 trations of the fact that in a world full of diversity, limitation, and 
 active competition, more effective results are obtained by using a 
 combination of efficiency agencies than by the use of any single one. 
 
 General Statement of Advantages 
 
 In general the employment of a combination of the primal instru- 
 ments of efficiency, instead of one only, usually makes possible a 
 closer contact with the actualities of the world of fact than is 
 otherwise possible. Hence result certain intense, and often sudden 
 and dynamic efficiency results which are of the highest importance 
 in a world of competition. Various efficiency methods when com- 
 
302 
 
 SOURCES OF EFFICIENCY 
 
 bined in a given process often interact also in ways so manifold 
 and complex as to be impossible to trace in detail. 
 
 For instance, in the rotation of crops in agriculture we evidently 
 have a use of the principles of diversity, directive, and rhythm. 
 But these result in other efficiency principles such as the retention 
 and reuse of farm laborers the year round, the greater reuse of farm 
 machinery, utilization of by-products, the prevention of waste as 
 by the destruction of insect pests, a uniformity of returns, and 
 many other useful results and agencies. 
 
 Similarly in various forms of business, in education, in govern- 
 ment, and in almost all actual, fruitful processes, we find a combina- 
 tion of efficiency agencies at work. Often by careful study such 
 combinations may be developed to a far higher degree of efficiency. 
 
 Apart from their so-called business or practical uses, various 
 bizarre combinations of efficiency agencies prevent work from de- 
 generating into a mere formalism, and go far to give spice, variety, 
 and charm to life. 
 
 Classes of Combinations 
 
 Evidently the possible forms and species of combinations of Effi- 
 cients is without limit in form and number. In the preceding chap- 
 ters the different forms which each Efficient may assume have been 
 outlined, and plainly the number of different combinations that may 
 be made of these various species vastly exceed the varieties of any 
 one agent. A realization of some of the principal forms of com- 
 binations will be an aid in selecting the best combination for use 
 in any given case, and will be useful in many other ways. 
 
 Loose Combinations of Efficients 
 
 In the first place we have those combinations of Efficients which 
 are comparatively loose and incoherent. A situation may be so 
 difficult that in it, especially at first, it is possible to use only what 
 may be termed efficiental opportunism; that is, to employ such local 
 and fragmentary efficiency methods as may be available from time 
 to time and to leave the rest to future development. Simple in- 
 stances of this process are that of looking at a subject from 
 various points of view, or of working at a problem along various 
 lines. So in business greater efficiency is obtained by applying 
 adapted methods of obtaining results, to buying, manufacturing, 
 
COMBINATIONS OF EFFICIENTS 
 
 303 
 
 selling, and accounting than could be obtained by trying to develop 
 all of these by one exclusive procrustean method. 
 
 The more abstract cases of this general type of combination are 
 illustrated by the advantages in combining and using different views 
 of electricity, no matter how contradictory these theories may appear 
 from some points of view. For if electricity be regarded in cer- 
 tain cases as composed of small units called electrons; in other 
 cases, as a combination of positive and negative fluids ; and in 
 still others, as stresses or undulations in the ether, it is found that 
 better results are obtained in the aggregate, than if any one of these 
 seemingly opposed views were used alone. 
 
 An important instance of somewhat different nature is that of 
 organizing a business or a nation in such a way that it shall be char- 
 acterized at the same time by the utmost system (or multiplicative 
 group organization) and also by the greatest possible freedom 
 (diversity) and initiative (directive) on the part of the individuals 
 and other units composing it. 
 
 Often it is well (or even necessary) for a time to develop each 
 strand or element of efficiency in a given situation, with little or 
 no regard to the other sources or strands, and to wait or work for 
 later, more definite combinations and crystallizations. 
 
 As a transition to the next general class of combinations mention 
 may be made of the conscious formation of habits as a source of 
 efficiency. This involves the combined use of the following effi- 
 cients: reuse both objective and subjective, specialism (or diversity) 
 and uniformity in kinds of activity, externality in the shape of extra 
 educational practice, a resulting speed and force of action, and the 
 substitution of lower for higher and more costly energy. 
 
 Close Combinations of Efficients 
 
 Another important form of combinations of efficiency agents is 
 that in which the component agents are so closely knit together that 
 their individuality is largely lost in that of the whole. Thus the 
 efficiency of the human body arises to a great extent from the fact 
 that the various agents and sources of effectiveness in it are in 
 many places and respects so completely fused together. We here 
 find, for example, various uniformities and diversities among the 
 cells, tissues and organs ; multiplicative groups of many species, 
 both articulate and constitutive ; orders of materials, as illustrated by 
 the series, brain, nerve, flesh, bone; externality operating through 
 
304 SOURCES OF EFFICIENCY 
 
 the eye and hand, and many subjective reciprocal externalities; 
 varied reuse of each organ; and symbolisms, force, motion, directive, 
 rhythms, and dialectics of various kinds. But the whole aggre- 
 gate is so closely knit together as to form a solid contexture of 
 efficientisms ; in fact a unity is present which is perhaps beyond 
 analysis. This fact is the source of efficiency results which are far 
 beyond those which could be obtained from the agents specified in 
 the above list if used in scattered fashion. The same principle holds, 
 in even higher degree of the human mind. The efficiency relations 
 involved in a thoroughly united human family are of like nature. 
 
 Many of the sources of success, that is, methods of obtaining re- 
 sults, as popularly stated, are of this mixed and closely fused nature. 
 Illustrations are the terms shrewdness, good health, magnetism, 
 native ability, or even genius. Thus shrewdness includes power to 
 perceive differences (or diversities) where other persons see only 
 uniformity; to look beyond the immediate present (externality); 
 to penetrate beneath the surface of things (use of orders of ma- 
 terial) ; and the avoidance of error. Any highly developed or 
 thoroughly mastered art of doing things, as contrasted with the 
 science or knowledge of them is largely a thoroughly fused com- 
 bination of efficiency processes of the general type under discussion. 
 Instances in another field are the concepts of harmony, beauty, and 
 sublimity. Thus many mechanical and formal rules are combined in 
 a statue like the Venus of Milo, but they are so completely com- 
 bined, or interact so subtly, that their complete analysis is impossible. 
 
 In an even more abstract world, it may be shown that concepts 
 like those of space, time, and cause are instruments of the highest 
 efficiency, and that this efficiency is greatly increased if, in certain, 
 respects, each of them be regarded as a closely knit aggregate 
 of primal Efficients. 
 
 Combinations built up progressively 
 
 Systems of Efficients which have been built up progressively in 
 time, or are the result of a species of growth, even though these 
 systems contain elements which are in large part mere survivals by 
 virtue of inertia, are often peculiarly rich and effective. An example 
 is the English form of government. The human body and human 
 mind as described above, and most of the general concepts in use.: 
 are of the same general nature. 
 
COMBINATIONS OF EFFICIENTS 305 
 
 Mottled Combinations of Efficients 
 
 As a result of human directive action and of processes of natural 
 development, many combinations are of a varied or mottled char- 
 acter with respect to the closeness with which their components 
 are aggregated. Thus in some parts of any highly developed busi- 
 ness the Efficients are loosely aggregated and in others they are 
 highly fused. The same will be found to be true of almost all 
 efficiency processes in actual operation in the concrete world if thor- 
 oughly examined. In many cases this diversity is the result of what 
 seems caprice or even error, in others it means a closer adaptation to 
 limitations and qualities beyond control, and hence is a source of 
 important added efficiency. 
 
 The above considerations suggest certain remarks as to the best 
 methods of using combinations of Efficients in actual practice. In 
 the first place it may be noted that such combinations in some cases 
 form a crude, initial instrument by which to attack a problem or 
 treat a situation ; but that in other cases they form a highly finished, 
 final instrument; and that they may have every degree of develop- 
 ment and value between these extremes. 
 
 Efficient Transitions 
 
 Again in order to obtain results of the highest order from the 
 use of groups of Efficients, especially of the more developed 
 combinations, it is often important to make the transition from one 
 component in them to another with a certain deft and invisible 
 swiftness. The changes in the moods and methods of an accom- 
 plished orator illustrate this. Frequently added efficiency is ob- 
 tained by the concentration of some one or more of the involved 
 Efficients into a momentary intensity. This principle also is illus- 
 trated by some single word, tone, or gesture of the orator. These 
 intense master strokes of action are characteristic of workmanship 
 of the highest order in all fields however diverse, as in trimming 
 a woman's hat, or painting a picture ; driving an automobile, or 
 governing a nation. 
 
 Application of Directive and Dialectic 
 
 Similarly in employing combinations of the primal instruments of 
 efficiency it is of great importance to know when to allow them to 
 act of themselves in whole or in part. By practice their use in 
 many ways may be made subconscious and instinctive, and it often 
 
306 SOURCES OF EFFICIENCY 
 
 pays not to interfere with such methods of use when these have 
 been acquired. In other words, often the most efficient way of 
 using efficiental pluralisms is to treat them much as if they were 
 living organisms. 
 
 Two Principal Forms of Combinations 
 
 It is important to note that, in this relation, highly developed 
 combinations of Efficients take two principal forms, viz. : ( i ) those 
 characterized by peculiarly intense adaptations to the local pecu- 
 liarities of a given field, and (2) more general and abstract aggre- 
 gations of the Efficients. It is well, if possible, always to use the 
 latter of these two species in connection with the former. The 
 close contact with so-called realities involved in the first species, 
 together with the resultant momentum and dynamic, often leads 
 to a certain narrowness when this kind of combination alone is 
 used. The concurrent application of the general ideal species not 
 only tends to prevent these drawbacks but to produce other more 
 positive results by the externality thus supplied, and the interactions 
 and dialectic which arise as a consequence. 
 
 Universal Efficiency Machine 
 
 The general observation may also be made that it is often a 
 source of efficiency to regard the entire aggregate of the Efficients as 
 a kind of universal machine, capable of variation by marginal reuse 
 in different ways, and thus made applicable to special problems and 
 situations. 
 
 General Summary 
 
 At this point it will be of advantage to sum up the results arrived 
 at in the present and preceding chapters. 
 
 An efficient process is one in which the results exceed the expendi- 
 ture. The primary instrument of efficiency is the group. 
 
 The group principle takes several different forms called the Effi- 
 cients. Among the most important of these are reuse, the unit and 
 multiplier, multiplicative groups, orders of material, uniformity and 
 diversity, externality, symbolism, kinematic and dynamic, directive, 
 dialectic, rhythm, combinations, with limitation and error as nega- 
 tive species. 
 
 The primary aim and end of efficiency is subpersonal surplusage 
 
COMBINATIONS OF EFFICIENTS 307 
 
 or positive non-equivalence. This is the common essence of value, 
 happiness, blessedness, gain, and even of more special and concrete 
 terms such as wealth, fame, food, and life. 
 
 In the excess of the result over the datum, the idea of the one 
 to the many, or of the group, appears again. Hence many-to-oneness 
 has two principle aspects (1) that of the means or method (2) 
 that of end or result. In this double way, in the realm of efficiency, 
 the fundamental principle is the group. 
 
 By multiplicative principle is meant the group with the aspect of 
 force or dialectic which is inherent in it made prominent, and hence 
 suggestive of the different forms which the group assumes and of 
 the results which it produces. 
 
 In order to apply the above scheme of toolage, it is important 
 explicitly to recognize that this scheme is built on a full recognition 
 of the principle of limitation. Limitation is primarily subpersonal 
 in nature, and multiplicative in its properties. 
 
 Hence for efficiency purposes the totality of things is to be re- 
 garded as composed of two giant opposed multiplicative systems, 
 positive and negative, the one which produces positive Results 
 being, on the whole, dominant. 
 
 EXERCISE 19 
 
 1. Three men working independently in one year earned $3000, $3500, and 
 $4000. After combining as a corporation they together earned $20,000 in 
 one year. State the degree of efficiency involved, and some of the Efficients 
 which might operate to produce this result. 
 
 2. A blacksmith and a wheelwright together can make a shovel for $2. 
 This can be made in a factory for 20 cents. State the degree of efficiency 
 involved in the machine made tool and the sources of this efficiency. 
 
 3. State the principal Efficients which make the aeroplane possible. 
 
 4. Answer the same for the dirigible. 
 
 5. What Efficients are combined in the modern processes of spinning 
 threads and yarn as compared with the former use of the distaff and 
 spinning wheel. 
 
 6. What Efficients are combined in modern methods of weaving cloth as 
 compared with more primitive methods. 
 
 7. State in both efficiental and more conventional terms the advantages in 
 using garments made of cloth as compared with the use of bark or the 
 skins of animals as clothing. 
 
 8. Multiply S bu. 2 pk. 5 qt. by 17. Also multiply 427 qt. by 17. Estimate 
 the labor efficiency of the second process as compared with the first. Name 
 the prime sources of this increased efficiency. 
 
308 SOURCES OF EFFICIENCY 
 
 9. One steamer crossed the Atlantic Ocean in 9 days 10 hours, and another 
 steamer crossed by the same route in 5 days 2 hours. Compute the time 
 efficiency of the second as compared with the first steamer. State some of 
 the possible efficiental sources of this efficiency. 
 
 10. A herd of cows when fed in a more or less haphazard fashion pro- 
 duced $3600 worth of milk in one year at a cost of $2200. Later, when fed 
 at the same expense with rations compounded scientifically, they produced 
 $4800 worth of milk in one year. State the degree and sources of the 
 efficiency involved. 
 
 11. In a certain poultry establishment, the 15,000 hens which are kept are 
 divided into groups of 100 each. A record is kept of the daily food and 
 number of eggs laid by each group. When the number of eggs laid by any 
 one group falls below a certain standard, the food of the group is changed. 
 What Efficients are involved in this method of conducting the business? 
 
 12. Instead of paying $600 a year for a teacher for his children, $400 for 
 a private watchman for his property, and $100 for upkeep of roads near 
 his property, a man pays $108 taxes. The financial efficiency of the second 
 method is how many times that of the first? State the fundamental sources 
 of this efficiency. 
 
 13. Give an instance where a number of Efficients are in such close fusion 
 as to have largely lost their individuality. 
 
 14. Express in terms of the Efficients the meaning of each of the following 
 conventional categories of success : foresight, energy, prudence, reliability, 
 popularity, punctuality, tact, sagacity, thrift, industry, health, cooperation. 
 
CHAPTER XVIII 
 
 APPLICATIONS 
 
 Many more or less concrete applications of the principles arrived at 
 have been given incidentally in the preceding pages. It will throw 
 new light on these principles and be of service .in other ways if a 
 more systematic, though brief application of the efficiency methods 
 advocated be made to specimen departments of human thought and 
 endeavor. Since all applications to the world as it is must, in the 
 ultimate analysis, be made by persons, we first consider the relation 
 of the principles under discussion to the department of psychology. 
 
 PSYCHOLOGY 
 Memory as an Efficiency Agency 
 
 If a person can recall by act of memory the way in which a given 
 word is spelled, he is often saved the labor of going to the dictionary 
 and looking up the word. In this and similar ways one's memory 
 is a means of obtaining economy and efficiency. As such it may 
 have very great, even infinite or absolute values. For example if 
 a person can remember, in case of need, the methods to be used 
 in resuscitating a drowned person, memory may be the means of 
 saving a life. 
 
 It should also be added in this connection that memory is groupish 
 and efficiental in its organization. For instance facts are stored 
 up by the mind in groups and recalled by means of this group rela- 
 tion (called the association of ideas). Hence a knowledge of the 
 multiplicative principle in its various ramifications should be an 
 aid in improving the memory subjectively. Objectively, also, a 
 grasp of the general efficiental organization of the universe will be an 
 aid in recalling and using any part of this whole. 
 
 Reason as an Instrument of Efficiency 
 
 If a savage man observes an animal floating down a stream on 
 a log, he may infer that he himself can be transported in like manner, 
 and that thus he may save the labor involved in walking on the land 
 or in swimming. This one act of inference, when fully developed, 
 
 309 
 
310 SOURCES OF EFFICIENCY 
 
 becomes the whole science and art of navigation, and this simple 
 instances of the saving of labor becomes the vast and often transcen- 
 dent fruitage flowing from world wide travel and commerce. Hence 
 the reasoning faculty in man is an efficiency organ of great impor- 
 tance. Like memory it acts both subjectively and objectively by the 
 group method in some form. Thus, after facts have been arranged 
 in like groups, we may often infer that what is true of one member 
 of a group is true of the other members also. Hence the reasoning 
 faculty in man should be greatly improved in grasp and action by 
 explicit knowledge of the efficiental group theory in its various 
 aspects. 
 
 Efficiencies in the Various Senses 
 
 The faculty of perception in its elementary form is so primal 
 that it is difficult of analysis. However it is evident that in 
 the act of perceiving, a person is made aware of uniformities 
 and diversities and hence of groups, both in himself and in the 
 external world. To a certain extent also in an act of perception, 
 the observer arranges objects and facts in groups. Another of the 
 services of perception is to put the perceiver directly or potentially 
 in useful relations with externality of various kinds. In this respect 
 the senses may be arranged in an important order of materials scale. 
 Thus at the lower end of the scale, the sense of touch gives notice, 
 as a rule, of somewhat vague and small externality, while, at the 
 other end, the sense of vision, by acquainting us with the fixed stars 
 for instance, reveals a highly organized externality extending for 
 untold millions of miles from the observer. 
 
 It is to be noted also that the organs of sense act by the aid 
 of various auxiliaries which are multipliers or group organs in 
 essence. Thus the sense of vision operates through a lens embedded 
 in the eyeball, the sense of hearing is aided by bones which act as- 
 multiplying levers, and touch by hairs and papillae serving in like 
 manner. Similarly the efficiency of perception is often increased by 
 external objects used as auxiliaries and which concentrate or multi- 
 ply the data apprehended, illustrations being the telescope, micro- 
 scope, galvanometer, sounding board, and microphone. 
 
 Other Psychic Powers as Instruments of Efficiency 
 
 In like manner it might be shown that the imagination, will, and 
 feelings are efficiental instruments of different kinds, and capable 
 
APPLICATIONS 311 
 
 of much improvement by efficiental methods. In this connection it 
 may be remarked that what is often termed common sense is per- 
 ception of, or judgment as to, primal groups in the efficiency organi- 
 zation of things, and may be cultivated in the ways indicated for 
 the more conventional psychological powers which have been 
 mentioned. 
 
 The Group Principle as Fundamental in Psychology 
 
 It is often desirable to be able to reduce mental processes, if 
 only approximately, to some single primal principle. Various mental 
 categories have been suggested for this central principle, the most 
 prominent being feeling, cognition, or volition. But it is easy to 
 show that each of these three mental categories contains or im- 
 plies the other two. For example both action and feeling in some: 
 form are essential elements in cognition. From our point of view the 
 central or essential element of mind is the multiplicative, or group 
 principle operating within the domain which we term personality. 
 Feeling, cognition, volition, and other mental processes are certain 
 specific forms of this central principle. According to efficiency con- 
 venience they may be regarded either as somewhat distinct faculties, 
 or as the modes in which a unitary mentality acts. A central mental 
 principle like that suggested has important uses in that it enables 
 us to apply our knowledge of groups to all mental processes and 
 phenomena, and, for example, to use marginal reuse of various 
 kinds in dealing with them. 
 
 Appreciation of Diverse Psychic Processes 
 
 This unitary category also has the advantage of aiding us to realize 
 psychological processes widely different from our own, as for in- 
 stance those of children, primitive peoples, and the lower animals. 
 Since all these processes are multiplicative and efficiental in nature 
 it is easy to comprehend that some of them in some particular, may 
 be far more highly developed than our own corresponding powers, 
 and also that animals, for example, may have some mental instru- 
 ments or faculties very different from those of man. 
 
 This instrumental view of mind also gives us added insight into 
 the processes of what we term genius. Thus we are enabled to 
 realize, for instance, that every really great man is master in some 
 form of part or all of the fundamental efficiental processes. Colum- 
 
312 SOURCES OF EFFICIENCY 
 
 bus had the externality and directive faculties to an unusual de- 
 gree, and Napoleon possessed great powers in the use of the group 
 principle in its different forms. We are also able to understand the 
 simplicity which characterizes many great men, since the mastery 
 of even one item of the fundamental efficiency processes may mean 
 vast power in the more concrete world. This view of genius also 
 •enables us to comprehend the fact that a great nature may be frag- 
 mentary, contradictory, and have other serious faults, and yet 
 produce vastly useful results. 
 
 If mind is regarded as essentially a multiplicatively grouping 
 entity, it is made easier to conceive that it, or the germs of it, may 
 be present in the primordial atoms, monads, or substance which 
 evolution presupposes ; or, to state the matter in another form, we 
 may conceive of both mind and matter as developing from some 
 more primal form of the group principle by radial evolution. 
 
 Deductions from Efficiental View of Mind 
 
 Specific mention should be made of certain deductions from the 
 above views concerning mind, which are capable of immediate and 
 general application. 
 
 ( i ) The view presented makes obvious the importance of acquir- 
 ing the power of rapidly and accurately reading the efficiental powers 
 and habits of other persons, especially their externality scope, their 
 multiplicative grouping faculties; .and their surplusage tastes and 
 preferences. In other words the analysis of the mind in terms of 
 the Efficients should be made primary and essential and that into 
 perception, memory, etc., secondary and auxiliary. 
 
 (2) The above view also shows in a general way how the psycho- 
 logical faculties, as conventionally regarded, may be greatly improved 
 in grasp and efficiency. Thus if the mind realizes the general effi- 
 ciency organization of things as a whole, a multitude of new means 
 of perceiving uniformities and diversities will be supplied and the 
 faculty of perception will also be stimulated to greater depth and 
 acuteness of action by the realization that every uniformity or diver- 
 sity may have enormous mutlipliers with corresponding values or 
 dangers. So courage is greatly increased by noting that, owing to 
 the groupish nature of the universe, danger comes only in spots, and 
 that, because of the dominance of the positive multiplicative system, 
 evil tends in the long run to cancel itself. So, also, we can conceive 
 
APPLICATIONS 
 
 313 
 
 -of memory and reason, feelings and conscience as developed and 
 improved by efficiental means. 
 
 (3) The above view also makes it readily conceivable that with 
 practice, and often by the method of dialectic, new efficiental mental 
 organs and powers may be developed. An example is the species 
 •of pleasure which may come to be associated with an efficiental 
 process or fact. Similarly new and higher processes of memory, 
 imagination, and moral judgment may spring from efficiental data. 
 We may conceive also that powers of mental grouping and obtaining 
 results may be generated which shall transcend such terms as per- 
 ception and reason. 
 
 EDUCATION 
 
 Man's Activities Statable in Efficiental Terms 
 
 If the daily activities of a reasonably intelligent farmer, for ex- 
 ample, be examined, it will be found that by far the greatest part of 
 them consists of acts and elements such as have been described in 
 the preceding pages of this book. Thus by him or under his super- 
 vision in a single day scores or hundreds of acts of reuse will be 
 performed. These will include the reuse of tools, machines, soils, 
 animals, the farmer's experience, and that of other persons. Simi- 
 larly the day's activities will contain many uses of auxiliary objects; 
 of groups of objects ; of multiplicative groups either in the form of 
 organization as directly applied to the work of the farm, or of 
 external multiplicative groups such as the post-office system, rail- 
 roads and various social and political organizations. The farmer 
 will need to use symbolisms in keeping his accounts, in buying and 
 selling, and in directing his subordinates. Various rhythms will be 
 present in his work due to the alternation of day and night, the 
 change of seasons, and the use of processes such as the rotation of 
 crops. His work will also include many kinds of directive and of 
 utilized motion and force, and will be held in check by various forms 
 of limitation and error. 
 
 Also if his life is to be successful in the higher sense, the farmer 
 must cultivate uniformity in various forms such as accuracy, truth 
 and justice; externality in the shape of sympathy and breadth of 
 view ; and other Efficients in various social and moral forms. 
 
 The successful agriculturalist also needs a certain amount of 
 technical knowledge. Thus a considerable and more or less minute 
 
^14 SOURCES OF EFFICIENCY 
 
 acquaintance with scientific facts concerning plant and animal life 
 (biology) will evidently be of service to him. The efficiency of his 
 work in dealing with fertilizers will be appreciably increased by a. 
 knowledge of chemistry, in dealing with machinery by a knowledge 
 of physics, and with soils by a knowledge of both these sciences. An 
 acquaintance with psychology or the principles of the mind will be 
 useful to him in commercial operations and in dealing with his 
 employees. But the larger part, if not all, of this more technical 
 knowledge is found on examination to consist of the Efficients 
 clothed or combined in special ways. Hence we may say by way of 
 summary that 99 per cent of a farmer's work and life consists of 
 efficiental processes such as have been described in this book. 
 
 A like examination would show that by far the larger parts of 
 the activities of other callings, as, for instance, the legal profession 
 or electrical engineering, are, in like manner, primarily and essen- 
 tially common sense efficiency processes. 
 
 Woman's Activities in Efficiental Terms 
 
 It is equally important to realize that the domestic work of woman 
 has a similar significance. Thus in the work of the kitchen, groups 
 of many kinds are used in combining articles of food to make meals 
 and dishes, in storing appliances and supplies, and in systematizing 
 activities. Externalities are employed in the form of utensils, heat 
 (to produce diversity and re-multiplicative-grouping), the experi- 
 ence of other persons, and the application of departments of knowl- 
 edge like chemistry, physics, biology, agriculture, and ethics. Reuse, 
 either entire or marginal, occurs in plain forms such as the repeated 
 use of a recipe or a menu. This principle is also applicable in less 
 obvious ways as when articles of diet of different rates of digestion 
 are combined in a given meal, so that the stomach can, in a measure, 
 digest them in succession and thus reuse its powers. Rhythms are 
 to be observed in the form of daily, weekly, and seasonal changes 
 of work, and of articles prepared for food. Directive occurs in 
 many different forms and is capable of being made a source of 
 efficiency in many new ways each day. Every good dish, meal, day's 
 or week's diet is a pluralism or combination of Efficients and in the 
 preparation of these combinations a knowledge of pluralisms may be 
 utilized and developed constantly. Similar applications in kitchen. 
 
APPLICATIONS 315 
 
 work of other Efficients such as units and multipliers, orders of 
 material, and dialectic might be indicated. 
 
 An examination of other domestic activities would show that they 
 are statable in terms like those just given for kitchen work and have 
 a like wide significance. For instance in house furnishing and orna- 
 mentation, the externalities and other Efficients which may be 
 employed are almost without limit. A similar statement applies to 
 dress and personal adornment. The same essential artistic and 
 efficiental principles may be used by a woman in trimming a hat that 
 were applied by Milton in writing his Paradise Lost. Social usages 
 are full of groupings, regroupings, symbolisms, and other Efficients. 
 This fact is illustrated by various social assemblages, by the recipro- 
 cal reuses at these of the efficiencies in which each person present 
 excels, by letters of introduction, calling cards, bowings, tipping of 
 hats, shaking of hands, and by all that is included under such 
 terms as tact, courtesy, and friendship. 
 
 Education Should be primarily Efficiental 
 
 Since life in general and work in different callings consist essen- 
 tially of efficiental activities, it follows that education should consist 
 primarily of the setting free and development, in the most economical 
 and effective way, of the efficiental powers of a person. This view 
 of the matter, when fully realized, should lead to improvements in 
 the processes of education, and should increase both the technical 
 and general efficiental value of study. For instance, it suggests as a 
 basis of educational work, a careful examination of the child's mind 
 with respect to its powers and habits of grouping, multiplicative 
 grouping, reuse and the other primary principles of efficiency. It 
 indicates the value of training and selecting teachers with reference 
 to their ability in developing the above powers in children. 
 
 Value of Different Studies in terms of the Efficients 
 
 It also throws new light on the relative educational value of 
 different subjects of study and on the methods to be followed in 
 obtaining the maximum of results from each study at the minimum 
 of cost. Thus in linguistic study it is of fundamental importance to 
 realize the efficiental elements which enter into the subject. In 
 language as a subject of study, besides specific principles of symbol- 
 ism, are found striking examples of reuse, groups, multiplicative 
 
316 SOURCES OF EFFICIENCY 
 
 groups, and all of the other Efficients. Thus as an example of 
 economy and reuse we have the fact that by reading a book of travels 
 which costs a dollar (and often in fact may be had free) we may 
 obtain in a few hours many of the results which could otherwise 
 be procured only by an actual journey costing hundreds of dollars 
 and weeks of time. Marginal reuse is illustrated by the employment 
 of prefixes and suffixes in connection with word stems. A book is a 
 multiplicative group in many ways. Since a large number of concrete 
 words may often be replaced by a single abstract word, the use of 
 the latter illustrates the group and order of materials principles. 
 The comparison of various grammatical forms in different languages 
 is a valuable training in the use of diversities and externality. The 
 fact that language has been built up in a complex and bizarre 
 fashion makes it a useful representative of all efficiency pluralisms. 
 It is well to note in this connection the highly condensed form and 
 small cost of the subject matter of linguistic study as compared with 
 the materials employed in the study of branches of science like 
 engineering and agriculture. As a further result of this difference, 
 language study as a part of education has the advantage that pupils 
 can be trained in it in large groups and hence at small cost. 
 
 Most of the Efficients are present in mathematical subjects also, 
 and often in a much more explicit and detachable form than in 
 languages as ordinarily studied. For a further development of this 
 idea the reader is referred to the various textbooks and articles by 
 the author on mathematical subjects. 
 
 As a subject of educational study, physical and biological science 
 when compared with language, has the advantage of being in large 
 part directly related with concrete objects and hence being free from 
 the errors which arise from the abstractions and detachment of 
 language. In science also, as compared with mathematics, the Effi- 
 cients often appear in more individual, tangible, and striking forms. 
 Instances are externalities in the form of various kinds of appara- 
 tus, the units and multiplier characteristic of the experimental 
 method, and directive of various concrete and abstract kinds. 
 
 Increasing the Efficiency Value of Studies 
 
 The above analysis not only indicates methods of determining 
 the relative values of different studies, but also suggests methods of 
 giving greater usefulness to such studies as are selected and pur- 
 
APPLICATIONS 317 
 
 sued. For instance it is made clear that in the study of science, the 
 Efficients involved in a process should be made as explicit as possi- 
 ble and that much may also often be gained by giving a leading 
 place to the functions and results of a process. Frequently it will 
 be best to bring out the advantageous results (or efhciental functions) 
 of a process first in a qualitative or mass form, and later to take 
 up quantitative methods as a means of making results more 
 manageable and increasing them in various ways. Thus in order 
 to interest pupils and enable them to get their efficiency bearings, it 
 is an advantage in the first presentation of the matter, to develop 
 the various kinds of useful results which can be obtained from 
 water falling over a dam. Later it may be shown that the utility of 
 these results will be greatly increased by learning the laws of falling 
 bodies and of the transformation of energy, and by thus reducing 
 the processes involved to an exact commercial basis. 
 
 Informal Efficiental Training 
 
 The above view of education greatly enlarges the means by 
 which the most fundamental and important part of education, viz.. 
 the development of the child's efhciental powers, may be carried on. 
 Charles Dudley Warner has said that a training in doing chores has 
 been an essential part of the development of every great man. The 
 truth in this statement is based on the fact that doing chores consists 
 essentially in grouping common objects, in reusing and directing 
 them, and in other primary efficiency processes. Play and games 
 may also be analyzed into these elements and hence may be made 
 to have fundamental educational values. The study of music, eti- 
 quette, or even of changes in the weather may be shown to have 
 similar uses. In fact, every field or species of occupation, however 
 informal, when properly viewed will prove to be a means of master- 
 ing efficiental methods. This explains the fact that many men have 
 been great who have been without special technical training of any 
 kind, but who have thoroughly grasped the primal efficiental basis 
 of life. It also explains why, after this basis has been mastered, 
 the technique of one department after another may often be rapidly 
 assimilated with little or no outside help. 
 
 Efficiency Treatment of Current Educational Problems 
 
 The above principles of education are also an aid in solving impor- 
 tant special problems in educational methods. Thus efficiental 
 
3i8 SOURCES OF EFFICIENCY 
 
 ideas throw light on the matter of attention and interest, on methods 
 of discipline, on the functions of memory, on the relations of books 
 to things, on the place and nature of heuristic methods, and on the 
 best ways of treating both defective and exceptionally able pupils. 
 It tends to culturize vocational studies and vocationalizes culture 
 subjects. 
 
 General System of Efficiental Education 
 
 Perhaps the view presented should also lead to a radical recon- 
 struction of the general system of education. Thus we can conceive 
 of a study which underlies and in a measure includes the various 
 conventional branches and which essentially consists of the science, 
 art, and philosophy of obtaining results ; that is, of efficiency. 
 
 The germs of this discipline could be instilled in the young mind 
 during the processes of elementary training ; its main outlines would 
 be a specific, formal branch of the high school course ; in college, 
 the thoroughly developed subject could be taught along with the 
 leading facts and processes of every department of knowledge and 
 action; in the university, the system of efficiency principles which 
 had been thus mastered could be applied in learning every possible 
 fact about some one specialty and in developing that specialty to a 
 new degree of perfection. It would seem that such a study would 
 greatly accelerate and deepen education processes and enhance 
 their values. 
 
 SOCIOLOGY 
 
 Efficiental Solution of Sociological Problems 
 
 From various points of view it is evident that the principles 
 presented in this book have important applications to the subject of 
 sociology. Thus the adoption of the views under consideration 
 apparently would contribute toward the solution of certain current 
 social and political problems. For if it became evident that all 
 callings are analyzable into the same efficiental elements and that 
 consequently the occupations of cook, engineer, and lawyer are, for 
 example, not unlike in certain essentials, many social distinctions 
 which now hinder progress and limit man's happiness, would be 
 largely modified and perhaps in a measure would disappear. Among 
 these are the distinctions between higher and lower social classes, 
 and between noble and menial occupations. Similarly the distinction 
 
APPLICATIONS 319 
 
 between work and play would to a considerable extent pass away. 
 For the two are resolvable into an activity which is back of and 
 includes both of them as details. These changes would make easier 
 the distribution of that residuum of work necessary in any social 
 system; or, to express the matter in another way, the solution of 
 the difficult and fundamental problem of the distribution of the 
 rewards of human activity would be facilitated. In this connection 
 a full realization of the many costless or inexpensive sources of 
 efficiental pleasure, power, and wealth which are open to all, is of 
 prime importance. 
 
 The principles advanced in this book also have an application to 
 more special problems. For instance, with respect to race suicide, 
 it is made clear that, apart from other considerations, in children are 
 found Efficients and efficiental values in their highest and best forms. 
 It will be realized that these far transcend any values and pleasures 
 obtainable through elaborate dress, expensive foods, constant travel, 
 and other forms of personal luxury the fondness for which is 
 now dwarfing so many families. 
 
 A grasp of the Efficients which constitute the essence of every 
 form of work would tend to prevent the narrowing and blighting 
 effects of the division of labor in its extreme forms as now practised. 
 For every item of work however specific is seen to be resolvable into 
 and related to elements of activity and life of the widest possible 
 significance. 
 
 The relation of the general conceptions under consideration to the 
 problem of forms of government has been considered in various 
 places in the preceding chapters ; other like applications are indicated 
 by such terms as efficiental wealth, labor, equality, freedom, trade 
 and competition. 
 
 An Efficiental Sociology 
 
 The efficiency principles which have been presented suggest not 
 only improvements in existing social methods, but also more funda- 
 mental reorganizations. For these principles, when fully applied, 
 mean, on the one hand, a new and more profound personal free- 
 dom and development and, on the other hand, point to equally new 
 and strikingly effective methods of cooperation and social organiza- 
 tion. For if each person realizes the fulness of efficiental wealth 
 available to him, he will feel free and will be eager to appreciate 
 and develop this, no matter what views others may hold, and this 
 
320 SOURCES OF EFFICIENCY 
 
 course when adopted by individuals will lead to the formation of 
 new methods of social cooperation. The efficiental forces tending 
 to social reorganization will also act in more general ways. 
 
 It is estimated that, at the time of the highest development of 
 Greek civilization, every Greek freeman had on the average five 
 helots or slaves who worked his farms and mines and performed 
 virtually all other manual labor for him. Hence the Greek freeman 
 had leisure to think and discuss and to develop the more abstract 
 efficiental side of his life, and thus to create an efficiency in art, 
 literature, and philosophy which has never been surpassed. The 
 Romans had equal leisure, but largely wasted their surplusages in 
 senseless and debasing luxury. Owing to the use of coal and 
 machinery some modern nations have twenty steam and electric 
 slaves at work for each adult male citizen, that is they possess four 
 times as much servile labor as the Greeks had. These modern forms 
 of surplus energy and the leisure obtained through them, are being 
 employed in part as the Greeks used theirs, in part as the Romans 
 theirs, and partly in an earnest and organized search for still greater 
 leisure and power. Hence the raw material is already at hand for a 
 far higher and more efficient civilization than the Greeks enjoyed. 
 When the efficiental activities already in sight shall have been fully 
 coordinated and developed, the result will be a civilization far sur- 
 passing any the world has yet seen. 
 
 BUSINESS 
 Analysis of Scientific Management in terms of the Efficients 
 
 In recent years much attention has been given to the methods of 
 conducting business which have been termed scientific management 
 and which were largely originated by Mr. F. W. Taylor of Phila- 
 delphia. Briefly summarized the principles of scientific manage- 
 ment are as follows : 
 
 i. The dissection of any process of work (as brick laying) into 
 its elements or motions. (In terms of the Efficients as presented in 
 this book, this means the application of diversity and of units.) 
 
 2. The study of the most economical and efficient way of perform- 
 ing each of the elements in a given piece of work. (This includes 
 the application of groupism, multiplicative groupism, directive and 
 most of the Efficients.) 
 
 3. Standardizing the work; that is, determining how much work 
 
APPLICATIONS 321 
 
 a good (or bogey) workman following the most approved methods 
 may be expected to perform in a given time. (This means a study 
 of limitations and specific quality, and the consequent formation 
 of uniformities and multiplicative groups.) 
 
 4. Instruction of workmen in the best methods of work. (This 
 means an externality and scale of teachers, and a reuse of 
 knowledge.) 
 
 5. Selection of the workmen best adapted for each given kind of 
 work. (This includes reuse of work done by nature, use of 
 diversity and specific quality, and hence in one aspect of limitation.) 
 
 6. A planning, organizing, and instructing department of workers 
 (i.e., externality, orders of material, multiplicative groups, reuse). 
 
 7. Charting and routing of each extensive and complicated piece 
 of work (i.e., use of linear multiplicative groups, graphs, and other 
 multiplicative groups and symbolisms). 
 
 8. Sharing the increase in profits (i.e., a recognition of positive 
 surplusage, externality, and uniformity). 
 
 By use of the above methods, for example, the amount of pig 
 iron handled by one man in one day has been increased from 12^ 
 tons to 47 tons, and the number of bricks laid from 1000 to 2700. 
 
 Applications of the Efficients are Wider 
 
 From the above analysis it is evident that the principles presented 
 in this book underlie, surround, and include, so- to speak, the methods 
 advocated in the above system of scientific management. Hence if 
 the individual workman is familiar with the Efficients as such, each 
 day numberless ways will occur to him in which he can, in addition 
 to the above prescribed methods, use the groups, unit and multiplier, 
 reuse, directive, and other primal means to efficiency. The same is 
 true of the employer, superintendents, and foremen. 
 
 Furthermore the more general efficiental point of view also makes 
 plain, for instance, that systems of accounting are but systems of 
 multiplictive grouping according to the categories of time, place, 
 material, personality, etc., and that a mastery of the principles of 
 multiplicative grouping opens the way for the development of a 
 special system of accounting particularly adapted to any given 
 business. The same statement applies to all forms and kinds of 
 system and organization included in any given business. 
 
 Hence the efficiental principles stated in this book relate not only 
 to the processes of manufacture, but to those of buying and selling 
 
3212 SOURCES OF EFFICIENCY 
 
 as well. For example, the reuse by other agents of the experience 
 and methods of the most successful selling agents is provided for, 
 as well as the grouping, standardization, and codification of such 
 experience and methods. 
 
 Uses of the Efficients are More Fundamental 
 
 It will be seen that the principles presented in this book will also 
 necessarily modify the methods and processes of business in more 
 fundamental ways, as, for example, by modifying the views which 
 men hold of life in general. Thus a sane view of the aims and 
 ends of life will diminish the passion for senseless luxury, and hence 
 transform the processes of manufacture and business which cater 
 to such luxury, and also simplify the problem of profit sharing. 
 
 The ideas here presented also aid in a grasp of the underlying 
 principles of business in other ways. For instance every form of 
 business is in some way a case of intake and output, that is of 
 externality and re-multiplicative-grouping, with surplusage results. 
 Hence a specific knowledge of these efhciental processes is of use 
 throughout the technique of any species of business. Again if we 
 view the universe as in a state of almost exact balance between 
 gigantic positive and negative multiplicative systems, the world is 
 realized as a solid domain of opportunities of high order for him 
 who is able to perceive and utilize such opportunities. Yet the 
 same point of view makes clear the wisdom of making it a rule to be 
 content with large sales and small margins of profit, while at the same 
 time ever being on the lookout for a sudden explosive opportunity 
 due to some extreme action of the multiplicative principle. The law 
 of multiplication also makes peculiarly evident the importance of 
 holding reserves and in other ways being prepared for sudden ex- 
 plosions in the commercial world. 
 
 Primary Aim of Business 
 
 It is of equal or greater importance to remember that the aim 
 of business is the making of positive surplusage in every possible 
 way, with special emphasis on those ways which are broad and 
 fundamental. This method of conducting business brings the largest 
 and best returns to the individual business man as well as to society 
 in general. Thus business is carried on most profitably and success- 
 fully when both parties to a bargain are the gainers thereby. Also 
 an employer conducts his business most successfully when he con- 
 siders not only his technical business relations with his employees but 
 
APPLICATIONS 
 
 323 
 
 also their general welfare and interests, including their food, recre- 
 ation, health, education, morals, and religion. In like manner em- 
 ployees will receive the best pay and largest rewards of all sorts when 
 they take an interest in promoting all the elements and relations of 
 the business in which they are engaged. 
 
 Similarly an intelligent commercial house perceives that its returns 
 are in proportion not merely to the direct value of the goods sold, 
 but to the surplusage of all kinds conveyed to their customers, in- 
 cluding, for example, the pleasure and instruction imparted through 
 works of art exhibited in salesrooms, through the artistic presenta- 
 tion of goods, musical entertainment, courtesy of employees, and 
 through well served food supplied in attractive lunch rooms. 
 
 A Universal Practical Instrument 
 
 Finally if we look at the so-called practical world as a whole 
 the system of Efficients as here presented forms a kind of universal 
 tool or instrument, applicable in some form to every problem or 
 opportunity that may arise. Thus the use of diversity, units, and 
 groups supplies at least an initial method by which to attack any 
 situation. Later, by marginal variation and adaptation, the whole 
 system of Efficients forms a completer instrumentalism for dealing 
 with the developed problem. 
 
 ART 
 
 General Statement 
 
 Since art is a special and somewhat technical form of symbolism, 
 the discussions in Chapter X show in general how the principles 
 under consideration in this book have an application to various 
 kinds of artistic work. If the matter be looked into in more detail, 
 it is found that grasp of the Efficients helps to determine the 
 subject matter most desirable in works of art, the principles and 
 forms which should be applied to this subject matter, and perhaps 
 will suggest new and more efficient species of art. The result on the 
 subjective side should be greater ease in the mastery of art, added 
 pleasure and profit from the technical appreciation of art, and still 
 broader results owing to the grasp of the general efficiental mean- 
 ings and values of any given artistic work. 
 
324 SOURCES OF EFFICIENCY 
 
 Efficiental Subject-matter 
 
 As to the subject matter of art our point of view leads to an 
 emphatic preference for constructive, optimistic themes. Promi- 
 nence is to be given to that which is noble and uplifting; not only 
 to that which is beautiful in the more sensuous aspect, but even more 
 emphatically to those forms of beauty which are capable of the 
 most efficiental treatment for the most efficiental ends. For instance 
 the theory in hand makes clear that the dominant part of Dante's 
 Divine Comedy is the Paradiso, and that the greater attention given 
 to the Inferno is due to a morbid form of interest, and to a lack of 
 a grasp of life in all of its relations and in right perspective. 
 
 Efficiental Elements in Highest Forms of Arts 
 
 As to the forms of a^rt, the principles under consideration aid one 
 in realizing, for instance, that mere profusion of ornamentation 
 cannot produce art of a high order. For such profusion means only 
 a set of units without multipliers ; or even worse, an assemblage of 
 units which largely cancel and destroy each other. In contrast with 
 this method the unit and multiplier principle would suggest the use 
 of a few units of a high order of artistic excellence placed on a 
 massive and constrained background which serves in various ways as 
 a multiplier of the given units. Such a combination recognizes the 
 limitation that is in all things, but it also has other more positive 
 values. It often means economy in material used and hence in 
 cost, and in energy expended by the observer in learning to under- 
 stand and appreciate a given work. More important still, large 
 margins or backgrounds constitute an externality of space in which 
 self activity can function, and at the same time challenges and stimu- 
 lates this self activity to fill in details, and to propagate and develop 
 the given units according to personal taste or need. Similar results 
 are obtained by an atmosphere of twilight or by any "noble dim- 
 ness", in connection with one or more well developed units of art 
 symbolism. 
 
 In like manner other Efficients are often found to be fundamental 
 sources of power in works of art of a high order. An important 
 case of the use of groupism in art is the combination of several suc- 
 cessive phases or elements of an act or process in a single picture 
 or statue. This principle is strikingly illustrated in many of the 
 works of the sculptor Rodin. So in literature the mere use of 
 "words, words, words" is additive, while the use of "local habitation 
 
APPLICATIONS 
 
 3 2 5 
 
 and a name" is multiplicative. This principle is widely illustrated 
 by the almost paradoxial importance, in any linguistic statement, 
 of the small words, like since, thus, hence, for etc., which are em- 
 ployed to denote space, time, number, cause, and other prime group 
 relations, and whose right use is essential to a clear presentation 
 of the multiplicative group essence of a subject. 
 
 An examination of works of art of the highest order also seems 
 to suggest that each of these contains some expression or indica- 
 tion of infinite externality. This characteristic is illustrated, for 
 instance, by the Sistine Madonna as contrasted with the Madonna of 
 the Chair. In the first of these paintings, the mother of Christ is 
 gazing at something distant and inspiring, perhaps at the epoch- 
 making work to be performed by her son, or at the source of this. 
 Another illustration of this principle of a widely different type 
 is the avenue of trees receding in the distance in Hobbema's Avenue 
 of Middleharnais. 
 
 Efficiental Elements in Other Departments of Art 
 
 This suggestion of infinite vistas of expansion and development 
 is also found in various forms in literature of high order. In fiction 
 one of the most subtle and powerful of these forms is that super- 
 poise of the author by which he is enabled to project his characters 
 against the background of the general efficiental organization of 
 things, to measure them thus in various ways, and to suggest their 
 further development. In accordance with this principle also we find 
 the highest type of literature, not in Shakspere, in spite of his mar- 
 velous profusion of local excellence, nor in Dante's Inferno, so 
 vivid in its artistic qualities but so negative in its main content, but 
 in Dante's Paradiso with its spiral unlimited development of the 
 individual soul. 
 
 Similarly other of the Efficients are often present in great works 
 of art in more striking form. When thus present, they not only 
 govern the form, but also constitute the most important part of the 
 subject matter. Hence in them form and content coalesce. 
 
 It is well to note in this connection that each of the fine arts 
 contains certain characteristic efficiental elements. Thus orchestral 
 music of a high order is a swiftly changing combination of systems of 
 groups and other Efficients which is highly educative as well as the 
 source of the noblest pleasure. 
 
326 SOURCES OF EFFICIENCY 
 
 Schools of Art 
 
 It is evident that in such conceptions different schools of art find 
 a common principle or essence; that in the beauty of a primal and 
 perhaps ultimate efficiency, realism and idealism, truth and beauty 
 as ordinarily understood, utility and art merge or melt together. 
 Thus the highest art expresses a pure surplusage which is indepen- 
 dent of time and of any eccentricity of personal or national mood. 
 This form of art is approximated by an object like the Parthenon 
 which gives the impression of being neither large or small, young 
 or old. This pure efficiental art may be regarded as at times acting 
 in special channels and thus, on occasion, giving rise to certain 
 individual forms or schools of art, each having its own peculiar 
 efficiencies, examples being the classical, romantic, and impression- 
 ist schools. 
 
 Advantages of Efficiental View of Art 
 
 This view of the matter leads to varied and often profound mar- 
 ginal reuse in the appreciation of art. It also greatly enlarges the 
 scope of artistic expression and pleasure. Thus the furnishings of a 
 home, while in themselves simple and inexpensive, may be made 
 to express artistic data of the first importance, as, for instance, the 
 various efficiental principles. The same statement applies to the 
 architecture and the external surroundings of the home, to dress 
 and personal adornment, and to speech and personal manners. So 
 also Ruskin has shown that the sky and clouds form a changing 
 picture gallery to the properly trained eye, and he and others have 
 made clear that the same is true of the landscape both as a whole 
 and in its details. The ideal aimed at in the whole field of rela- 
 tively unconventional art is that the individual, the home, the town 
 or city, and nature shall each radiate positive surplusage in a con- 
 tinuous esthetic form. 
 
 The principles arrived at in the preceding discussion also enable 
 us to conceive of the possibility of new and higher forms of art than 
 those in current use. Such forms may express efficiental themes 
 to efficiental sensuous powers in efficiental ways for efficiental ends, 
 more explicitly and effectively than do the current types of art. 
 
APPLICATIONS 
 
 327 
 
 ETHICS 
 
 Efficiency in Christian Ethical Principles 
 
 If we examine Christ's injunction to return good for evil we find 
 that, apart from other considerations, the principle involved, in the 
 long run, is a highly efficient one, and far more so than the princi- 
 ple of retaliation. For the fruits of retaliation are single or local 
 and negative, while the mode of life implied by the forgiveness of 
 injuries is positive and means a continuous radiation of positive 
 surplusage in spite of all injustice or misunderstandings, and hence 
 is superior to retaliation in a dual infinite way in its general effi- 
 ciency properties. An examination of the other paradoxical ethical 
 principles taught by Christ would show that they have similar effi- 
 ciency properties. 
 
 Efficiency in Various Fundamental Principles in Ethics 
 
 In like manner if we consider the various ideas which have been 
 proposed, from time to time, as a fundamental principle of a system 
 of ethics, we shall find that each of the more meritorious of these 
 possesses efficiency properties of a high order. This is true of such 
 primal ethical concepts as knowledge, harmony, moderation, benevo- 
 lence, sympathy, utility, altruism, complete life, and happiness. 
 Almost or perhaps all of these it will be noted, directly or indi- 
 rectly, mean fundamental groupism of some sort. 
 
 Efficiental Analysis of the Different Virtues 
 
 In like manner it may be shown that the different virtues, so- 
 called, have efficiental values of the first importance. Thus for 
 instance modesty is a realization of diversity, externality, and limita- 
 tion, and has the uses connected with these principles. Truthfulness 
 has the values which come from a correspondence (or uniformity) 
 between fact and symbol ; patience those of externality and dialectic ; 
 sympathy and generosity those of externality and groupism. In fact 
 the virtues may be arranged in groups according to the Efficients 
 prominent in them. Thus we have 
 
 (1) The externality group, containing altruism, love, self-denial, 
 modesty, reverence, patience ; 
 
 (2) The directive group, containing charity, generosity; 
 
 (3) The order of materials group, of good will or motive, charac- 
 ter, intention ; 
 
328 SOURCES OF EFFICIENCY 
 
 (4) The uniformity group, of honesty, truthfulness, justice; 
 
 (5) The diversity and limitation group, of chastity, temperance. 
 The more conventional classification of virtues in groups relating 
 
 (I) to the individual, (II) to other persons and (III) to God, may 
 be regarded as essentially a grouping with respect to different 
 degrees of externality. 
 
 Solution of Ethical Problems 
 
 The above analysis of ethical principles in terms of the Efficients, 
 aids in the solution of certain ethical problems. One of these is 
 the problem of the relation of self-interest to altruism. In cases 
 where these two principles seem to be in conflict the proper course 
 to follow would seem to be that which would produce the greatest 
 and highest surplusage independently of personal considerations. 
 Sometimes self-development, and in other cases a primary atten- 
 tion to the interests of others will do this. In order to decide be- 
 tween these courses in specific cases, much study of the peculiarities 
 of the given situation is necessary, such study being conducted as 
 far as possible in terms of the fundamental categories of efficiency. 
 At times a point is reached where self-interest and altruism merge, 
 or are lost, in the deeper principle of the subpersonal or non- 
 jective making of positive non-equivalence in all possible ways at 
 all times. 
 
 Advantages in the Efficiental View of Ethics 
 
 So also from the efficiental standpoint, certain new developments 
 of the conventional virtues are possible, and also perhaps the for- 
 mation of what may be termed new virtues, with new vices corre- 
 sponding to them. Thus any perfected mastery of an Efficient might 
 be an efficiental virtue; and any habitual or intentional violation of 
 the same, an efficiental vice. We are also enabled to arrive in this 
 way at the conception of a summun bonum or goal of all effort such 
 as has been indicated in other places. 
 
 A farther advantage of the above efficiental treatment of virtues, 
 vices, and ethical principles seems to be that it can be embodied 
 in systems of education without running counter to personal or re- 
 ligious bias in such matters. It also aids in the mastery and appli- 
 cation of these principles in other ways. Rightly understood it adds 
 a new imperativeness to moral laws. 
 
APPLICATIONS 329 
 
 RELIGION 
 Efficiency Values of Religion 
 
 Whatever his views as to conventional religions and doctrines, 
 every one must admit that abundant evidence exists of the effi- 
 cacious results which frequently follow the use of that vast and 
 unbounded externality implicit in every religion worthy of the name. 
 The word religion means a relaying or regrouping, and this re- 
 grouping in connection with and under the influence of infinite 
 externality often leads to extraordinary efficiency results. These 
 have many times been illustrated in the phenomena of religious 
 conversions. 
 
 The efficiency values in religion have however often been greatly 
 obscured by the abuses which from time to time have grown up in 
 connection with religious principles. These abuses have frequently, 
 indeeed, been of a gravity which corresponded to the enormous 
 power for good inherent in an efficiental use of infinite externality, 
 and constitute a striking illustration of the law of rhythm and 
 backeddyism. 
 
 An examination of the conventional doctrines and ceremonies 
 which characterize various religions would show that each of these 
 technical details and outward forms is usually the source of cer- 
 tain special efficiencies though often marred in practice by drawbacks 
 and evils. But the detailed examination of these matters lies be- 
 yond the scope of this book. 
 
 Advantages of the Efficiental View 
 
 The above method of viewing religion possesses certain advantages, 
 which should, at least, receive mention. For instance it opens the 
 way to a free and aggressive development of the primary and fun- 
 damental values in religion apart from those questions as to details 
 and outward forms which, in the past, have been the source of so 
 much bitter conflict. Perhaps it makes possible the study of such 
 values as a part of a general system of education. 
 
 Possibly also it should lead to the development of some religious 
 ideas into higher and transcendent forms. Thus as an outcome 
 of it we can conceive of new ways of clothing infinite externality 
 with auxiliary efficiental toolages. These in turn may react on the 
 principles which they aid, the result being fruitages or categories 
 of value of which we cannot now form an adequate conception. 
 
330 
 
 SOURCES OF EFFICIENCY 
 
 General Outlook 
 
 The above statement concerning the efficiency meaning of reli- 
 gion, concludes our illustrative application of the principles arrived 
 at in the preceding chapters, to certain specimen departments of 
 human knowledge and action. These prime agents of efficiency 
 might, of course, in like manner be applied to other departments 
 of life and thought. The principle of limitation will, apparently, be 
 always at work, but if the universe be regarded as a combination of 
 two multiplicative systems, one positive and the other negative, in 
 proportion as the negative one is overcome, the positive system will 
 predominate in accelerating multiplicative fashion, with correspond- 
 ing fruitages which cannot be fully anticipated. 
 
 EXERCISE 20 
 
 General Review 
 
 1. On a given machine an efficiency engineer found that compared with what 
 it should have been, the width of the cutting point of the tool was Y\, the 
 speed was J/j, and the amplitude of the stroke 4 times (i.e. the stroke over- 
 ran threefold). Express the efficiency of the machine as a per cent. 
 
 2. A crop of 600 bushels of corn which might have been sold at 84 cents 
 a bushel was fed to farm animals and was thus made worth $1120. If the 
 labor of feeding coist $84, compare the efficiency of the two methods of dispos- 
 ing of the corn. What Efficients are involved in the second process? 
 
 3. When potatoes were raised without spraying, on a given field, it cost 
 $4000 to raise a crop worth $6400. A crop produced in a later year was 
 sprayed at an additional cost of $400 and was worth $8800. State as a per 
 cent the efficiency of the first crop in terms of the second. 
 
 4. What Efficients are involved in the process of reducing fractions to a 
 common denominator and adding them? 
 
 5. If a modern cotton gin and compress are operated by one half the 
 number of men required by a former type and turn out twice as much baled 
 cotton, express the labor efficiency involved. 
 
 6. A city factory was using 1500 tons of soft coal per year thirty per cent of 
 which went up the chimney as smoke. Later, after installing a smoke consum- 
 ing grate and by utilizing some of the gases which had gone up the chimney, 
 the amount of coal was reduced to 1050 tons. State the degree of fuel effi- 
 ciency involved. State also the Efficients employed and indicate the resulting 
 dialectic. 
 
 7. What principles of efficiency are used by a housekeeper who buys eggs 
 when they are cheap and keeps them in liquid glass till they are dear? 
 
 8. What principle of efficiency was involved when a primitive man in 
 making a fire accidently melted copper and tin ore together and thus made 
 bronze? 
 
APPLICATIONS 331 
 
 9. State in efficiental terms the different methods of making "a little go a 
 long way". 
 
 Explain the efficiental meaning of each of the following: 
 
 10. There are more ways of killing a dog than hanging him. 
 
 11. Patience and shuffle the cards (Spanish proverb). 
 
 12. The early bird gets the worm. 
 
 13. Give him rope enough and he will hang himself. 
 
 14. He can't see farther than the end of his nose. 
 
 15. Fine feathers don't make fine birds. 
 
 16. By indirection find direction out. 
 
 17. All waste comes from isolation of some sort. 
 
 18. Sweet are the uses of adversity. 
 
 19. He has something up his sleeve. 
 
 20. Explain the advantage to a business man of keeping his capital as far 
 as possible in a fluid state. 
 
 21. To a general of keeping his forces concentrated as far as possible. 
 
 22. Why is a street corner near the center of a city usually a superior 
 location for a place of business. 
 
 23. What is the reason for the statement that it does not make so much^ 
 difference what subject we study as how we study it. 
 
 24. In terms of the Efficients discuss the utilities in play. How could a 
 knowledge of the Efficients be made a means of increasing these utilities? 
 
 25. State the advantages in having one man in a factory distribute the 
 supplies to the machines before the work is begun, as compared with having 
 the workmen who use the supplies go to the store room for them as they are 
 needed. 
 
 26. Explain the efficiency significance of the motto "e pluribus unura". Also 
 of "non multa, sed multum". 
 
 Explain in efficiental terms. 
 
 27. The advantage to a large firm in employing a general purchasing agent. 
 
 28. The meaning of the phrase, cross fertilization of the sciences. 
 
 29. The advantages and disadvantages of combining several small businesses 
 as a corporation, 
 
 (1) With reference to the owners of the business; 
 
 (2) To the employees ; 
 
 (3) To the general public. 
 
 30. What Efficients make it possible to photograph a star which cannot be 
 seen through the best telescope. 
 
 31. Explain the source or sources of efficiency in watching the eye of a 
 boxer instead of his hands. 
 
 State the various Efficients prominent in the subject of 
 
 32. Arithmetic 33- Algebra 34- Geometry 
 
 35. Physics 36. Botany 37. Language study 
 
 38. Before the appearance of the Colorado beetle a farmer in raising 
 potatoes spent $26 per acre and produced 87 bushels per acre. After the 
 
3$2 SOURCES OF EFFICIENCY 
 
 appearance of the beetle, he spent $42 and raised 170 bushels per acre. Com- 
 pare the efficiency of the two processes. State the sources of increased effi- 
 ciency. 
 
 39. Napoleon estimated his own presence with one of his armies as 
 equivalent to the addition of 100,000 common soldiers to its strength. Explain 
 as far as you can the efficiency of Napoleon as compared with a common 
 soldier. 
 
 40. Explain the sources of efficiency in the use of a bicycle as compared 
 with walking. 
 
 41. Explain as far as you can the non-equivalence between the energy used 
 in pulling the trigger of a gun and the energy in the action of the bullet. 
 
 42. It is estimated that the cost of human unskilled labor is 1000 times the 
 cost of the same work when done by the best steam engine. Name the princi- 
 pal reasons for his difference. 
 
 43. State in efficiental terms the meaning of each of the following elements 
 of success : honesty, intelligence, accuracy, self-reliance, loyalty, shrewdness, 
 courage. 
 
 44. State in efficiental terms the advantages of knowing the cause or causes 
 of an event. Also in knowing the results of a process before they happen. 
 
 45. Give the efficiental reasons for the following statement: At a certain 
 stage in a process of thought a certain vagueness of thought is useful. 
 
 46. Discuss in terms of the Efficients the reservoirs of power unconsciously 
 possessed by every person. 
 
 47. Discuss the meaning of the following statement : "Culture is that which 
 is left after you have forgotten everything which you have learned." 
 
 48. Explain the advantage in not trying to remember everything but only 
 where everything may be found. 
 
 49. Also in not trying to form once for ail a system which shall include 
 every detail and situation of life but rather in having the means of making 
 a system in any given situation. 
 
APPENDIX 
 
 A. THE CATEGORIES AND A GENERAL PHILOSOPHY 
 
 OF LIFE 
 Preliminary Illustration 
 
 Beside the prime sources of efficiency which have been investi- 
 gated in the preceding pages, certain other abstract and general 
 instruments of thought and action have long been in use which it 
 will be of advantage to examine, if only briefly. As an illustration 
 we may take the category of space. 
 
 If a set of pigeonholes is used for any given purpose it is usually 
 much more convenient to arrange the set of compartments in the 
 form of a square or rectangle rather than in linear order. Among 
 the advantages which result from the areal arrangement are the 
 economy to eye and hand in using the system owing to the fact that 
 the distance between any two pigeonholes is greatly diminished on 
 the average. Also after long use of such an arrangement, other 
 benefits arise such as the utilization of various positional symbolic 
 relations and various other groupages. 
 
 Similarly other areas, as the wall of a room or the surface of 
 a farm, in time are often instinctively realized as saturated with 
 facile reciprocal externalities and highly condensed groupages of 
 many kinds, from which various dialectics result which would not 
 be possible with a merely linear object. Hence a surface is fre- 
 quently, if not always, a special efficiency instrument of great power. 
 
 The above illustration may be extended to space of three dimen- 
 sions. For if a set of drawers be constructed each of which consists 
 of a rectangularly arranged set of pigeonholes (or checkerboard 
 arrangement of some sort), we shall have a still higher conden- 
 sation (or groupism) of parts, with a consequent higher manifold 
 and more facile externality and a dialectic of cross multiplicative 
 groupings. In this way we are brought to realize that space itself, 
 from a certain point of view, is an efficiency instrument of great 
 importance; that it, in effect is a multiplicative group system of 
 three orders, manifold, continuous, and saturated with many result- 
 ing efficiency properties. This conception of space is an important 
 
 333 
 
334 
 
 SOURCES OF EFFICIENCY 
 
 aid in mastering the properties of space as commonly understood, 
 in conceiving of additional properties possessed by it, and in making 
 the most effective use of all these properties as sources of efficiency. 
 
 General Statement 
 
 A like point of view holds with respect to other and perhaps all 
 of the so-called categories, such as time, cause, reality, substance, and 
 quality. These entities may often be usefully regarded as special 
 instruments of efficiency. They may have been evolved in a some- 
 what haphazard way, but with respect to certain uses they have 
 been developed to a high pitch of instrumental power, accompanied, 
 however, by equally high degrees of danger and limitation. A study 
 of the more important of these categories from this point of view 
 will not only be of direct advantage but will be useful as an aid in 
 removing certain fundamental and pervasive efficiency errors, such as 
 the tendency on the one hand to overuse the category of personality, 
 and on the other those of mechanism and equivalence reality. Hence 
 such a study should be an aid to the appreciation and extended use 
 of the broadest and most permanent kind of efficiency, as distin- 
 guished from that which is narrow and personal. It will also be an 
 aid in relating the idea of efficiency to other approximately ultimate 
 ideas, and realizing its place in a general scheme or philosophy 
 of life. 
 
 The categories under consideration are so interwoven in meaning 
 that it is necessary to discuss each of them more or less in terms of 
 the others, it being noted that our main object is to obtain efficiency 
 results, and that the development of a simple filiar system among 
 the concepts studied is merely secondary and auxiliary to the main 
 purpose. However the cancellations and other dialectic results which 
 arise, will produce this filiar ordering of the categories to a certain 
 extent. 
 
 Classification of the Categories 
 
 It will be an advantage first to make an approximate grouping of 
 the categories to be examined. This classification will be made 
 primarily with reference to certain leading Efficients. We thus 
 obtain 
 
 I. The Reality, or Uniformity Group, consisting of the concepts, 
 Reality, Substance, Matter. 
 
CATEGORIES 335 
 
 II. The Quantity, or Pure Group, containing Quantity, Space, 
 Number, Infinity, Zero. 
 
 III. The Quality, or Diversity Group, containing Quality, Time, 
 Order, Negation. 
 
 IV. The Dynamic, or Motion and Force Group, consisting of 
 Motion and Force, Change, Cause, Teleology. 
 
 (The category of Teleology also forms a transition link to the 
 next group.) 
 
 V. The Vital or Directive Group, containing Life, Mind, Personal- 
 ity, Subject (vs. object). 
 
 VI. The Absolute Group, in which the principle of orders of 
 material is carried to an extreme development. It contains such 
 concepts as the Absolute, Fundamental, and Ultimate. 
 
 I. REALITY GROUP OF CATEGORIES 
 
 Matter 
 
 It has been said by a certain scientific worker that the carbon 
 molecule and other chemical elemental ideas are mere concepts 
 (i.e., primal groups) to enable us to deal more efficiently with phe- 
 nomena, and that the whole idea of matter itself is merely a sec- 
 ondary and auxiliary phenomenon. It is important to realize more 
 definitely from the efficiency standpoint, what is meant by these 
 and like statements. 
 
 As an illustration of the utility inherent in the idea of materiality 
 and substantiality and similar concepts, we may take Democritus' 
 theory of vision and the various useful results which have followed 
 from it. According to this theory any given object is constantly 
 giving off effluvia in the shape of fine atoms ; and when these atoms 
 enter the eye they produce an impression (or image) which results in 
 the given object being seen. With all its imperfections this theory 
 has the merit of suggesting that something exists between the eye 
 and the object seen, and that, by directing or working with this 
 something, the process of vision may in a measure be controlled and 
 made more efficient. For instance, it is but a step from this view to 
 the thought that by interposing a lens between the eye and the 
 seen object the atomic effluvia from objects may be collected and 
 vision so powerfully reinforced that the very distant or the very 
 minute be made visible as in the telescope and microscope; or to 
 Newton's idea that the corpuscles given off, if they be of different 
 
336 SOURCES OF EFFICIENCY 
 
 sizes, may be sorted into groups, the prismatic colors and spectrum 
 analysis being the result. 
 
 If we enlarge this idea of atoms given off by objects to the con- 
 ception of a universal fluid in which all objects are immersed and 
 which objects can cause to undulate in various ways, we have, in 
 general, the modern idea of the ether. Regarding the ether as 
 having certain of the properties of materiality, Faraday formed the 
 idea that a forward thrust of the ether in one direction would result 
 in a backward thrust in some nearby adapted channel, or what is. 
 called the principle of electrical induction. The efficiency outcome 
 of this was the invention of the dynamo, and of electrical machinery 
 in general. It also resulted in Clerk Maxwell's electro-magnetic 
 theory of light, and wireless telegraphy. 
 
 Hence we may take John Stuart Mill's conception of matter,, 
 viz. : as the permanent possibility of sensation, and extend it into 
 the statement that matter is the permanent possibility of groupisms. 
 and efficiencies of certain specific sorts. From this point of view 
 matter means the combined use of externality in both space and 
 time, of multiplicative groups (see for instance the various methods 
 of dividing and subdividing and combining parts of matter), of 
 rhythms and other positive Efficients, along with limitations or 
 special qualities such as are implied in the terms impenetrability,, 
 incompressibility, and inertia. The various scientific theories of 
 matter, such as the ethereal stress and strain theory, and the molecu- 
 lar-atomic hypothesis, in like manner may be viewed as special 
 combinations or aspects of the toolage properties of matter. 
 
 It is ever to be borne in mind that while the concept matter is 
 thus a powerful efficiency agent in certain relations, it also has 
 connected with it serious dangers and limitations. Thus the over 
 use of it, or the crude use of it, may prevent the recognition and 
 application of other important sources of efficiency in a given case. 
 
 However the dangers will be somewhat prevented if instead of the 
 conventional somewhat crude and lumpish view of matter, we sub- 
 stitute the above view which makes matter a special combination 
 of the Efficients and hence a special instrument of efficiency. 
 
 The view of the categories of matter and substance here advo- 
 cated also opens the way to using, aggressively yet safely, these 
 categories as special sources of efficiency under some circumstances. 
 Thus when forms of abstract groupism have become familiar, it: 
 
CATEGORIES 337 
 
 is frequently a source of added efficiency to regard them as possessing 
 certain of the attributes of materiality, or as more or less substan- 
 tial, and thus to obtain the advantages of being able to manipulate 
 such forms swiftly, readily, and by a low order of force, and also of 
 conceiving them as always at hand and ready to act of themselves 
 in certain ways. 
 
 By emphasizing or otherwise modifying one or more of the 
 efficiental elements which go to make up the concept of matter, it 
 is possible readily to conceive of different species of matter, and also 
 of different degrees of materiality, and then to use these widely 
 in the special efficiency channels for which they are adapted. 
 
 Substance and Reality 
 
 By substance is ordinarily meant a substratum underlying the 
 special qualities of an object; or that which is left after an object 
 has been stripped of its so-called qualities and attributes. Hence 
 the idea of matter may be refined and generalized into that of sub- 
 stance; or substance may take the special form of matter. Thus 
 substance is a kind of prime group, or efficiency abstract essence of 
 matter and other objects. Hence much that has been said about the 
 efficiental nature and uses of matter applies also with slight modifi- 
 cations to the category of substance. 
 
 The concept of reality differs from that of substance in that reality 
 often has connected with it the idea of positive and aggressive action, 
 while substance is mainly negative or resistant. In the reality 
 concept the mechanical triggerlike properties which are prominent 
 in the categories of matter and substance are less explicitly developed. 
 The term reality, since it is applicable to ideal entities, as to thoughts 
 and forces, is far broader in scope than are matter and substance in 
 their conventional connections. Looked at more independently, 
 reality from our point of view, is the possibility of permanent and 
 certain reuse. Thus when we say that a specified man or entity is 
 the real thing, we mean that he or it can be depended upon as a 
 source of vital and fundamental efficiencies. 
 
 It follows that the efficiencies involved in the categories, matter, 
 substance, and reality form an approximate order of materials suc- 
 cession, increasing in abstractness and comprehensiveness. 
 
 So valuable are the efficiencies contained in the idea of reality and 
 so widely are these applicable, that in many cases this concept has 
 come to be regarded as the most fundamental source of efficiency, 
 
338 SOURCES OF EFFICIENCY 
 
 and has even at times been so overused as to exclude all other 
 methods of obtaining results except as subordinate details. In this 
 connection may be noted the tendency to regard the discovery of one 
 fundamental reality as the aim of all philosophic study, even of 
 life itself. 
 
 As an aid in preventing an exaggerated emphasis of the reality 
 concept, it is well to keep in mind the defects of this concept as an 
 agent of efficiency. It is to be remembered that the reality concept 
 is characterized by a tendency to premature, crude, and exclusive 
 finality, by a lack of diversity, and by a certain negative or resistant 
 element. These limitations tend constantly, so to speak, to fossilize 
 the concept in hand. 
 
 Viewing the category of reality as a special aggregate of efficien- 
 cies opens the way to the idea of different degrees and forms of 
 reality, and hence to a wider use of the concept in its efficiency 
 relations. 
 
 II. QUANTITY GROUP OF CATEGORIES 
 
 Space 
 
 In the preceding series of categories the concept of matter was 
 taken and refined and generalized, primarily with reference to our 
 sense of touch. In like manner we may refine and extend it 
 primarily with respect to our sense of vision, and we shall thus arrive 
 at the concepts of space and quantity. Space then is a special effi- 
 ciency method of treating objects or entities of any kind, as was 
 indicated in the opening paragraphs of this chapter. 
 
 Other considerations may be adduced which will be an aid in 
 realizing as subordinate and auxiliary that view which regards space 
 as an object or thing (that is, the substance or thinghood aspect of 
 space). A misapprehension of the purpose with which the first 
 treatises on the properties of space were written, is largely respon- 
 sible for the exaggerated emphasis on the latter aspect of the above 
 category, and for the desire for absolute certitude which springs 
 from this view. The title of the first systematic treatise on space, 
 viz. : the one written by Euclid, is Elements of Geometry, and the 
 word here translated Elements is exactly the same word which 
 the early Greek philosophers used when they described the universe 
 as composed of the elements earth, air, fire and water. In, other 
 words, just as the Greek philosophers sought to reduce the physical 
 universe to systematic form and thus by the use of uniformity 
 
CATEGORIES 
 
 339 
 
 and diversity and by various kinds of groupisms, to economize 
 man's labor in mastering and extend his power of manipulating 
 it, so Euclid's primary purpose was to reduce the various properties 
 of space to a few primal units, and thus give man an efficient mastery 
 of the multitudinous variety of geometrical facts. Flawless certi- 
 tude of deduction was secondary and auxiliary in accomplishing 
 this primary end. Similarly his so-called axioms were named by 
 him "common notions"; that is, by them he meant general and 
 primal groups, or agents, in obtaining results, not primal elements of 
 certitude. If two things are equal to the same thing, we are able 
 to save the labor of a direct comparison of the two things. Simi- 
 larly two points form a simple and highly efficient representative 
 of a straight line; and three points, of a plane. In like manner it 
 might be shown that all the different definitions and theorems of 
 geometry are each an individual agent of efficiency, and that the 
 combination of these into a system is made merely with a view 
 to obtaining a higher order of efficiency. It will be found also that 
 space may be regarded as a multiplicative system built up out of 
 different elements in an unlimited variety of ways. 
 
 One advantage of the above view is that it facilitates the forma- 
 tion and recognition of a great number of different kinds of space, 
 and also the groupings of any given set of objects so as to form 
 what is in effect a space, and thus of reusing our knowledge and 
 grasp of ordinary space in order to obtain increased efficiency in 
 treating an aggregate of given objects. For example, if sensations 
 be classified according to their differences in quality, intensity, and 
 duration, they may be grouped and treated as a space. Similarly we 
 are able to conceive of degrees, germs, and seeds of spatiality, and to 
 make these ideas sources of efficiency under certain circumstances. 
 
 Number 
 
 In like manner from the efficiency point of view, numbering is 
 more important than number, number itself being but a special 
 existential tool aspect or element in numbering. In other words, the 
 category of number is to be regarded primarily as a method or 
 instrument for obtaining efficiency, rather than as a static object. 
 Hence it is important to realize so far as possible the efficiental 
 components of the category of number. 
 
 Evidently the unit and multiplier principle constitutes a special 
 case or application of number. Also in its more general aspect 
 
340 SOURCES OF EFFICIENCY 
 
 number is to be regarded as a form of linear multiplicative groups 
 characterized by the uniformity among its elements, by their sepa- 
 rateness or discreteness, and by the special and highly efficient form 
 of symbolism used in representing them. This symbolism obtains its 
 efficiency from the uniformity in the size of the unit symbols em- 
 ployed, from the extreme use of the principle of neighborhood 
 symbolism, and from the fact that the symbolism for each number 
 indicates not only a magnitude but also a position in a scale. Be- 
 cause of its relative simplicity and wide applicability the number 
 toolage becomes highly assimilated in the mind and often acts with 
 great inherent speed and force, and with dialectic power. An 
 illustration is the way in which the reuse method termed generaliza- 
 tion frequently acts of itself, when the number concept or a few 
 number symbols are present with given material. 
 
 The efficiencies connected with number are so important that 
 the presence of number in some form seems necessary to a high 
 degree of efficiency in the treatment of any domain of material. 
 Thus Plato says, "If arithmetic, mensuration, and weighing be taken 
 away from any art, that which remains will not be much." In like 
 manner Lord Kelvin says, "I often remark that when you can 
 measure what you are speaking about and express it in numbers, 
 you know something about it; but when you cannot measure it in 
 numbers, your knowledge is of a meagre and unsatisfactory kind; 
 it may be the beginning of knowledge, but you have scarcely in your 
 thoughts advanced to the stage of science." In another connection 
 by way of illustration, Kelvin adds, "Arrhenius did not originate 
 the doctrine of electrolytic dissociation or of free ions ; that was 
 enunciated in 1857 by Clausius, and remained relatively barren. 
 What Arrhenius did was to introduce measured quantities into the 
 doctrine, and show its simple quantitative applicability to aqueous 
 solutions; immediately it became fertile." 
 
 Quantity 
 
 The category of quantity differs in general from space and number 
 in that it is of a higher and more abstract order and for many effi- 
 ciency purposes may be regarded as including the two categories 
 just treated as special cases. Hence much that has been said of space 
 and number is true also of quantity, but with the difference that the 
 efficiental elements and properties of quantity are more general 
 and comprehensive. In particular it should be noted that quantity 
 
CATEGORIES 347 
 
 is characterized by an unlimited possibility of uniformities, diver- 
 sities, groups, and multiplicative groups. Its pervasiveness also adds 
 to its importance as an instrument of efficiency. 
 
 Zero and Infinity 
 
 The conventional meaning assigned to zero is that of absence of 
 quantity or substantiality of any particular kind. But to obtain the 
 full efficiency significance of the term, the context (or externality) 
 associated with a zero in any particular case must be considered. 
 For instance an absence of the kind described is often due to a 
 concentration of material in a process of group making. Hence 
 such absences and emptinesses are often closely associated with 
 corresponding groupages, and these absences may become important 
 instruments of efficiency in connection with the corresponding group- 
 ages. Thus a person may often express his intentions or attitude 
 in a highly efficient way by doing nothing. A Fabian policy is an 
 approximation to this method of obtaining results. A more abstract 
 case is the use of x for ix 1 . 
 
 Much more important is the fact that zero frequently means a 
 balance between two opposites, these opposites often being two 
 extensive and highly developed multiplicative systems. The zero 
 involved may be made a source of efficiency in connection with these 
 systems in various ways. For instance when we can write = — a, 
 if we know or can control one of the a's, we can often learn or 
 control the other with little or no expenditure of effort. In other 
 words, often, where only blankness apparently is present, two equal 
 and opposed systems may really be at work, and the wise use of 
 these two systems in relation to each other may be made the source 
 of efficiency. Also, frequently a convenient and powerful way 
 of applying externality is to substitute for zero or emptiness two 
 equal and opposed aggregates of some kind. 
 
 For efficiency purposes, infinity is best regarded as the group 
 principle acting without limit, either as to the extent of its action or 
 in some other respect. Hence it is primarily a method rather than 
 an object. Nevertheless, as with other categories, the thinghood 
 aspect of infinity has certain special uses under special circumstances. 
 Thus the idea of infinite externality as an object has a more re- 
 straining and stimulating effect for certain persons in some forms 
 of religion than infinity as a principle or method. The objectivity 
 form of the infinity concept however brings with it peculiar dangers 
 
342 SOURCES OF EFFICIENCY 
 
 also, such as its tendency to crush and overwhelm, or at least to 
 create a feeling of mere dependence. On the other hand infinity 
 when viewed as unlimited groupism is easier to grasp, and can be 
 applied more widely and freely. This view also opens the way to 
 devise infinities of various sorts and to reuse the specific efficiency 
 grasp which we already have of this category. 
 
 III. THE QUALITY AND TIME GROUP OF CATEGORIES 
 Quality 
 
 A quality of an object, for our purpose, is to be regarded pri- 
 marily as an extremely close resultant of a number of efhciental 
 elements. Thus hardness (as of a piece of glass for instance) 
 means force, acting particularly as a limitation to other specific 
 forces, and hence persistence in time, and hence certain group-making 
 powers (as with respect to the transmission of light and heat). It 
 is to be noted that the frequent difficulty of analysing a quality into 
 various elements is often an advantage in that it enables us quickly 
 and readily to manipulate qualities by the use of a low order of force. 
 It may however be a disadvantage because of the lack of diversity 
 which it entails. 
 
 A broader and often more useful view is that which regards 
 qualities and objects, when considered together, as forming a reci- 
 procal group system. According to this view an object is com- 
 posed of a substratum (or underlying substance) in which a number 
 of qualities inhere. Also any one quality may be present in many 
 different objects, and therefore bind these objects together as a 
 group. Thus glass has the qualities of hardness, transparency, a 
 certain specific gravity, etc. But transparency is a property of 
 other objects besides glass, as of water, air, alcohol, quartz crystals, 
 etc. A danger in this view of the matter is that it brings the idea 
 of substance into what is perhaps an unduly prominent position. 
 At the same time other dual reciprocal group relations involved 
 tend to diminish this danger. 
 
 A realization of quality as essentially groupistic in nature should 
 increase its value as an instrument in obtaining efficiency. For 
 example, in a soil the quality of fertility is composed of a group of 
 component qualities such as the physical qualities of looseness, and 
 cohesion, and other textural properties ; also of certain chemical 
 properties due to the presence, in right proportions, of nitrogen, 
 
CATEGORIES 
 
 343 
 
 phosphorus, potash, and other elements ; also of certain biological 
 qualities due to the presence of the proper bacteria. A knowledge 
 of these elements of fertility gives great efficiency in rendering a 
 given soil more productive. 
 
 Time 
 
 For efficiency purposes time is to be regarded as a special method 
 of grouping phenomena. This multiplicative grouping is usually 
 regarded as predominantly linear in form, though there is a sense 
 in which time may be regarded as of two or more dimensions, or 
 even as a stratum or other detail in some more comprehensive 
 multiplicative group system. Hence, as with space and number, 
 the substantiality aspect of time is merely special, incidental, and 
 even superficial. Since time is often used as a symbol for one or 
 more forces, it forms a convenient transition to the next group of 
 categories to be considered. 
 
 IV. THE DYNAMIC GROUP OF CATEGORIES 
 Force and Motion 
 
 The categories of force and motion were discussed at length in 
 chapter XII (p. 210) and are now referred to again merely with a 
 view to safeguarding their use from certain errors and to developing 
 their more efficient use with reference to certain of the categories 
 under discussion in this chapter. For instance, a motion takes 
 place in space and time, and the remarks which have been made 
 concerning space and time in the present chapter should render the 
 utilization of motion more accurate and fruitful. 
 
 Mechanism and Cause 
 
 In the idea of mechanism the groupages which are characteristic 
 of matter and force are combined to produce certain new groupages 
 and efficiencies, often higher and more intense than the component 
 ones. Thus when a domain of material has been reduced to the 
 mechanical state, large parts of this domain can be operated in a 
 trigger-like way at a slight cost of effort and by a low order of 
 force. Hence, in certain relations, mechanism is a highly useful 
 source of efficiency. It is probably universally applicable in some 
 forms or aspects. Hence it has often been the tendency to overuse it, 
 just as its components, matter and force, have been overused; at 
 times to make it the primary, fundamental, and perhaps exclusive 
 
344 SOURCES OF EFFICIENCY 
 
 method of obtaining results; or even to regard it as something 
 final in itself and, by overuse to the point of contradiction, exclu- 
 sive of the very idea of surplusage in results. As a matter of fact 
 from what has already been said in connection with matter and 
 force it follows that mechanism holds a subordinate and super- 
 ficial place in the general scheme of groupage. 
 
 A few additional words may also be said in regard to the category 
 of cause. As has already been remarked, for our purpose the cause 
 of an event is best regarded as a precedent, dynamic externality to 
 the event. Hence a grasp of the causes of a fact is an important 
 means of obtaining efficiency results. For instance, such a grasp is 
 often an important aid in systematizing knowledge, or in directing 
 processes. In many cases a cause may be regarded as a handle by 
 which to control or even create effects. But here again it is to be 
 remembered that there is nothing final or ultimate in the idea of 
 causation, and that it is merely an item or aspect in the general 
 scheme of groupage. 
 
 Teleology 
 
 The category of teleology forms a convenient transition to the 
 next group of categories to be considered. The aims and ends of 
 efficiency processes have already been discussed at length in Chapter 
 IX (p. 152) and this matter of teleology (or final cause) is now re- 
 ferred to again only with a view of so restating the matter in con- 
 nection with certain other categories as to make it safe to use this 
 principle more aggressively for efficiency purposes than is often 
 done in some connections. From the point of view here prominent, 
 an aim (or final cause) is an externality which subjectively precedes 
 but which objectively follows an act. In the past undue prominence 
 has often been given to immediate, personal aims and results. Per- 
 sonality is frequently very capricious and erratic in its operations. 
 Hence teleology which consists of personal aims, uses, and values has 
 often led men into the grossest errors. As a consequence numerous 
 scientific workers and investigators have gone to the other extreme 
 and sought to discard all teleology, and thus have lost the help, 
 often powerful, which is inherent in this particular species of 
 externality when properly applied. The kind of teleology which is 
 always safe to apply and which is almost invariably productive of 
 useful results, is subpersonal, efficiental teleology. This consists of 
 aiming to obtain groups and other Efficients, and hence, ultimately, 
 
CATEGORIES 
 
 345 
 
 surplus of some kind. Almost all important results in scientific inves- 
 tigations in the past have been obtained by the use, consciously or 
 unconsciously, of some teleologic aim of this kind. In this class 
 of purposes belongs the aim of discovering uniformities and diversi- 
 ties, and later of classifying facts in groups. A higher species is 
 the aim to obtain a good working hypothesis and later to develop 
 it into a final theory (or multiplicative group system). More specific 
 illustrations are the studies which Harvey made of the uses of the 
 valves in the blood vessels and which helped him to his discovery of 
 the circulation of the blood, and Darwin's investigations of the pur- 
 poses and uses of parts of organisms in connection with the survival 
 of the fittest and the evolution of forms of life. From the point 
 of view here advocated, it should be an aid in obtaining results in 
 all fields of work to regard the discovery and development of groups, 
 multiplicative groups, externality, and other Efficients, as a certain 
 primal, subpersonal aim and end of processes. As has already been 
 suggested, we can in this connection even conceive of one final and 
 comprehensive aim or summum bonum, viz. : a thoroughly perfected 
 and universal groupage yielding the utmost surplusage to every 
 entity and mode of existence. If not itself final, this aim should 
 form an aid, not a hindrance, in obtaining a more ultimate result. 
 
 V. THE DIRECTIVE GROUP OF CATEGORIES 
 
 We now come to a group of categories closely related to the Effi- 
 cient termed directive. This group includes the categories con- 
 ventionally known as life, mentality, personality, and subject (vs. 
 object). 
 
 Life 
 
 For our purpose a living organism may be regarded as essen- 
 tially a set or domain of groups combined and acting in certain 
 specific ways. In it directive, externality, and rhythm, and resulting 
 surplusages are prominent. As has already been indicated in various 
 places such aggregates have connected with them certain character- 
 istic limitations and aptitudes for error commensurate with the 
 extraordinary powers inherent in them. 
 
 If life be thus viewed as consisting of certain essential and specific 
 groupages it becomes easy to conceive of a great variety of forms 
 of life many of them widely different from those usually included 
 under this term. Thus looking at the matter from the chemical 
 
346 SOURCES OF EFFICIENCY 
 
 standpoint, just as our present terrestrial life seems based on carbon 
 groupages, so it seems possible to conceive of a system of life 
 based on silicon groupages, and hence to conceive of life of this 
 kind as present in the hottest stars. Similarly we may conceive of 
 vital groupages different in many non-chemical ways from those 
 familiar to us on the earth, as present, for instance, on the planet 
 Mars or other planets. Similarly, by development of the groupages 
 involved, we may conceive of far higher orders and degrees of 
 life than any with which we are at present acquainted. 
 
 If the category of life be viewed essentially in the above way, it 
 also becomes easy to reuse our present grasp of this source of effi- 
 ciency in an aggresive and somewhat artificial way. Thus we gain 
 a certain confidence in the use of some Efficients and groupage 
 aggregates by regarding them as agents possessing powers of inde- 
 pendent action, and to be relied upon to produce results of them- 
 selves. We may even regard them as endowed, in a sense, with 
 some attributes of personality or even of hyper-personality. 
 
 Mind 
 
 In continuance of the above views mind may be regarded as 
 life plus (or with an especial development of) a high order of ex- 
 ternality and directive. Consciousness, as is indicated by the ety- 
 mology of the word {con, meaning together, and scio, to know) 
 is a knowing of things together, or an awareness of them in groups ; 
 and mind is a development and use of these groups with reference 
 to a varied and increasing externality. Hence it is easy to see that 
 mind must be an efficiency instrument of the highest order of 
 importance. This view of mind enables us to conceive of a great 
 variety of mentality, including types very different from those 
 familiar to us in human beings; as, for instance, of methods of 
 sense perceptions in the animals widely different from those in 
 man, and also of very superior and transcendent mental processes 
 perhaps attainable in time by us and perhaps glimpsed in the intel- 
 lectual processes of so-called geniuses. It also enables us to make 
 certain aggressive and, in a sense, artificial uses of mentality similar 
 to those suggested for the category of life. 
 
 Personality is life and mind in connection with a single organism 
 and usually developed in some striking and specific way. 
 
 By subject, in this connection, is meant a personality, as con- 
 trasted with the rest of the universe, or some part of it, taken as 
 object. 
 
CATEGORIES 347 
 
 VI. THE CATEGORY OF THE ULTIMATE OR ABSOLUTE 
 Efficiency Properties of an Absolute 
 
 If we could discover a primal (ultimate, fundamental, central, 
 dominating) category or entity, in terms of which all other entities 
 could be stated, or from which they could be derived, we should evi- 
 dently have a highly important source of efficiency. For if this 
 fundamental entity should prove to be a thing or object, by con- 
 trolling or directing it we could reduce the universe to a mechanical 
 or triggerish state. If it were more abstract in nature it would still 
 furnish an all-comprehensive unity (or uniformity), with vital and 
 comprehensive uses such as that of furnishing the material or 
 basis for unlimited group formations, or that of supplying an omni- 
 present and manifold externality, or that of opening the way to 
 universal marginal reuse. Because of this inviting vista a large part 
 of the history of human thought has consisted of the search after 
 some one fundamental reality with the (often subconscious) hope of 
 obtaining a single final and complete instrument of efficiency or 
 means of obtaining results. Various names have been suggested for 
 this primal category among these being the fundamental reality, 
 truth, or principle; the ultimate reality, or the absolute. 
 
 It may be suggested at this point that the present investigation 
 thus far points to the conclusion that all that is useful in the pro- 
 posed category of efficiency now under discussion is obtained by 
 taking the group concept itself as the ultimate and inclusive principle 
 for the present. 
 
 In this connection it may be noted that if we examine the various 
 ultimate principles which have been suggested in the past, we find 
 that each of these may be regarded as a modification or aspect of 
 the group principle. 
 
 List of Proposed Absolutes 
 These suggested ultimates may be classified as follows : 
 
 I. The materialistic class : matter, water, air, fire. 
 
 II. The force or energy class: energy, force, light (and dark- 
 ness), motion, change. 
 
 III. The biologic class : life. 
 
 IV. The psychological or personal class : mind, reason, conscious- 
 ness, pleasure, love, faith, will, idea, spirit, soul, God. 
 
 V. The ethical and practical class : good, duty, value. 
 
348 SOURCES OF EFFICIENCY 
 
 VI. The methodological class : becoming, evolution, the way, 
 unity, number, the category of order, relation, interaction, or 
 system. 
 
 VII. The reality class : absolute, substance, being. 
 
 The Multiplicative Principle as a Provisional Absolute 
 
 The analysis which has already been made in this chapter of the 
 various categories, and also that made of other of the above con- 
 cepts in the course of preceding chapters, shows in a general way in 
 what sense each of the above proposed ultimate principles may be 
 regarded as a special form or modification of the group principle. 
 When the multiplicative principle is taken as ultimate, the narrowness 
 or special individuality of many of these primal categories is reme- 
 died by the tendency to expansion which is characteristic of the 
 group idea. For instance, the multiplicative principle by its power 
 of self-correction and of developing unity, remedies the chaotic ten- 
 dency inherent in a personality or an ethical principle when each 
 one applies it to suit himself, as when each one forms his own sys- 
 tem of values. 
 
 For this and other reasons, by regarding each of the above pro- 
 posed central principles as a modification of the group principle, the 
 way is opened to use each of them, and the system derived from it, 
 aggressively as a special form of instrumentation. 
 
 It is also to be noted that if something more underlying and in- 
 clusive than the multiplicative principle is discoverable, the expan- 
 sive and corrective properties of this principle would seem to lead 
 on to and to compel the attainment of this something in the end, 
 in case such attainment is possible. Hence we arrive at the con- 
 clusion that for the present the largest results are to be obtained 
 by regarding the group or multiplicative principle as the most 
 ultimate in sight, and by viewing personality (in the conventional 
 sense of the term), reality, thinghood, and all forms of equivalence 
 as relatively secondary toolages. 
 
 The Categories in General 
 
 With respect to the categories as a whole, it should be remarked 
 that each of them probably contains something characteristic and 
 unique, which may at any time become the source of hitherto un- 
 realized efficiencies; and also that, by modification of the different 
 categories and by various combinations of them, what are in effect 
 
CATEGORIES 
 
 349 
 
 important new and more or less independent species of them may 
 be obtained. 
 
 Phenomena 
 
 Before closing the discussion of the categories, some mention 
 should be made of what are conventionally known as phenomena ; 
 that is, of sights, sounds, and other sensations and perceptions, and 
 of the objects which are taken as directly represented by these. Since 
 phenomena may be almost altogether analyzed into matter, force, 
 mind, and the other categories which we have been studying, it 
 follows that phenomena are often special instrumentalisms. Many 
 of these apparently have been evolved in a crude and haphazard 
 manner, but almost all of them possess some peculiar and highly 
 finished efficiency property. As illustrations we may mention the 
 efficiency functions of wood, stone, light, and the change of seasons. 
 
 Efficients, Categories, and Phenomena 
 
 As a result of our investigations we have therefore found three 
 general classes of efficiency instruments, viz. : those which have been 
 respectively termed Efficients, Categories, and Phenomena. No one 
 of these classes can be determined independently of the other two, 
 and each can be resolved largely into the others. But in this cir- 
 cuit of transformation, positive surplusage everywhere may arise, 
 and a varied cancellation of assumptions takes place. In this man- 
 ner, from a new and more comprehensive point of view, the group is 
 made to stand forth in the first place both as method and result, and 
 as leading on to other more ultimate ideas, if such are called for, 
 or are possible. We thus arrive at a general conception of the 
 relation of efficiency to other primal ideas and to a general philosophy 
 of life, which, in order to obtain the advantages connected with a 
 name, we may term efficientism. 
 
B. HISTORICAL SURVEY 
 
 Value of History of Efficiency Principles 
 
 A brief survey of the historical development of the principles 
 which have been presented in this book will be of service in different 
 ways. For instance it will clarify and develop these principles by 
 presenting them in certain new relations to each other. It will exhibit 
 the uses of the Efficients in the special forms in which they have 
 been applied in the past. It may suggest new individual forms which 
 they may take. It should shed light on the best places at which 
 and methods by which to apply these principles to the present-day 
 world. It will also aid in realizing the place of efficiency in a general 
 philosophy of life. 
 
 Certain of the primal efficiency instruments (as uniformities, 
 diversities, groups, rhythms) appear, though often in a crude form, 
 in inanimate nature, and in various plants and animals. In man 
 also we find them developed to a certain point before the dawn of 
 any distinctive efficiency consciousness. 
 
 Primitive Instruments of Efficiency 
 
 We begin our more detailed survey with a statement of the initial, 
 semi-conscious efficiency efforts of man. We shall first present in 
 tabular form (see p. 351) the early instruments devised by man for 
 making his exertions more productive. In this table the conven- 
 tional names for these aids to efficiency are used, but we shall also 
 state the more important of them in terms of the Efficients. 
 
 Thus it will be observed that each item in the table, as the use of 
 caves, clubs, metals, and animals, involves externality of some sort. 
 
 Each of these items also arises by directive action of some kind, 
 and is made more productive by means of reuse. 
 
 Each of the tabulated devices and arts involves some species of 
 groupism. Multiplicative groupism appears in many highly con- 
 densed forms, but also in some which are more explicit and elaborate, 
 such as tribal organization and articulate language. The order of 
 materials concept is illustrated in the series of materials, wood, 
 
 350 
 
HISTORICAL SURVEY 
 
 351 
 
 INORGANIC 
 
 BIOLOGIC 
 
 PSYCHOLOGIC 
 
 SOCIAL 
 
 RELIGIOUS 
 
 Caves (as dwel- 
 
 Trees (as 
 
 Articulate 
 
 Family 
 
 
 lings) 
 
 dwellings) 
 
 language 
 
 
 
 Stones (as wea- 
 
 
 
 
 
 pons) 
 
 Clubs 
 
 Opposable 
 thumb 
 
 Right handed- 
 ness 
 
 Wild animals 
 (as food) 
 
 Pictorial arts 
 
 Tribalism 
 
 Fetishism 
 Taboo 
 
 Shaped stones 
 
 
 
 
 
 (as arrow 
 
 Skins and 
 
 
 
 
 and axe 
 
 tendons 
 
 
 
 
 heads, pes- 
 
 
 
 
 
 tle and 
 
 Tomahawk 
 
 Graphic sym- 
 
 
 Animism 
 
 mortar) 
 
 (bow and ar- 
 
 bols 
 
 
 
 
 row) 
 
 
 Totemism 
 
 Magic 
 
 Sun-dried pot- 
 
 
 
 
 
 tery 
 
 
 
 
 
 Fire (baked 
 
 
 Music 
 
 Exogamy 
 
 
 pottery) 
 
 
 
 
 
 Copper 
 
 Domesticated 
 Animals 
 
 Written lan- 
 guage 
 
 
 Confucianism 
 
 Bronze 
 
 Pastoral life 
 (human sla- 
 very) 
 
 Astronomy 
 (beginnings 
 of science) 
 
 
 
 Iron 
 
 Agriculture 
 
 
 
 
 Steel 
 
 
 
 
 
 stone, copper, bronze, iron, steel ; in right handedness ; and in the 
 succession of linguistic forms, and of the mental processes which 
 accompanied these. 
 
 Primitive Combinations of Efficients 
 
 It should also be realized that usually several of the primal in- 
 struments of efficiency are found operating together in one of the 
 items tabulated above. 
 
 Thus man's erect position by raising the eye to a higher position 
 gives a larger outlook and hence increased externality in human life 
 processes. It also leaves the hands free for efficiency functions which 
 
352 SOURCES OF EFFICIENCY 
 
 are higher as a whole than those of the feet, and has thus pro- 
 duced an order of materials development of man's limbs, which in 
 time has led to the formation of other orders of material. 
 
 The use of fire constitutes an externality which is useful both 
 directly and also indirectly by the formation of diversities and 
 re-groupings. The resulting actions and reactions form a rhythm of 
 increasing power. 
 
 Crude as it is at first sight fetishism contains an important 
 externality. In fact in fetishism and like practices are found the 
 germs of the use of unlimited externality, together with certain 
 consequent groupings, forms of reuse, and other efficientizings. 
 
 It is important to note that in all this early efficiental life, sur- 
 plusage or profit holds a dominant place as compared with certi- 
 tude or reality. The primitive man lived and worked for definite 
 and directly useful results. This view of life so far as it is a general 
 view or theory, takes the form of what is called animism or spiritism 
 (or personeity). Spiritism is essentially that view of life in which 
 the principal method of obtaining results is that of treating all 
 nature processes as the acts or under the control of persons (beings, 
 spirits), who can be propitiated and converted into friends and help- 
 ers. Hence animism puts surplusage and the personal methods of 
 obtaining it in the first place as compared with the mechanical 
 equivalence idea of life later called natural law. The use of spirits 
 suggesting as it does large immediate returns at little cost, appealed 
 to men in several important ways and, for the time being, was devel- 
 oped in preference to pure groupism with its better results attainable 
 after a larger period of effort. 
 
 Crude as they were in many respects, the essential efficiencies 
 involved in man's first inventions and discoveries produced in the 
 aggregate remarkable gains. Thus land used pastorally was one 
 hundred times as efficient as land used for the hunting of wild 
 game; and, when used agriculturally, was four times as productive 
 as when employed pastorally. 
 
 Efficiencies in Early Empires 
 
 The large alluvial plains of Egypt, Babylonia, India, and China in 
 which men first applied agriculture extensively, fostered the devel- 
 opment of efficiency in certain ways, but also gave rise to some 
 backward tendencies. Such plains are characterized by vast unifor- 
 mities which led to the promotion of giant homogeneous political, 
 
HISTORICAL SURVEY 
 
 353 
 
 social, linguistic, religious, and intellectual groups. Often one of 
 these vast groups in the end took the form of a multiplicative 
 group system, the most explicit example being the empire of the 
 Medes and Persians with its satrapies, provinces, and subprovinces. 
 In each individual empire, and between empires, also naturally 
 developed forms and vast amounts of reuse, reciprocal externality,, 
 directive, symbolisms, and permanencies in time. Hence also arose 
 important efficiency arts and sciences, such as systematic irriga- 
 tion in agriculture, the astronomy of the Babylonians, the land 
 measurement (or geometry) of the Egyptians, and the arithmetic 
 of the Hindoos. The large size of the groups involved together with 
 the accompanying lack of diversity led however to some evils, chief 
 among which were certain extreme forms of uniformity. Con- 
 spicuous illustrations are the caste system of the Hindoos and the 
 oriental doctrine of fatalism. 
 
 Similarly the category of personality was developed in striking 
 ways in these early civilizations. One of the more concrete forms 
 of such development was Confucianism among the Chinese; more 
 sublimated species were Brahmanism and Buddhism among the 
 Hindoos and the worship of Jehovah among the Hebrews. Be- 
 sides giving other advantages, these highly developed views of 
 spiritism were useful in making infinite externality a near and 
 useful fact. Associated with these ideas were positive non-equiva- 
 lence, or surplusage, taken as dominant over equivalence in the 
 form now termed natural law. Connected with personality and 
 surplusage in the highly developed forms however were grave evils 
 such as magic and necromancy, certain views as to miracles, and 
 a failure to recognize pure groupism as in many respects back 
 of and dominant over personality, and leading to and requiring 
 important kinds of universal equivalence or law. 
 
 Greeks discover the Group Principle 
 
 It is the immortal glory of the Greek mind to have discovered, 
 in essential respects, the group as an abstract, primal, and inclusive 
 principle. Near enough to Orientalism to benefit by its results, 
 and yet far enough away to be able to perceive and to attempt 
 to remedy its defects, aided by the geographical diversity of the 
 land in which he lived and the variety of its natural resources, 
 familiar with the sea and its efficiency uses, and influenced by other 
 factors, the Greek was led to recognize the value of uniformity 
 
354 SOURCES OF EFFICIENCY 
 
 and of grouping. His attempts to form comprehensive efficiency 
 systems along this line naturally at first took somewhat concrete 
 forms. 
 
 As an example we have the views of Thales. In his idea of 
 water as the primal material out of which all things are made 
 or generated, Thales, in effect, conceived of a universal first prin- 
 ciple, free from the caprices of personality (but annexing the ele- 
 ments of personality occasionally in a subordinate manner), and 
 therefore capable of being grouped and multiplicatively grouped in 
 reliable ways, and hence open to mechanical trigger control. 
 
 Water of course has radical imperfections as a first principle, and 
 other early Greek philosophers tried to get rid of these by using 
 instead of water some other element, as air, fire, mind, being, motion, 
 rest, or matter. Of these immediate successors of Thales, Democri- 
 tus performed the greatest service in that he first developed in explicit 
 group form some of the properties latent in the substance which he 
 regarded as primordial, viz. : matter. He obtained this result by 
 regarding matter as divided into units termed atoms, and by com- 
 bining atoms in what were essentially groups to explain phenomena. 
 The advantages thus attained are illustrated for instance in Democri- 
 tus' theory of vision and its consequences as presented elsewhere 
 
 (PP- 335-336). 
 
 All of the early Greek thinkers erred however in paying primary 
 attention to the category of reality and in leaving the efficiency 
 functions of their ideas to take care, so to speak, of themselves. 
 
 The Sophists performed a negative service by showing that cer- 
 titude and ultimate reality could not be attained along the route 
 by which these were being pursued. They performed a more 
 positive service by making gain or advantage the primary aim of life 
 and by developing certain grammatical and rhetorical groups and 
 multiplicative group systems, of which the moods and tenses of 
 verbs are examples, as instruments in attaining their ends. They 
 erred however in adopting narrow and superficial views as to the 
 nature of gain and profit. 
 
 Socrates was the first to discover and apply the group in an 
 abstract, general form. The group as used by him is what is now 
 usually termed the concept. Socrates also developed this into the 
 incipient multiplicative group form embodied in the use of the 
 terms genus and species. He applied the group, as thus conceived, 
 
HISTORICAL SURVEY 
 
 355 
 
 in the special and somewhat personal fields of ethics and sociology, 
 and not at all in the domain of natural science. His primary aim also 
 in thus applying the group was certitude and not utility. He could 
 not however use it even in this narrow way without to a certain 
 extent developing its abstract and general properties. Hence the 
 work of Socrates, in spite of his failure to give the group a pure 
 subpersonal form and free development, constitutes a prime epoch 
 in the history of efficiency. 
 
 Plato and Aristotle 
 
 Plato took the group instrument invented by Socrates and de- 
 veloped it in important ways. In his hands it took the form of 
 the idea or, as we would perhaps describe it, the seen or graphic 
 efficiental essence of an object or domain, though he often gave it 
 much more general and untrammelled meanings. For Plato sepa- 
 rated the special form of the group which he termed the idea, from 
 the world of concrete limitation and quality, and developed it freely 
 with respect to various categories. Thus owing to his work the 
 group acquired a name, became subpersonal, objective, self -existent, 
 and creative of phenomena. Plato not only developed his group idea 
 in these ways, but he also applied it to all departments of life and 
 knowledge as they then existed. In the more abstract of these 
 departments, as in mathematics, logic, ethics, and sociology, he by 
 this means obtained results of importance; but his undue emphasis 
 on certitude and his lack of appreciation of the enormous profusion 
 of highly developed diversities in the world, make his investigations 
 in the field of more concrete science, crude and unsound. His sepa- 
 ration, for the time being, of ideas from the world of concrete 
 phenomena, and his consequent free and aggressive development 
 of their properties, form a work of the first importance. It is to 
 be noted that in this work of Plato's we find an application of 
 diversity, externality, and orders of material in some of their highest 
 forms. 
 
 With Aristotle the group took the specific and dominant form of 
 the category. Aristotle recognized more fully than did Plato the 
 fundamental richness of diversity and of individual quality in 
 phenomena, and the consequent need of using special adapted 
 primal forms of the group when applying it in different fields and 
 relations, and hence also the need of careful progressive steps in 
 such applications. Among the special forms in which the group and 
 
356 SOURCES OF EFFICIENCY 
 
 multiplicative groups appear in Aristotle, are his categories, his 
 various kinds of causes, his syllogisms, and his methods of classifi- 
 cation and organization. In certain important ways he also realizes 
 substantiality or thinghood as subordinate to or as a special cause of 
 grouphood and value. Thus he regards things as their purposes, 
 ends, and relations, rather than as the matter composing them. 
 Motion he also explains as the result of the desire of things for 
 form. Similarly matter according to him is a potency of form; 
 soul is an actuality of this; and God is purus actus (or pure 
 groupism) . 
 
 Aristotle's treatment of the group lacks the freedom and sweep 
 of Plato's but it fits the details of the naive phenomenal world 
 far more closely. Because of his careful, direct application of what 
 is essentially the group method to the facts of life as they are 
 immediately apprehended, Aristotle was able to initiate important 
 new departments of study and efficiency attainment, such as physics, 
 botany, zoology, and medicine, and to' put logic in what is essentially 
 its present form. 
 
 Other similar products of the Greek use of the group were 
 sciences like psychology, ethics, and esthetics ; or more special pro- 
 ducts such as Greek literature, architecture, and sculpture. To 
 this fundamental source also are to be traced the principles of 
 measure, proportion, moderation, and symmetry, which pervaded 
 the Greek civilization and filled it with a manifold creative life. 
 
 Limitations in Greek Grasp of Efficiency Principles 
 
 From the ideal standpoint, however, the Greek systems of effi- 
 ciency had serious defects. One of these was the failure to realize 
 the self-corrective power in the multiplicative principle when freely 
 used. Hence results the tendency in the Greek mind to invent and 
 employ elaborate and costly methods of preventing error. This char- 
 acteristic is illustrated by Aristotle's use of his system of syllo- 
 gisms primarily as a means of detecting fallacies, rather than as a 
 method of putting knowledge in a productive and readily usable 
 form. Other deficiencies are the undue prominence given to truth 
 and reality as aims and ends, and the lack of a grasp and free use 
 of infinite externality. 
 
 Cramped in these ways, the Greek efficiency systems were not 
 able quickly to grasp and handle the world life as a whole on coming 
 into sudden contact with it after the conquests of Alexander the 
 
HISTORICAL SURVEY 
 
 357 
 
 Great. Hence the primal Greek instruments of thought and action 
 came to be used in a narrow and personal way as in Stoicism and 
 Epicureanism, or in a mystical and flighty way as in Neo-Platonism. 
 Hence while the use of the group concept continued to produce 
 certain useful results in mathematics, art, literature, and some de- 
 partments of science, it was prevented from quickly reaping its 
 full fruitage by the fact that its use was made tributary to the 
 search for a final reality. 
 
 Efficiencies Characteristic of Christianity 
 
 The next great advance in the development of the principles of 
 efficiency was made by Christianity and consisted in putting infinite 
 externality in a near and usable form. Orientalism had made 
 familiar the idea of the infinite group, but in the unlimited group as 
 thus conceived the individual was lost and immersed, or with respect 
 to it was regarded as insignificant, the result being a tendency to 
 fixity and fatalism. On the other hand in Christianity the individual 
 was conserved, and the infinite group had to him the relation of 
 infinite externality with all the possible uses of the same. Thus in its 
 essence Christianity is a combination of oriental and Greek effi- 
 ciency processes. With this union the broad and complete founda- 
 tion was laid for every ultimate advance. 
 
 The Middle Ages 
 
 During the middle ages there was steady progress in the major 
 elements of efficiency. Thus there was a constantly increasing appre- 
 ciation of the brotherhood of man and the fatherhood of God, and of 
 the vast groupages which these ideas imply. The Greek system 
 of groups was also used to advantage, in a supplementary way, in 
 Christian theology, and the church was made more effective, in some 
 respects, by the adoption of the Roman-oriental system of govern- 
 mental organization. However, in certain important respects the 
 efficiency life of the world retrograded during the medieval epoch. 
 The tendency to seek in some easy and immediate way the fruits 
 latent in the Christian infinities was prominent. Hence, following 
 the method of Plato, the vast amount of concrete limitation in the 
 world and the need for patient study of detailed facts, and for their 
 grouping and regrouping, were overlooked, the detailed activities 
 of many centuries being given up to theoretic speculation, and 
 mystical rhapsody. Nevertheless the major elements of efficiency 
 
358 SOURCES OF EFFICIENCY 
 
 which were at work were so powerful that important special new 
 elements of efficiency were being discovered or invented from 
 time to time. Among these advances were the invention of 
 the horseshoe which made the age of chivalry possible, the 
 discovery of the magnetic needle, the invention of gunpowder, 
 the discovery of many chemical facts by the alchemists, and the 
 introduction into Europe of the Arabic arithmetic. Perhaps we may 
 fairly add to the list the Copernican astronomy with the concrete 
 externalities, and the re-multiplicative-groupings which it implies, 
 and the invention of printing by movable type with the various effi- 
 ciental processes inherent in it and flowing from it. 
 
 Relation of Bacon to Efficiency Principles 
 
 Bacon, like Aristotle, realized the vast richness of diversity and 
 the great variety of limitations which characterized the world of 
 nature and life as we find it. Hence he understood the need of a 
 careful, methodic study of nature at first hand, in order to obtain 
 results of vital and permanent value. He advocated the patient 
 collection of facts and the arrangement of these in groups, with 
 subsequent constructions from them of hierarchies of inclusive prin- 
 ciples or laws. In other words, in essence he urged the discovery 
 and formation of elementary groups and the building up of these 
 into multiplicative group systems. Bacon's use of groups differs 
 from that of Aristotle in important particulars. It is superior in 
 its advocacy of the investigation, in cases of difficulty, of mere 
 uniformities and diversities ; in the analysis given of the sources of 
 error in the process of forming groups; in a realization of the 
 value of formal written tabulations of facts; in the use of the objec- 
 tive world as the best starting place for such studies ; and in the 
 orderliness and comprehensiveness of his proposed study of the 
 objective world. 
 
 Bacon however was inferior to Aristotle in that he failed to realize 
 the value of an early general group schematism, obtained from an 
 examination of categories like space, time, substance, force, as well as 
 phenomena, as an aid in mastering facts, even though such a schema- 
 tism be subject to much later modification. 
 
 Of like nature is Bacon's failure to recognize the value of the 
 working hypothesis. Rarely, if ever, has an important discovery 
 been made by the application of the Baconian method pure and 
 simple. The effective method of arriving at multiplicative group 
 
HISTORICAL SURVEY 
 
 359 
 
 systems of facts, is not to try as a first process to collect all possible 
 facts and then at one stroke to frame them into a final system. 
 Rather the successful method is to collect facts till an intelligent 
 working hypothesis, or provisional multiplicative group system can 
 be formed; to test this provisional system by deduction (i.e., reuse), 
 by experiment (i.e., by externality and the use of units and multi- 
 pliers) ; to arrive thus at new facts in a far more efficient way than 
 could otherwise be done ; to reconstruct the working hypothesis from 
 time to time by the aid of the new facts thus obtained ; and to 
 proceed thus by rhythmic progression till a highly developed or even 
 final result is obtained. An example is the process by which the law 
 of gravitation was discovered, extending as this process does through 
 periods of alternate observation of the heavenly bodies and the 
 framing of theories from the time of the Babylonians to Newton. A 
 more concise illustration is supplied by the succession of steps by 
 which Darwin developed the doctrine of the evolution of species. 
 
 Descartes and Leibnitz 
 
 The general provisional multiplicative group schematism, broad 
 enough to include the categories as well as the then known or ascer- 
 tainable concrete facts, which Bacon failed to make, was attempted 
 by Descartes, Spinoza, and others. The most important of these 
 comprehensive toolages for our purpose is that of Leibnitz. The 
 monads employed by him from one point of view are units or ele- 
 ments ; from another are groups ; and from still another constitute 
 strands in a pluralism. The principle of preestablished harmony 
 which in effect combines the monads, is the group principle taken as 
 underlying and controlling. Its use in essence, makes subpersonal 
 groupism primal and dominant, and hence more fundamental than 
 either personality or material mechanism. The emphasis placed by 
 Leibnitz on the principles of continuity and differentials also consti- 
 tutes a recognition of the special value of uniformity and diversity. 
 Hence in the system of Leibnitz as a whole we find our main instru- 
 ments of efficiency, but in a peculiar and highly individualized form. 
 The value of these principles even in this form is demonstrated by the 
 important results obtained by Leibnitz through their use, the most 
 valuable of these being the differential and integral calculus in 
 mathematics. 
 
360 SOURCES OF EFFICIENCY 
 
 Locke and His Successors 
 
 Locke applied the Baconian method to the domain of mind. His 
 aim was to build up all mental phenomena out of a few primal 
 elements, as all language is formed out of the alphabet, or as Euclid 
 built up his geometry out of a few fundamental properties of space. 
 Locke thus obtained efficiency results of the greatest importance. 
 These were applied by him and his successors, particularly in France, 
 not only to psychology, but also to ethics, education, and government. 
 
 Berkely and Hume ignored the economy and efficiency significance 
 of Locke's work, and spent much time and effort in showing that 
 Locke's method did not reveal an ultimate reality or give fundamental 
 certitude. This drove Kant, like Socrates under similar circum- 
 stances, to a recognition of the group. For Kant regards time, 
 space, and the other categories as group methods in which the mind 
 acts in relation to the objective world, and his synthetic judgments 
 indicate the surplusages or advantages which result. Notwithstand- 
 ing its great apparent emphasis on mind and personality, this point 
 of view is closely related to that which regards groupism as the 
 primal principle with mind, matter, space, time, etc., and as special 
 modes in which the group principle acts or manifests itself. 
 
 Kant, Hegel, and Herbart 
 
 Kant also made an important contribution to the efficiency schema- 
 tism by obtaining a principle of certitude in his categorical impera- 
 tive. This principle is arrived at in effect by a use of unlimited 
 externality with a consequent order of materials and dynamic result. 
 Hence it constitutes a special manifestation of the self-corrective 
 and unity-giving power of the multiplicative principle. 
 
 However in Kant's system the lack of explicitness as to whether 
 the group is to be taken as more fundamental than mind and matter, 
 leaves the world of principles and the world of phenomena largely 
 uncoordinated. Hegel tried to combine these two worlds by taking 
 the "idea", which, in spite of the element of mentality seemingly 
 implied in it, is fundamentally a group principle, as primal and con- 
 stitutive of all things. By this method he obtained many efficiental 
 results, but in its application he failed to take the principle of limi- 
 tation and of specific quality adequately into the account. 
 
 Herbart avoided the element of mentality which warps and cramps 
 Hegel's system from the efficiency point of view, by taking as a funda- 
 mental principle what is essentially the abstract and subpersonal 
 
HISTORICAL SURVEY 361 
 
 group discussed in Chapter IV. This is found in his idea of particu- 
 lars forming a unity (his realen and susammen). However he retro- 
 grades in that he uses this fundamental conception primarily as a 
 means of obtaining certitude or reality rather than efficiency, and in 
 that he fails to realize its power when developed as an extended mul- 
 tiplicative series and in various qualitative forms. He nevertheless 
 obtained useful results by an application of his method in the field 
 of education; the most important of these being his principle of 
 apperception. The use of apperception in education means, essen- 
 tially, the statement of what is new in the terms of what is already 
 known. Hence in it are contained the use of uniformity and diver- 
 sity, reuse, and often of the unit and multiplier. 
 
 Evolutionary as related to Efficiency Principles 
 
 The method of evolution as presented by Darwin, Herbert 
 Spencer, and others, may be regarded as a special combination of 
 certain efficiency processes. 
 
 Thus in Darwin's principle of the survival of the fittest we have 
 a multiplicative expansion of objects by reproduction, a resulting 
 homogeneous externality and a re-multiplicative-grouping into a 
 more effective system. The continuity characteristic of such a pro- 
 cess involves an almost continuous stream of marginal reuse, each 
 organism reusing almost in an entirety the organism which preceded 
 it in the stream of development. 
 
 Similarly Herbert Spencer's more comprehensive view of evolu- 
 tion as a series of alternate integrations and dissipations may be 
 viewed as a rhythm of groupings, new externality, and re-groupings. 
 In these processes the principles of limitation and motion and force 
 are also fully recognized. In certain forms of evolution still other 
 groups are suggested, as in the idea of Mendel and de Vries that 
 the elements of an organism may vary and be adapted in groups. 
 The use of the order of materials is also suggested in the thought, 
 for instance, that the capacity of an organism for variation may vary. 
 
 It is to be observed, however, that, as ordinarily considered, evolu- 
 tion is a slow and costly system of obtaining results, as compared 
 with certain other existent or conceivable efficiency systems. Thus, 
 from the ideal efficiency standpoint evolution is deficient because of 
 its slight use of externality, orders of material, directive, symbolisms, 
 and other similar highly efficient instruments. Hence, as usually 
 understood, it forms a special detail in the general efficiency system 
 which we are investigating. 
 
362 SOURCES OF EFFICIENCY 
 
 Concrete and Scientific Developments 
 
 As has been suggested and illustrated at various points, parallel 
 with the development of the abstract principles of efficiency, there 
 has proceeded a development of these principles in certain more 
 concrete and special fields, as in agriculture, mechanics, govern- 
 ment, and the various arts and sciences. These two streams of 
 progress have often interacted helpfully. As an illustration of the 
 development of the Efficients in one of these special concrete forms 
 we may take the changes which have characterized the progress of 
 agriculture. 
 
 Similarly the progress of science, as a whole, has been essentially, 
 a progressive development of efficiency instruments and methods. 
 Thus the axioms and laws of science are primarily fundamental 
 instruments of efficiency. For instance the principle that action and 
 reaction are always equal is a primary source of economy, since when 
 either action or reaction is known, the other is known also, and the 
 labor of an independent investigation of it is saved. So also progress 
 in science is made by the extended use of various kinds of auxiliaries, 
 by units and multipliers, and reuse, and by combining results in mul- 
 tiplicative group systems which are full of both economy and dialectic 
 power. 
 
 Pragmatism and Its Services 
 
 The brief examination of the history of the principles of efficiency 
 made thus far shows that the realization of these principles has 
 been greatly hindered by the fact that throughout by far the greater 
 part of definitely recorded history, the discovery of an ultimate 
 reality has been taken as the primary goal of human endeavor. 
 It would seem that the concept of a fundamental reality cannot be 
 ultimate; that if an ultimate were discovered we would at once 
 proceed to put it to certain uses; and that the uses of this reality 
 would therefore be more fundamental than the reality itself. If 
 however the human mind during this long record has been uncon- 
 sciously searching for a fundamental reality not for its own sake, but 
 for the sake of its uses, such a fact has usually been so far in the 
 background that no systematic investigation of these uses, or of 
 methods of their individual attainment, has been attempted. In 
 other words up to within a few years any supremacy attributed to 
 efficiency or a kindred concept has been unconscious, or unsyste- 
 matic and undeveloped. 
 
HISTORICAL SURVEY 363 
 
 Recently however in the movement termed pragmatism, a con- 
 scious and somewhat organized attempt has been made to put utility 
 in the dominant place in human thought and processes. According 
 to this view of life the certitude of a principle is determined by the 
 consequences of that principle. Reality depends on workability, or 
 the useful is the real. This view of the matter seems to make value 
 or surplusage more primal and determinative than reality. But by 
 their elaborate a priori discussions of the nature of reality and by 
 requiring utility to satisfy certain rationalistic tests laid down as 
 determinative of reality, the pragmatic thinkers again in effect put 
 reality in the first place. They also do this in a negative way by 
 failing to make any thoroughgoing examination and development of 
 efficiency methods and instruments, and by omitting to show that 
 reality may be accounted for as one of these instruments. The addi- 
 tional failure to make personality (as ordinarily understood) subor- 
 dinate to efficiency in general, makes possible the chaos which arises 
 when each person is allowed to construct his own efficiency (and 
 hence reality) world, unharmonized with those of others by any 
 systematic comprehensive means. In other words instead of making; 
 the group primary and fundamental, at least for the time being, the 
 pragmatic movement spends its force in rationalistic discussions of 
 the relations between two special forms or results of the group, viz. : 
 reality and personal utility, and alternately giving the dominance to 
 each of these. Even this imperfect treatment of the utility concept 
 however has produced a number of widely useful results. 
 
 The pragmatic movement, for instance, has, in a measure, inspired 
 the recent direct study of efficiency in more or less concrete fields, 
 as in business management and in civic and governmental affairs. 
 In these movements many special results of importance have been 
 arrived at. The more important of these results have, however, 
 been referred to in the chapters which precede, and no repetition 
 of them is called for at this point. 
 
 Summary of History of Efficiency 
 
 The preceding historical survey may be conveniently summarized 
 as follows. In the early stages of human history we find the group 
 utilized in the form of the family, tribe, or clan ; in flocks and herds ; 
 in various mechanical devices; in different kinds of language; and 
 in ideas as to various forms of spirits. All this use of the group 
 
364 SOURCES OF EFFICIENCY 
 
 is dominated by a naive assumption of gain or surplusage as primal, 
 with slight development of the idea of reality. 
 
 Later the great alluvial plains fostered the development of enor- 
 mously large groups both concrete and abstract. These larger groups 
 mastered and often absorbed the smaller ones formed earlier, and 
 also those systems of groups which came into the great river plains 
 from outside sources, principally Aryan. The ultimate result often 
 was the formation of a gigantic multiplicative group system, operated 
 from the apex, and illustrated by the Persian and Roman empires. 
 In contrast with this was developed what may be termed the federal, 
 <or Greek-Christian-Teutonic multiplicative group system. In this 
 form of group organization action originates mainly in the individual 
 units or elements and proceeds toward the apex. The system how- 
 ever is so full of freedom that multiplicative action also proceeds 
 from the apex toward the elements, and in many cross and mixed 
 directions. In general the multiplicative principle acting thus tends 
 to give unity along with the maximum of freedom. The Greek- 
 Christian-Teutonic method when developed in the most abstract 
 and inclusive way gives rise to a federal system of Efficients, 
 acting in connection with a similar but weaker system of limitations, 
 the two systems intersecting to form many special agencies and re- 
 sults. It makes fundamental neither the One nor the Many, but the 
 One-in-the-Many. Hence this general schematic conception may be 
 regarded as including monism, dualism, pluralism, idealism, mechan- 
 ism, and the other special systems touched upon in the preceding 
 historical survey, as details of itself, especially when the systems 
 just mentioned are regarded as methods of obtaining results. 
 
INDEX 
 
 Absolute, 347 
 
 Abstract, 105 
 
 Aeroplane, 130, 132 
 
 African, 83 
 
 Agriculture, 2, 10, 16, 22, 41, 96, 138, 
 
 144, 197, 265, 313, 362 
 Algebraic symbols, 173, 183 
 Alloys, 133, 134 
 Alphabet, 17, 29 
 Amoeba, 16, 24, 218 
 Anglo-Saxon, 202 
 Animism, 351, 352 
 Ants, 301 
 
 Apperception, 17, 361 
 Arabic arithmetic, 29, 52, 170, 358 
 Architecture, 106 
 Aristotle, 251, 355, 358 
 Army, 70 
 Art, 29, 323 
 Assaying, 42 
 
 Astronomy, 17, 19, 96, 141, 212 
 Atom, 36, 96 
 Automatic, 31 
 Automobile, 15 
 Auxiliaries, 28, 124 
 Axioms, 339, 362 
 
 Bacon, 260, 275, 358 
 
 Barometer, 165 
 
 Bell, Graham, 272 
 
 Bessemer, 112 
 
 Biology, 19, 39, 45, 14s, 193, 250 
 
 Bird, 136 
 
 Blind, language for, 166 
 
 Bogey efficiency, 6 
 
 Bolometer, 117 
 
 Book, 67, 74, 136 
 
 Bookkeeping, 132 
 
 Botany, 3, 78, 91, 174 
 
 Boy, 157, 294 
 
 Brain, 145 
 
 Bricklaying, 210, 216, 321 
 
 Bridges, 21, 286 
 
 British Empire, 51 
 
 Browning, 102 
 
 Burbank, Luther, 172, 199 
 
 Business, 164, 175, 320 
 
 By-products, 154 
 
 Calculus, 90, 244 
 Cancellation, 113 
 
 Carbon compounds, 3 
 
 Card index, 76, 89, 135 
 
 Caste system, 103, 147 
 
 Catalysts, 22 
 
 Categories, 333, 348 
 
 Cause, 223, 344 
 
 Cell, 45 
 
 Change, 222 
 
 Charts, 175, 176 
 
 Chemistry, 3, 89, 144, 160 
 
 Chinese alphabet, 29, 43, 185 
 
 Christ, 46, 196, 213, 327 
 
 Christianity, 118, 357 
 
 Civilization, 103 
 
 Classification, 86 
 
 Club, 15, in, 121 
 
 Cold storage, 114 
 
 Columbus, 249, 311 
 
 Combinations of efficients, 301 
 
 Comparative method, 114 
 
 Competition, 226 
 
 Competitive efficiency, 7 
 
 Complex efficiency, 9 
 
 Compromise, 125, 261 
 
 Concrete, 105 
 
 Confucius, 353 
 
 Consciousness, 123, 346 
 
 Conservation, 194 
 
 Conservation of energy, 140 
 
 Constitutive multiplicative groups, 74 
 
 Continuity, 143 
 
 Corporation, 18 
 
 Crane, traveling, 19 
 
 Crookes, William, 249 
 
 Dante, 324, 325 
 
 Darwin, Charles, 17, 146, 275, 293, 
 
 345, 361 
 Darwin, G. H., 237 
 Death rate, 2 
 Democritus, 335, 354 
 Descartes, 359 
 Dialectic, 249 
 Dictionary, 80 
 Diesel engine, 1, 2 
 Diet, 102 
 
 Digestion, 119, 136 
 Directive, 192 
 Diversity, 130 
 Division of labor, 138 
 Domestic work, 314 
 
 36S 
 
366 
 
 INDEX 
 
 Domesticated animals, 16 
 Drum signals, 165 
 Duality, 125, 142 
 Dynamic, 210, 223 
 Dynamo, 65 
 
 Economy, 7, 23, 61, 79, 80, 90, 101, 117, 
 
 174, etc. 
 Eddies, back, 223, 239 
 Education, 99, 125, 131, 313 
 Efficacy, 8 
 Efficiency, 1, 4, etc. 
 Efficiency engineer, 197, 210 
 Efficientism, 349 
 Efficients, 67 
 Efficiental, 67 
 Efficiental essence, 173 
 Egypt, 353 
 
 Electricity, 42, 63, 138, 303 
 Electrification, 62 
 Elements of a group, 64 
 Emerson, Harrington, 1 
 Energy, 17, 62 
 English government, 304 
 English weights and measures, 276 
 Enzymes, 22 
 Equivalence, 8, 143, 154 
 Erect position, 253, 351 
 Error, 281 
 Esperanto, 186 
 Ether, 96, 115, 336 
 Ethics, 285, 327 
 Euclid, 338 
 Euler, 178 
 
 Evolution, 45, 260, 361 
 Exercise, physical, 106 
 Expenditures and results, 152 
 Externality, 11 1 
 
 Family, 60 
 Family tree, 72, 78 
 Faraday, 272, 293, 336 
 Federal group system, J2> 
 Fetichism, 351, 352 
 Food, 102 
 
 Foremen, functional, 26 
 Formulas, 78, 221 
 France, 192 
 Franklin, 62 
 Freights, 102 
 Fuegians, 17 
 
 Galvanometer, 39 
 Gang plow, 57, 139 
 Gas engine, 39 
 Generalization, 43, 140 
 Genius, 311, 3*7 
 
 Geography, 29 
 
 Geology, 125, 168, 233, 237 
 
 Geometry, 339 
 
 Geometric symbols, 173, 184 
 
 German agriculture, 278 
 
 Glass making, 118 
 
 Gold, 42 
 
 Golf, 212 
 
 Government, 82, 84, 85, 319, 320 
 
 Gravitation, 121, 130, 145 
 
 Great men, 120, 311, 317 
 
 Greek, 25, 276, 320, 353, 356 
 
 Group, 56 
 
 Gun firing, 265 
 
 Habit, 303 
 
 Harvey, 345 
 
 Hegel, 360 
 
 Hellriegel, 254 
 
 Henry, Joseph, 136 
 
 Herbart, 360 
 
 Herz, 237 
 
 Heterogeneous efficiency, 5, 160 
 
 Hindoos, 353 
 
 History, 201, 287, 350 
 
 Homogeneous efficiency, 5, 160 
 
 Hook eyelet, 53 
 
 Horse power, 36, 37 
 
 Human body, efficiency of, 303 
 
 Humus, 3 
 
 Hypothesis, working, 89, 359 
 
 Imitation, 22 
 . Induction, mathematical, 24 
 Inertia, 220, 272 
 Infinite efficiency, 8 
 Infinity, 341 
 Influence, 22 
 Initiative, 201, 204 
 Insects, 301 
 Insurance, life, 102 
 Invar, 134 
 Inverse groups, 59 
 Ion, 96, 147 
 Irrigation, 115, 196 
 
 Jackson, Stonewall, 239 
 
 James, William, 63 
 
 Japan, 23 
 
 Jehovah, 171, 185, 353 
 
 Joule, 62 
 
 Joy, 120 
 
 Jurisprudence, 98, 104 
 
 Kant, 118, 259, 287, 360 
 Keller, Helen, 183 
 Kelvin, 340 
 
INDEX 
 
 3fy 
 
 Kepler, 160 
 .Kinematic, 210, 222 
 Koch, 140 
 Krupp', 275 
 
 Labor, unskilled, 1 
 
 Language, 19, 74, 186, 351 
 
 Latitude, and longitude, 74, 78 
 
 Leibnitz, 359 
 
 Lens, 38, 254, 269, 274 
 
 Lever, 24, 38 
 
 Library, travelling, 21 
 
 Life, 345 
 
 Lignite, 8, 201 
 
 Limitation, 265 
 
 Linear multiplicative groups, 76, 88 
 
 Linneus, 90, 185 
 
 Locke, 360 
 
 Logic, 21, H2, 356 
 
 Lucifer match, 22 
 
 Machinery, 79, 82, 121 
 
 Maize, 137 
 
 Man, definitions of, 120 
 
 Marginal multiplicative groups, 74 
 
 Marginal reuse, 19 
 
 Mathematics, 82, 183 
 
 Matter, 96, 103, 243, 335 
 
 Mayer, 62 
 
 Mechanism, 343 
 
 Medievalism, 357 
 
 Mendel, 361 
 
 Mendeleveff, 237 
 
 Metal cutting, 9, 218 
 
 Metaphysics, 106 
 
 Microphone, 45 
 
 Microscope, 115 
 
 Mill, J. S., 336 
 
 Mind, 346 
 
 Money, 97, 99, 107, 130, 181 
 
 Mosquito, 29 
 
 Motion, 210, 344 
 
 Mottled efficiency, 305 
 
 Moving pictures, 24 
 
 Multiplicative groups, 70 
 
 Multipliers, 34 
 
 Multuse, 34, 175 
 
 Napoleon, 119, 195, 224, 274, 284, 289, 
 
 294, 312 
 Navigation, 121 
 Negative reuse, 21 
 Neighborhood symbolism, 90, 167 
 New England, 89, 252 
 Newspapers, 158 
 Newton, Isaac, 25, 130, 160 
 Niagara Falls, 51 
 
 Non-equivalence, 156 
 Number, 339 
 
 Oersted, 62 
 
 Oolites, 39 
 
 Opportunistic efficiency, 302 
 
 Order, 21 
 
 Orders of groups, 71 
 
 Orders of material, 95 
 
 Organization, 86 
 
 Outflank, 116 
 
 Panama Canal, 1 
 Paradox, 281, 291 
 Parallel efficiency, 9 
 Pascal, 286 
 Pasteur, 258 
 Patience, 125 
 Paul, 46 
 Peaty soils, 288 
 Pedagogy, 114, 313 
 Perkin, W. H., 249, 258 
 Persia, 353 
 Personality, 346 
 Phenomena, 349 
 Photography, 42, 138, 145 
 Physics, 126 
 Pigeon holes, 79 
 Plant breeding, 51 
 Plato, 63, 251, 340, 355, 357 
 Polar dialectic, 252 
 Positive non-equivalence, 27, 156 
 Post Office, 123 
 Potential, 223 
 Pragmatism, 362 
 Preventive medicine, 20 
 Priestly, Joseph, 176 
 Prophetic reuse, 20 
 Psychological moment, 40 
 Psychology, 16, 39, 83, 96, 166, 277, 
 309, 346 
 
 Qualitative efficiency, 6 
 Quality, 342 
 Quantity, 340 
 
 Race suicide 319 
 Radium, 65 
 Railroad, 62, 80, 225 
 Ramsay, William, 238 
 Reality, 154, 337, 355, 3^3 
 Reaper, 96 
 
 Reciprocating action, 232 
 Rectangular network, 79 
 Religion, 46, 122, 285, 329 
 Relativity, 65, 87, 106, 124, 182, 183, 
 205, etc. 
 
3 68 
 
 INDEX 
 
 Relative efficiency, 4, 6 
 Resultant efficiency, 9 
 Reuse, 15 
 Rhetoric, 102 
 Rhythm, 230 
 Roentgen (see X rays) 
 Roman Catholic Church, 73, 74 
 Rotation of crops, 240, 302 
 Rothschilds, 113, 217 
 Rural free delivery, 249 
 
 Salesmen, 18 
 
 Savage, 15, in 
 
 Schools, 58, 62 
 
 School houses, 21 
 
 Science, 27, 52, 89, 160, 317, 362 
 
 Scientific management, 210, 320 
 
 Seasons, change of, 236 
 
 Semi-linear multiplicative groups, 76 
 
 Serum, 42 
 
 Sewage, 242 
 
 Sewing machine, 132 
 
 Shakespeare 25, 28, 102 
 
 Shorthand, 185 
 
 Shrewdness, 304 
 
 Slight-of-hand, 285 
 
 Slide rule, 91, 225 
 
 Sociology, 40, 97, 159. 3i8 
 
 Socrates, 282, 354 
 
 Sophists, 354 
 
 Space, 85, 123, 170, 204, 333, 338 
 
 Spectroscope, 19 
 
 Speed, 210, 217 
 
 Spencer, Herbert, 30, 361 
 
 Spider, in 
 
 Spiritism, 352 
 
 Staff organization, 78 
 
 Starch, 137 
 
 Steamboat, 20 
 
 Steam engine, 1, 6, 9, 39, 130, 243 
 
 Steel, 283 
 
 Strandal multiplicative groups, 75 
 
 Strategic point, 40 
 
 Subject, 346 
 
 Subpersonal, 156 
 
 Substance, 337 
 
 Suez Canal, 1 
 
 Suffrage, universal, 37 
 
 Sugar beets, 6, 267 
 
 Summary, general, 301, 306 
 
 Summum bonum, 278 
 
 Surgery, 130 
 
 Surplusage, 27, 156 
 
 Surveyor, 164 
 
 Syllogism, 282, 356 
 
 Symbolism, 164 
 
 Symmetry, 135 
 
 Symphony, 178 
 Syndicate, press, 34 
 System, 86 
 
 Taboo, 351 
 
 Tandem efficiency, 9 
 
 Tape worm, 30 
 
 Taylor, F. W., 26, 225, 230, 277, 320 
 
 Teleology, 152, 344 
 
 Telegraphy, 34, 39, 136, 171, 199 
 
 Telephone, 39, 74, 80, 117 
 
 Telescope, 115 
 
 Temperate zone, 136 
 
 Thales, 354 
 
 Thoreau, 117 
 
 Tides, 230, 236 
 
 Time, 343 
 
 Titanic, loss of, 219, 271, 291 
 
 Transformations of multiplicative 
 
 groups, 89 
 Transportation, 98, 121 
 Trigonometry, 26 
 Tubular boiler, 136 
 Tropism, 193 
 Truth, 133, 153, 160 
 Tugboat, 20, 135 
 Tungsten, 5 
 Twenty Questions, game of, 72 
 
 Uniformity, 130 
 
 Unit, 34 
 
 United States, 46, 62, 196, 252, 270 
 
 Universal machine, 20 
 
 Universal suffrage, 37 
 
 Usefulness, 8 
 
 Utility, 8 
 
 Utilization, 204 
 
 Value, 155 
 Van t'Hoff, 139 
 Von Moltke, 196 
 
 Wallace, Alfred, 146, 275 
 Warning colors, 165 
 Watt, James, 130, 201 
 Wave motion, 232 
 Weather bureau, 116 
 Westinghouse, George, 21, 257 
 Wireless telegraphy, 178 
 Worth, 155 
 
 « 
 X rays, 119, 186, 252 
 
 Yellow fever, 119 
 
 Zebra, 141 
 
 Zero, 112, 164, 341 
 
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