FIRST PRINCIPLES 
 
 CHEMICAL PHILOSOPHY. 
 
 JOSIAH P.fjQOOKE, JR., 
 
 ERVING PROFESSOR OF CHEMISTRY AND MINERALOGY IN HARVARD COLLEGE. 
 
 CAMBRIDGE: 
 WELCH, BIGELOW, AND COMPANY, 
 
 PRINTERS TO THE UNIVERSITY. 
 
 1868. 
 
, 
 
 " 
 
 Entered according to Act of Congress, in the year 1868, by 
 
 JOSIAH P. COOKE, JR., 
 in the Clerk's Office of the Wstrict Court of the District of Massachusetts. 
 
 UNIVERSITY PRESS: WELCH, BIGELOW, & Co., 
 CAMBRIDGE. 
 
ERRATA. 
 
 Page 
 
 39, 
 
 line 4, for 
 
 reactions read reaction. 
 
 40, 
 
 " 15, " 
 
 [17] and [18] read [21] and [22] 
 
 50, 
 
 " 22, " 
 
 (NHi) 2 ,(Al 2 )W s - 
 
 -(S0 2 )t,24:H 2 
 
 
 
 read (NH}^\ 
 
 [-4/o)viii0 a viii(' 
 
 50, 
 
 " 3, for 
 
 nitrobenzoel read nitrobenzole. 
 
 61, 
 
 " 5, " 
 
 C 2 H 6 B " 
 
 CAO- 
 
 63, 
 
 " 24, " 
 
 Oxzchloride " 
 
 Oxychloride. 
 
 72, 
 
 " 19, " 
 
 forms " 
 
 form. 
 
 73, 
 
 " 8, " 
 
 sextivalent " 
 
 sexivalent. 
 
 78, 
 
 " 10, 
 
 atrivalent " 
 
 trivalent. 
 
 85, 
 
 " 16, " 
 
 bibasic " 
 
 dibasic. 
 
 87, 
 
 " 16, " 
 
 61 " 
 
 85. 
 
 92, 
 
 " 11, " 
 
 bibasic " 
 
 dibasic. 
 
 95, 
 
 " 6, " 
 
 calcium " 
 
 caesium. 
 
 98, 
 
 " 2, " 
 
 symbols " 
 
 symbol. 
 
 102, 
 
 " 10, " 
 
 61 
 
 85. 
 
 112, 
 
 " 4, " 
 
 11 
 
 13. 
 
 114, 
 
 " 17, " 
 
 50 
 
 53. 
 
 121, 
 
 4, " 
 
 56 " 
 
 59. 
 
 136, 
 
 " 21', " 
 
 bibasic 
 
 dibasic. 
 
 169, 
 
 " 19, " 
 
 892 " 
 
 92. 
 
 170, 
 
 " 14, " 
 
 Sp. Gr. 
 
 Sp. Gr. 
 
 170, 
 
 " 10, " 
 
 R 
 
 r. 
 
 171, 
 
 " 3, " 
 
 [89] 
 
 (89).. 
 
 173, 
 
 " 9, " 
 
 would 
 
 could. 
 
 174, 
 
 " 4, " 
 
 53 
 
 61. 
 
 190, 
 
 " 12, " 
 
 these " 
 
 those. 
 
PREFACE. 
 
 THE object of the author in this book is to present the phi- 
 losophy of chemistry in such a form that it can be made with 
 profit the subject of college recitations, and furnish the teacher 
 with the means of testing the student's faithfulness and ability. 
 With this view the subject has been developed in a logical 
 order, and the principles of the science are taught indepen- 
 dently of the experimental evidence on which they rest. It 
 is assumed that the student has already been made familiar 
 with this evidence, and with the more elementary facts which 
 the philosophy of the science attempts to interpret. At most 
 of our American colleges this instruction is given in a course 
 of experimental lectures ; but for less mature students a course 
 of manipulation in the laboratory will be found a far more effi- 
 cient mode of teaching, and some preliminary training of this 
 kind ought to be made one of the requisites for admission to 
 our higher institutions of learning. 1 
 
 This book is intended to supplement such a course of prac- 
 tical instruction. It deals solely with the theories of the 
 science, and with those principles which can only be acquired 
 by study and application. The author has found by long 
 experience that a recitation on mere facts, or descriptions of 
 apparatus and experiments, is to the great mass of college 
 undergraduates all but worthless, while the study of the phi- 
 losophy of chemistry may be made highly profitable both for 
 instruction and discipline. Moreover, our college students 
 
 1 For such a course of practical study the student can desire no better guide 
 than the excellent work of Professors Eliot and Storer, recently published, 
 " A Manual of Inorganic Chemistry, arranged to facilitate the Experimental 
 Demonstration of the Facts and Principles of the Science." By C. W. Eliot 
 and F. H. Storer. New York, 1868. 
 
 6GSG29 
 
iv PREFACE. 
 
 begin the study of physical science with a degree of maturity, 
 and a kind of mental culture, which enables them to acquire that 
 limited knowledge and general view of the subject, for which 
 alone they have time and occasion, most rapidly when it is 
 presented in a condensed and deductive form. The author has 
 had especially in view this class of students, and has endeav- 
 ored to meet their wants. 
 
 However important a training in the methods and the in- 
 ductive logic of science may be in itself considered, it would 
 be vain and unprofitable to attempt to change the habits of 
 thought of those whose education has been almost wholly 
 classical, and who are preparing themselves for a professional 
 or literary career, where they will have occasion to use the 
 results more than the methods of science. On the other hand, 
 we find at our colleges a not inconsiderable portion of the stu- 
 dents, whose tastes arid abilities find their best exercise in the 
 study of natural science, and who are preparing for the medi- 
 cal profession or other spheres of practical life, for which a 
 training of the powers of observation and of inductive reason- 
 ing is an indispensable requisite. For such students the col- 
 lege should furnish the culture they require in a course of 
 elective study ; but beginning the study of chemistry as they 
 do in the present organization of our colleges, at an advanced 
 stage of their education, they will gain time if their practical 
 work is preceded or at least accompanied by the study of 
 what may be figuratively called the grammar of the science. 
 Lastly, to that ever increasing class of students who seek their 
 mental culture solely in " scientific studies," the philosophy of 
 science is especially important ; for in an exclusive devotion to 
 facts and methods, they are not likely to gain that breadth of 
 view and enlargement of mind which the study of theory is 
 calculated to give. In all experimental science, theory is un- 
 doubtedly subordinate to practice, but it gives form and dignity 
 to our knowledge, and the two should never be divorced in our 
 systems of education. 
 
 The value of problems as means of culture and tests of at- 
 tainment can hardly be overestimated, and they have therefore 
 been made a chief feature in this book. Since those which 
 are here given are chiefly intended as guides to the student, 
 the answers have always been added ; and where the method 
 
PREFACE. V 
 
 was not obvious, the chief steps in the solution have been given 
 as well. Every teacher will be able to multiply problems after 
 these models to suit his own requirements. 
 
 The questions, which accompany the problems, form another 
 essential feature in the plan of instruction here presented. 
 They are intended not only to direct the student's attention to 
 the most important points, but also to stimulate thought by sug- 
 gesting inferences to which the principles stated legitimately 
 lead. 
 
 These questions, moreover, will indicate to the teacher the 
 manner, in which it is intended that the book should be studied. 
 Care should be taken not to overstrain the memory, but to dis- 
 tribute the necessary burthen through many lessons. Thus, for 
 the first seven chapters, the student should not be expected to 
 reproduce the symbols and reactions, nor even to call the names 
 of the substances represented, except those of the more famil- 
 iar elements and simplest compounds. It will be sufficient for 
 the time if he understands the principles which the symbols 
 illustrate, and the relations of the parts of the reactions, al- 
 though as yet these conventional signs may have for him no 
 more definite meaning than the paradigms of a grammar. As 
 he advances through chapters VIII. and IX., he should be 
 expected to familiarize himself with the names of the com- 
 pounds, and should begin to reproduce the symbols. When 
 reciting on chapter X. he should be called upon to give not 
 only the names of all the symbols, but also the symbols corre- 
 sponding to all the names, and so on for the rest of the book. 
 In reviewing the book a full knowledge of the names and sym- 
 bols will be of course expected from the first. The questions 
 and problems appended to each chapter will give the student 
 a clear idea of what in any case will be required. The author 
 has been in the habit of writing out, for his own class, similar 
 problems on separate cards, together with the names, symbols, 
 reactions or other data, which may in any case be given. 
 These cards are distributed at the beginning of each recitation, 
 and the student is not called upon to recite until he has placed 
 his work upon the blackboard. This plan obviates many prac- 
 tical difficulties, and has been found to work with great success. 
 
 The philosophy of chemistry has been developed in this 
 book according to the "modern theories"; and the author 
 
VI PREFACE. 
 
 would acknowledge his obligations to the recent works of 
 Miller Frankland, Naquet, Roscoe, Williamson, and Wurtz, 
 all of which he has freely consulted. Careful attention has 
 been given to the chemical notation ; and a method has been 
 devised of writing rational symbols, which, while it fully ex- 
 hibits the relations of the parts of the molecule, condenses the 
 formulae, and saves space and labor in printing. From a 
 desire to secure uniformity, the nomenclature of the London 
 Chemical Society has been adopted ; but, in the chapter on this 
 subject, the old names are given with the new. Lastly, the 
 metric system of weights and measures, and the centigrade 
 scale of the thermometer, are used throughout the book. 
 
 CAMBRIDGE, December 1, 1868. 
 
 
 
 *1 
 
 ^ 9 . / 
 
 V 
 
 , *^ -7 T *" 
 . 
 
 : 
 
FIRST PRINCIPLES 
 
 OF 
 
 CHEMICAL PHILOSOPHY. 
 
 PART Iv^^H* Vk 
 CHAPTER I. 
 
 INTRODUCTION. 
 
 1. Definitions. The volume of a body is the space it fills, 
 expressed in terms of an assumed unit of volume. The weight 
 of a body, as the word is used in chemistry and generally in 
 common life, is the amount of material which the body con- 
 tains compared with that in some other body assumed as the 
 unit of weight. The specific gravity of a body is the ratio of 
 its weight to that of an equal volume of some substance which 
 has been selected as the standard. Solids and liquids are al- 
 ways compared with water at its greatest density, which is at 
 4 centigrade, and hence the numbers which stand for their 
 specific gravities express how many times heavier they are 
 than an equal volume of water at this temperature. Gases, 
 however, are most conveniently compared with the lightest of 
 all known forms of matter, namely, hydrogen, and in this book 
 the number which indicates the specific gravity of a gas ex- 
 presses how many times heavier it is than an equal volume of 
 hydrogen, compared under the same conditions of temperature 
 and pressure. 
 
 2. Volume and Weight. All experimental science rests 
 upon accurate measurements of these fundamental elements, 
 and it is therefore very important that there should be a gen- 
 eral agreement among scientific men in regard to them. This 
 
 1 
 
2 INTRODUCTION. 
 
 has been secured by the almost universal adoption of the 
 French system of measures and weights in all scientific inves- 
 tigations. The details of this system are given in Table L, 
 and they require no further explanation. Its great advan- 
 tage over our ordinary English system is not only in its deci- 
 mal subdivision, but also in the simple relation which exists 
 between the units of measure and of weight. Since the unit 
 of weight is the weight of the unit volume of water, and since 
 the specific gravity of solids and liquids is always referred to 
 water, as the standard, it is always true in this system that 
 
 % r ,tty 'Vc/lttftik i$ jglron/in cubic centimetres, the weight ob- 
 tained is' in grammes ; but if the volume is given in cubic deci- 
 metres or litres, the weight is found in kilogrammes. In this 
 formula, Sp. Gr. stands for the specific gravity referred to 
 water. If the specific gravity is referred to hydrogen, as in 
 the case of gases, the value must be reduced to the water- 
 standard before using it in the formula. The reduction is 
 easily made, by multiplying by 0.0000896, a fraction which 
 is simply the specific gravity of hydrogen itself referred to 
 water. Using Sp. Gr. to represent the specific gravity of a 
 gas referred to hydrogen, the formula becomes 
 
 W= VX Sp. Gr. X 0.0000896, [2] 
 
 and may then be used in all calculations connected with the 
 weight and volume of aeriform bodies. In such calculations, in 
 order to avoid the long decimal fractions which the use of the 
 gramme entails, Hofmann has proposed to introduce into 
 chemistry a new unit of weight which he calls the crith. This 
 unit is the weight of one cubic decimetre or litre of hydrogen 
 gas at the standard temperature and pressure, and is equal to 
 0.0896 grammes. If now we estimate the weight of all gases 
 in criths, and let W represent this weight, while W represents 
 the weight in grammes, and V the volume in litres, we shall 
 also have 
 
 W = V X Sp. Gr. and W= W X 0.0896, [3] 
 
 and all problems of this kind will then be reduced to their 
 simplest terms. 
 
INTRODUCTION. 3 
 
 The specific gravity of gases is also frequently referred to 
 dry air, which for many reasons is a convenient standard. 
 The weight of one litre of air under standard conditions is 
 1.293187 grammes. Hence, representing specific gravity re- 
 ferred to air by Sp. r. we have 
 
 Sp. Gr. : Sp. r. = 1.2932 : 0.0896, 
 or 
 
 Sp. Gr. Sp.(Sr. X 14.42, 
 and 
 
 Sp. ($r. = Sp. Gr. X 0.06929. 
 
 3. Chemistry and Physics. Among material phenomena 
 we may distinguish two classes. First, those which are mani- 
 fested without a loss of identity in the substances involved. 
 Secondly, those which are attended by a change of one or 
 more of the materials employed into new substances. The 
 science of chemistry deals with the last class of phenomena, 
 that of physics with the firsthand hence the terms chemical 
 and physical phenomena. An illustration will make this dis- 
 tinction plain. When a bar of iron is drawn out into wire, is 
 rolled out into thin leaves, is reduced by mechanical means to 
 powder, is forged into various shapes, is melted and cast into 
 moulds, is magnetized, or is made the medium of an electric 
 current, since the metal does not in any case lose its identity, 
 the phenomena are all physical. When, on the other hand, 
 the iron bar rusts in the air, is burnt at the blacksmith's forge, 
 or is dissolved in dilute sulphuric acid, the iron is converted 
 into a new substance, iron rust, iron cinders, or green vitriol, 
 and the phenomena are chemical. The distinction between 
 these two departments of human knowledge is not, however, 
 so strongly marked as the definition would seem to imply. 
 In fact they coalesce at many points, and a knowledge of the 
 elements of physics is an essential preliminary to the successful 
 study of chemistry. In the following pages it will be assumed 
 that the student is acquainted with the most elementary princi- 
 ples of this science, and references will be made to the sections 
 of the author's work on Chemical Physics. The same rela- 
 tion which physics bears to chemistry on the one side, chemis- 
 try bears to physiology and the natural-history sciences on the 
 other. 
 
INTRODUCTION. 
 
 Questions and Problems. 
 
 1. Reduce by Table I. at the end of the book, 
 
 30 Inches to fractions of a metre. Ans. 0.7619 metre. 
 
 76 Centimetres to inches. Ans. 29.92 inches. 
 
 36 Kilometres to miles. Ans. 22.38 miles. 
 
 10 Metres to feet and inches. Ans. 32 ft. 9.7 inches. 
 
 Cubic metre to quarts. Ans. 880.66 quarts. 
 
 Cubic foot to litres. Ans. 28.31 litres. 
 
 Pint to cubic centimetres. Ans. 567.8 c. m. 8 
 
 Litre to cubic inches. Ans. 61.027 cubic inches. 
 
 Pound Avoirdupois to grammes. Ans. 453.6 grammes. 
 
 Kilogramme to ounces avoirdupois. Ans. 35.27 ounces. 
 
 Ounce to grammes. Ans. 28.35 grammes. 
 
 2. If the globe were a perfect sphere what would be the circum- 
 ference and what the diameter in kilometres ? 
 
 Ans. Circumference 40,000 kilometres, 
 Diameter 12,732.4 " 
 
 3. The length of the metre was determined by measuring the dis- 
 tance between Dunkirk (in France), Latitude 51 2' 9" and For- 
 mentera (one of the Balearic Islands), Latitude 38 39' 56", both 
 on the same meridian. This distance was found by triangulation to 
 be equal to 730,430 toises. What is the length of a metre in terms 
 of this old French unit of measure ? What, also, was the length 
 measured in English miles ? No account is to be taken of the ellip- 
 ticity of the earth. Ans. The metre, 0.5314 toise. 
 
 The length was 854 miles. 
 
 4. The Sp. Gr. of iron is 7.84. What is the weight of 10 c. m. 3 
 of the metal in grammes ? What is also the weight in kilogrammes 
 of a sphere of iron whose diameter equals one decimetre ? 
 
 Ans. 78.4 grammes and 4.105 kilogrammes. 
 
 5. What is the weight in grammes of 50 c. ui. 3 of oil of vitriol, 
 when the Sp. Gr. of the liquid is 1.8? Ans. 90 grammes. 
 
 6. The Sp. Gr. of alcohol being 0.8, what volume in litres would 
 weigh 7.2 kilogrammes? Ans. 9 litres. 
 
 7. Assuming that the earth is spherical, and its mean Sp. Gr. 5.67, 
 what would be its weight, using as the unit of weight a kilometre 
 cube of water at its greatest density ? Ans. 6,130,000,000,000. 
 
 8. Determine the Sp. Gr. of absolute alcohol from the following 
 data: weight of empty bottle 4.326; weight of same filled with 
 water 19.654 ; weight of same filled with alcohol 16.741. 
 
 Ans. 0.8095. 
 
INTRODUCTION. 5 
 
 9. Determine the Sp. Gr. of lead from : weight of empty bottle 
 4.326 ; weight of same filled with water 19.654 ; weight of lead shot 
 15.456 ; weight of bottle filled in part with the shot and the rest 
 with water 33.766. Ans. 11.5. 
 
 10. Determine the Sp. Gr. of iron from: weight of iron in air 
 3.92 ; weight under water 3.42. Ans. 7.84. 
 
 11. Determine Sp. Gr. of wood from: weight of wood in air 
 25.35; weight of copper sinker in air 11 ; weight of same under 
 water 9.77 ; weight of wood with sinker under water 5.10 grammes. 
 
 Ans. 0.8445. 
 
 12. How much volume must a hollow sphere of copper have, 
 weighing one kilogramme, which will just float in water ? What 
 must be the volume of the copper ? 
 
 Ans. One cubic decimetre and 111.8 c. in. 8 
 
 13. How much volume must a hollow cylinder of iron have, which 
 weighs 10 kilogrammes and sinks one half in water, and what must 
 be the volume of the metal ? Ans. 20 and 1.276 cubic decimetres. 
 
 14. What is the weight in grammes (under standard conditions) 
 of 128 cTm. 3 of oxygen gas (Sp. Gr. = 16) ? 
 
 Ans. 0.1834 grammes. 
 
 15. How many litres of carbonic anhydride gas (Sp. Gr. = 22) 
 would weigh (under normal conditions) 4.480 kilogrammes ? 
 
 Ans. 2274 litres. 
 
 16. Solve the last two problems by [3], and show in what respect 
 the method differs from that indicated by [2]. 
 
 17. What is the weight in criths (under standard conditions) of 
 one litre of nitrogen gas (Sp. Gr. = 14), of one litre of chlorine gas 
 (Sp. Gr. = 35.5), of one litre of marsh gas (Sp. Gr. = 8), and of 
 one litre of ammonia gas (Sp. Gr. = 8.5) ? 
 
 Ans. 14, 35.5, 8, and 8.5 criths respectively. 
 
 18. What is the weight in grammes of one litre of each of the 
 same gases under the same conditions ? 
 
 Ans. 1.254, 3.180, 0.7165, and 0.7617 respectively. 
 
 19. The weight of one litre of hydrochloric acid gas is 1.635 
 grammes ; of carbonic oxide gas 0.9703 grammes; of cyanogen gas 
 2.328 grammes, and of hydrogen gas 0.0896 grammes. What is the 
 specific gravity of each of these gases referred to air ? 
 
 Ans. 1.265, 0.9703, 0.9007, and 0.0693 respectively. 
 
 20. What is the volume (under standard conditions) of 12.54 
 grammes of nitrogen gas, when specific gravity referred to air is 
 0.9703? Ans. 10 litres. 
 
6 INTRODUCTION. 
 
 21. What is the weight of one litre of air in criths? 
 
 Ans. 14.42. 
 
 22. What would be the ascensional force of one thousand litres 
 of hydrogen, under normal conditions ? 
 
 Ans. The ascensional force is the difference between the weight 
 of the hydrogen and that of the air displaced. Hence in 
 the present example, the ascensional force would be 14,420 
 _ 1000 = 13420 criths, or 1,201 grammes. 
 
 23. What is the value of a crith in grains, English weight. 
 
 Ans. 1.382 grains. 
 
CHAPTER II. 
 
 FUNDAMENTAL CHEMICAL RELATIONS. 
 
 4. Compounds and Elements. With sixty-three exceptions, 
 all known substances, by various chemical processes, may 
 be decomposed, and hence are called chemical compounds; 
 while the sixty-three substances which have as yet never 
 been resolved into simpler parts are called chemical elements. 
 There is some reason for believing that many, if not all, of 
 these elementary substances may hereafter be decomposed, and 
 hence they can only be considered chemical elements provis- 
 ionally ; but, however this may be, all known materials may still 
 be regarded as formed by the union of the particles of one or 
 more of these sixty-three substances. A list of the chemical 
 elements is given in Table II. The names of the more abun- 
 dant or otherwise more important elements are printed in Ro- 
 man letters. The others are very rare substances, and are 
 practically unimportant. Of these elementary substances more 
 than three fourths possess metallic properties, and among them 
 are all the useful metals, including the liquid metal mercury. 
 The rest present every variety of physical character. Oxygen, 
 hydrogen, and nitrogen are permanent gases. Chlorine, and 
 probably fluorine, though gases under ordinary conditions, may 
 by pressure and cold be condensed to liquids. Bromine is a 
 very volatile liquid ; and among the solids we have every gra- 
 dation between the highly volatile iodine, or the easily fusible 
 phosphorus, on the one hand, and carbon, which has never 
 even been melted, on the other. We find, also, among the ele- 
 ments every difference as regards density. Hydrogen gas is 
 the lightest, and the metal platinum the heaviest substance 
 known. Several of the elementary substances occur in a free 
 state in nature, for example, oxygen and nitrogen in the at- 
 mosphere, carbon in the coal beds, sulphur in the neighborhood 
 of active volcanoes, iron in meteoric stones, while arsenic, an- 
 
8 FUNDAMENTAL CHEMICAL RELATIONS. 
 
 timony, bismuth, copper, gold, silver, mercury, and platinum, 
 with a few other rare associates, are sometimes found in a 
 more or less pure state in metallic veins. Gold and platinum 
 are usually found in a free condition, though as a rule slightly 
 alloyed with their associated metals ; but all the other elements 
 are generally found in combination, and the greater number 
 appear in nature only in this condition. From such compounds 
 the elements may be extracted by various chemical processes, 
 which will appear as we proceed. Among these elements the 
 useful metals are the tools of civilization, carbon is our uni- 
 versal fuel, while sulphur, phosphorus, arsenic, chlorine, bro- 
 mine, and iodine have found important applications in the arts, 
 and are therefore articles of commerce ; but the greater number 
 of the elements are only to be seen in the chemist's laboratory, 
 and are solely objects of chemical investigation. The elements 
 are distributed in nature in very unequal proportions. At 
 least one half of the solid crust of the globe, eight ninths of 
 the water on its surface, and one fifth of the atmosphere which 
 surrounds it, consist of the one element, oxygen. Moreover, 
 the other elements are usually found in combination with 
 oxygen, so that oxygen may be regarded as the cement by 
 which these elementary parts of the world are held together. 
 Next in abundance is silicon, which, after oxygen, is the chief 
 constituent of the rocks, and makes up about one fourth of the 
 earth's crust. Silicon is always found combined with oxygen, 
 and more than one half of the oxygen of the globe is in com- 
 bination with this element. Hence, the compound of the two, 
 which we call silica or quartz, must make up more than one 
 half of our solid globe, at least as far as its composition is 
 known. After silicon in the order of abundance would follow 
 the elements aluminum, calcium, magnesium, potassium, so- 
 dium, iron, carbon, sulphur, hydrogen, chlorine, nitrogen, 
 which, without attempting to discriminate between them, make 
 up altogether very nearly the other fourth of the earth's mass ; 
 for the remaining fifty elements including all the useful 
 metals except iron do not constitute altogether more than 
 one one-hundredth. Of the sixty-three known elements, then, 
 thirteen alone make up at least y 9 ^ of the whole known mass 
 of the earth. 
 
 5. Analysis and Synthesis. The composition of a chemical 
 
FUNDAMENTAL CHEMICAL RELATIONS. 9 
 
 compound may be made evident in two ways. First, by break- 
 ing up the compound into its constituent parts ; secondly, by 
 reuniting these parts and reproducing the original substance. 
 The first of these methods of proof is called analysis, the sec- 
 ond, synthesis. The study of the processes by which the com- 
 position of a body may be discovered, and the relative amounts 
 of its various constituents determined, forms an important 
 branch of practical chemistry, which is known as Chemical 
 Analysis, and this is subdivided into Qualitative and Quantita- 
 tive Analysis, according to the object we have in view. Syn- 
 thesis is chiefly used to prove the results of analysis. 
 
 6. Law of Definite Proportions. Numberless analyses 
 have proved that any given chemical compound always contains 
 the same elements combined in the same proportions. Thus, 
 when we analyze water, sugar, and salt, we always obtain the 
 result given below ; and this result is invariable, saving small 
 errors of observation, from whatever source these materials 
 may be drawn. The composition is given in per cents, as is 
 usual in such cases. 
 
 Water (Dumas). Salt. Sugar (Peligot). 
 
 Hydrogen, 11.112 Sodium, 39.32 Carbon, 42.06 
 
 Oxygen, 88.888 Chlorine, 60.68 Hydrogen, 6.50 
 
 Oxygen, 51.44 
 100. 100. 100. 
 
 Chemists have not yet succeeded in making sugar by com- 
 bining its elements, but the synthesis both of water and salt is 
 easily effected, and illustrates still more, forcibly the same law. 
 Thus we may mix together hydrogen and oxygen gas in any 
 proportion, but when, by passing an electric spark through the 
 mixture, we cause the elements to combine, then the gases 
 unite in the exact proportion indicated above, and any excess 
 of one or the other which may be present is left over. The 
 law of definite proportions gives to chemistry a mathematical 
 basis ; for, since the analyses of all compounds have been made 
 and tabulated in a way that will be soon explained, it is always 
 possible, when the weight of a compound is given, to calculate 
 the weights of its constituents, and, when the weight of one of 
 its elements is known, to calculate the weights of all the other 
 elements present. 
 
10 FUNDAMENTAL CHEMICAL RELATIONS. 
 
 7. Mixture and Chemical Compound. The law of definite 
 proportions gives a simple criterion for distinguishing between 
 a mixture and a true chemical compound. In the first the ele- 
 ments may be mixed in any proportion, but in the true com- 
 pound they are always combined in definite proportions. Thus 
 we may mix together copper-filings and sulphur in any propor- 
 tion, but as soon as we apply heat, and cause the elements to 
 combine, then the copper combines with one half of its own 
 weight of sulphur, and the excess of either element above 
 these proportions is discarded. Again, in a mixture however 
 homogeneous, we can generally, by mechanical means alone, 
 distinguish the ingredients. Thus, in the mixture just referred 
 to, a microscope would show the grains of sulphur and metallic 
 copper, with all their characteristic appearances ; and by means 
 of carbonic sulphide we can easily dissolve out all the sulphur 
 from the mixture ; but .after the chemical union has taken 
 place, the characteristic properties of the elements are merged 
 in those of the compound, and no such simple mechanical sep- 
 aration is possible. But although these distinctions are gener- 
 ally sufficient, nevertheless we find in some alloys, in solutions, 
 and in a few other classes of compounds, less intimate condi- 
 tions of chemical union where these criterions fail. 
 
 8. Law of Multiple Proportions. It is generally the case 
 that the same elements unite in more than one proportion, form- 
 ing two or more different compounds. Now we always find 
 that the proportions of the elements in such compounds are 
 simple multiples of each other. This law is best illustrated 
 by the compounds of nitrogen and oxygen, which are five in 
 number, and have the names indicated in the table below. In 
 order to make evident the law, we give, not the percentage 
 composition as above, but the amount of oxygen, which is in 
 each case combined with one and three fourths parts of nitro- 
 gen. 
 
 COMPOUNDS OF NITEOGEN WITH OXYGEN. 
 
 Nitrogen. Oxygen. 
 By weight. By weight. 
 
 Nitrogen. 
 By volume. 
 
 Oxygen. 
 By volume. 
 
 Nitrous Oxide, 
 
 1.75 
 
 1 
 
 2 
 
 1 
 
 Nitric Oxide, 
 
 1.75 
 
 2 
 
 2 
 
 2 
 
 Nitrous Anhydride, 
 
 1.75 . 
 
 3 
 
 2 
 
 3 
 
 Nitric Peroxide, 
 
 1.75 
 
 4 
 
 2 
 
 4 
 
 Nitric Anhydride, 
 
 1.75 
 
 5 
 
 2 
 
 5 
 
CHAPTER III. 
 
 MOLECULES. 
 
 9. Molecules. In order to bring the facts of chemistry into 
 relation with each other, and unite them in an harmonious sys- 
 tern, the following theory, first proposed by the English chemist, 
 Dalton, and known as the Atomic Theory, is generally accepted 
 by cliemists. This theory assumes, in the first place, that every 
 body, whatever its substance may be, is formed by the aggre- 
 gation of minute particles of the same kind, which cannot be 
 further subdivided without destroying the identity of the sub- 
 stance. Thus a lump of sugar is an aggregate of minute 
 particles of sugar. If the sugar is burnt, these particles will 
 be further subdivided ; but the sugar will be thus changed into 
 new substances. In like manner, a drop of water is an aggre- 
 gate of minute particles of water. By passing a current of 
 electricity through the drop, these particles will be subdivided, 
 but then we shall have no longer water, but the two elemen- 
 tary gases, oxygen and hydrogen. The smallest particles of 
 any substance which can exist by themselves, we call molecules. 
 
 10. Physical Properties of Matter. The physical qualities 
 of a body depend solely on the relations of its molecules. The 
 physicist has therefore no occasion to continue the subdivision 
 beyond the molecule, which is his unit. 
 
 Solid. In a solid the molecules firmly cohere, and the 
 force which binds them together has been called cohesion. On 
 the form and size of the molecules, and also on the mode of 
 aggregation, is supposed to depend the crystalline form of each 
 substance, which is one of the most important and character- 
 istic properties of matter, and one to which we shall have 
 occasion hereafter to refer. On certain relations of the mole- 
 cules, which we do not fully understand, depend undoubtedly 
 elasticity, tenacity, ductility or malleability, hardness, transpar- 
 ency, diathermancy, and the allied qualities of solid bodies. 
 
12 MOLECULES. 
 
 Liquid. In the liquid condition of matter the molecules 
 have more freedom of motion than in the solid, but still the 
 motion is circumscribed within the liquid mass. Moreover, a 
 certain cohesion still exists between the molecules, and on this 
 depends the form of the rain-drop. The various phenomena 
 of capillary action also are effects of the cohesion of the liquid 
 molecules modified by their adhesion to the surfaces of solids, 
 and the solvent power of liquids is a still further effect of the 
 same mutual action. Connected also with this freedom of 
 molecular motion is the property of liquids of transmitting 
 pressure in all directions, and the well-known principles of 
 hydrostatics to which it leads; but this property belongs to 
 the third condition of matter as well. 
 
 Gas. In the aeriform condition of matter, the motion of 
 the molecules is only circumscribed by the walls of the con- 
 taining vessel, or by some force acting on the mass from with- 
 out. The molecules of a gas are constantly beating against 
 the walls which confine them, and were they not thus restrained 
 would fly off into space. The molecules of the atmosphere 
 are restrained by the force of gravitation, and, as they fly up- 
 wards like a ball thrown into the air, they are at last brought 
 to rest, and fall back again to the earth. Hence gases always 
 exert pressure against any surface with which they are in con- 
 tact, and we measure the pressure, or, as we frequently call it, 
 the tension of the gas, by the height to which it will raise a 
 column of mercury. Chera. Phys. (158). The instrument 
 used for this purpose is called a barometer. 
 
 The height of the mercury column which represents the 
 pressure or tension of a gas is always represented by H. 
 
 In our latitude, at the surface of the sea, the atmosphere in 
 its normal conditions will raise a column of mercury 76 c. m. 
 high. Hence H = 76, and to this standard we always refer in 
 comparing together the volumes of different gases. 
 
 1 1 . Mariotte's Law. The most characteristic feature of 
 the aeriform condition is the great change of volume which 
 gases undergo, under varying pressure, and the special law 
 of compressibility which they obey. If we represent by H 
 and H 1 two conditions of pressure to which the same body of 
 gas is at different times exposed, then the law is expressed by 
 the formula 
 
 V: V' H':H. [4] 
 
MOLECULES. 13 
 
 Moreover, since the specific gravity of a given mass of gas 
 must be the greater the less its volume, it is also true that 
 
 Sp. Gr. : Sp. Gr>. = H: H>, [5] 
 
 and lastly, since the weight of a given volume of gas is obvi- 
 ously proportional to its specific gravity, we also have 
 
 W : W = H : H', [6] 
 
 in which W and W represent the weight of an equal volume 
 of the same gas under the two pressures H and H 1 . 
 
 12. Heat a Manifestation of Molecular Motion. The 
 effects of what we call heat are supposed to be merely mani- 
 festations of the motion of the molecules of bodies. The 
 greater the moving power of the molecule, the more forcibly it 
 strikes against our nerves of feeling, and hence the more in- 
 tense is the sensation of heat produced ; and to the condition 
 of matter which produces this sensation we give the name of 
 temperature. The greater the moving power of the molecules, 
 the higher the temperature ; the less the moving power, the 
 lower the temperature. Moreover, since by the very defini- 
 tion all molecules at the same temperature are in the condition 
 to produce the same sensation of heat, we must assume further, 
 that, whatever their size or weight, they must all have, at the 
 same temperature, the same moving power. The light mole- 
 cule of hydrogen must move much faster than the heavy mole- 
 cule of carbonic anhydride in order to produce the same effect. 
 If now we represent the mass of any molecule by m, and by V 
 its velocity at any given temperature, then the moving power 
 will be represented by m F 2 , Chem. Phys. (42), and this will 
 have the same value for every molecule at the same tempera- 
 ture. With a few exceptions, all bodies expand with an in- 
 creasing temperature, and in the case of mercury the change 
 of volume is so nearly proportional to the change of tempera- 
 ture that we may use the varying volume of a confined mass 
 of this liquid as a measure of temperature. This is the sim- 
 ple theory of the common mercurial thermometer, and in this 
 book we shall refer all temperatures to the degrees of the cen- 
 tigrade scale. These degrees are purely arbitrary; but to 
 each one corresponds a definite value of %m F 2 , although we 
 have not as yet been able to connect our arbitrary with our 
 theoretical measure. 
 
14 MOLECULES. 
 
 When we increase the temperature of a body, we must of 
 course increase the moving power of all the molecules, each by 
 the same amount, and the sum of the moving powers which 
 they thus acquire is the legitimate measure of the amount of 
 heat which the body receives. Hence, while ^m V* represents 
 the temperature of a body, 2 m V 2 represents the whole 
 amount of heat which it contains. Practically, however, we 
 measure quantity of heat by an arbitrary standard, and we 
 shall use in this book as our unit the amount of heat required 
 to raise the temperature of a kilogramme of pure water from 
 to 1 centigrade. This we call the Unit of Heat, and it 
 has been found, by careful experiments, that this unit of heat 
 represents an amount of moving power which is adequate to 
 raise a weight of 423 kilogrammes ooe metre, or to do any 
 other equivalent amount of work. 
 
 13. Expansion by Heat. The 'amount of expansion which 
 bodies undergo when heated has been carefully measured for 
 many different substances, and the results are tabulated in all 
 works on physics. Chem. Phys. Table XV. In each case is 
 given the coefficient of expansion, which is the small fraction 
 of its volume which a body increases when heated one centi- 
 grade degree. If, now, K represents this fraction, V the initial 
 volume, V the new volume, t the initial temperature, and t? 
 the new temperature, then, if we assume that the expansion is 
 proportional to the temperature, we easily deduce the formula, 
 Chem. Phys. (239), 
 
 F'=F(1 + JT ('-<)> [7] 
 
 This formula serves to calculate the change of volume both 
 of solids and gases, which expand, nearly at least, proportion- 
 ally to the temperature. The same, however, is not true of 
 liquids, whose rate of expansion frequently increases, with the 
 temperature, very rapidly ; and for such bodies we are obliged 
 to use the following formula, which is of the general form in 
 which every algebraic function may be developed, and is much 
 less simple : 
 
 V = V (1 + A t + BP -f Cfi + $c.). [8] 
 
 In this formula, V represents the required volume at some 
 temperature, t, and V 9 the volume at 0, which is assumed to 
 be known ; while A, B, C, &c., are numerical constants, which 
 
MOLECULES. 15 
 
 have been determined by experiment in the case of most liquids. 
 Chem. Phys. (255). 
 
 Both solids and liquids expand with irresistible force, and 
 we have, therefore, only this one effect to consider in regard to 
 the action of heat upon them. It is different, however, with 
 gases. By enclosing a gas in a tight vessel, we can raise its 
 temperature without changing its volume, except so far as the 
 vessel itself becomes enlarged by the heat. The effect of the 
 heat is, then, to increase the tension or pressure of the gas. 
 Hence, in the case of a gas, we may have two distinct effects ; 
 first, an increase of volume, when the pressure is constant; 
 secondly, an increase of .tension, when the volume is constant. 
 The increased volume may always be calculated from the in- 
 itial volume and difference of temperature, by means of the 
 formula, 
 
 V = V (1 + 0.00366 (tf 0), [9] 
 
 which differs from that just given only in that the numerical 
 value has been substituted for K, this being the same for all 
 gases. On the other hand, the increased tension may always 
 be calculated from the initial tension, by means of the corre- 
 sponding formula, 
 
 H 1 = H(l + 0.00366 (tf *)), [10] 
 
 in which .^Tand H 1 stand for the heights of the mercury col- 
 umns which measure the initial and final tension respectively. 
 The last formula is easily deduced from the first, on the prin- 
 ciples of Mariotte's law, stated above. Chem. Phys. (261) 
 and [201]. 
 
 Variations of temperature produce such important changes 
 in the volume and specific gravity of all bodies, and especially 
 of gases, that it becomes frequently essential, before compar- 
 ing together different observations, to reduce them all to some 
 standard temperature. Most scientific men use, as this stand- 
 ard temperature, centigrade, and scientific measures are 
 generally adjusted to this standard ; but 60 Fahrenheit, corre- 
 sponding to 15.5 centigrade, is often a more convenient stand- 
 ard, because it is nearer the mean temperature of the air, and 
 is, therefore, not unfrequently employed. 
 
 14. Change of State. Many substances are capable of ex- 
 
16 MOLECULES. 
 
 isting in all the three conditions of matter. Now, we find that 
 whenever a solid changes to a liquid, or a liquid to a gas, heat 
 is absorbed ; and conversely, whenever a gas is liquefied, or a 
 liquid becomes a solid, heat is evolved ; although, as a general 
 rule, this change of state is accompanied by no change of tem- 
 perature. Thus, one kilogramme of ice, in melting, absorbs 
 79 units of heat, although the temperature remains at dur- 
 ing the change ; and when, by boiling, a kilogramme of water 
 is converted into steam, under the normal pressure of the air, 
 no less than 537 units of heat disappear, although the tem- 
 perature both of the steam and of the water is constant at 100 
 during the whole period. On the other hand, when the steam 
 is condensed or the water frozen, absolutely the same amount 
 of heat is set free as was before absorbed. The heat thus ab- 
 sorbed or set free is generally called the latent heat of the liquid 
 or gas, and in the case of many substances the amount has 
 been carefully measured. Chem. Phys. (277) and (299). Ac- 
 cording to the theory we are studying, these effects are the 
 direct results of the molecular condition of matter. The change 
 of state must be accompanied by a change in the relative position 
 of the molecules, or in their distance from each other ; and this 
 change, in its turn, must be attended with a destruction or pro- 
 duction of the moving power on which the effects of heat de- 
 pend. Chem. Phys. (215 bis.). 
 
 15. Sources of Heat. The sun is the original source of 
 almost all the heat we enjoy on the earth, for the effect of the 
 earth's internal heat, at its surface, is at best very small, 
 and all our artificial sources of heat have drawn their supply 
 either directly or indirectly* from the great central luminary. 
 According to our theory the effect of the sun's rays is a simple 
 result of the transfer of molecular motion from the sun to 
 the earth, either by some unknown influence exerted from a 
 distance, or else by an actual transfer of motion through the 
 material particles of the ether, which is assumed to fill the in- 
 tervening space. The great source of all artificial heat is com- 
 bustion in its many forms, and this, as we shall hereafter see, is 
 merely a clashing together of material molecules, and is neces- 
 sarily attended with a great development of that moving power 
 to which we refer all thermal effects. 2\\ 
 
 1 6. Specific Heat. The amount of heat required to raise 
 
MOLECULES. 17 
 
 to the same extent the temperature of equal weights of differ- 
 ent substances is by no means the same. The quantity is capa- 
 ble in any case of exact measurement, and is called the specific 
 heat of the substance. The amount of heat required to raise the 
 temperature of one kilogramme of water one centigrade degree 
 has been assumed as the unit, and we express the specific heat 
 of other substances in. terms of this measure. Moreover, since 
 with the exception of hydrogen the specific heat of water 
 is greater than that of any substance known, the specific heat 
 of all other bodies must be expressed by fractional numbers. 
 In every case, unless otherwise stated, the numbers indicate 
 what fraction of a unit of heat would be required to raise the 
 temperature of one kilogramme of the substance from to 1 
 centigrade. Chem. Phys. (232). 
 
 17. Molecular Condition of Gases. The aeriform state 
 is by far the simplest condition of matter, and there are two 
 peculiarities in its properties which lead to important conclu- 
 sions in regard to its molecular conditions. These character- 
 istics are as follows : First, All true gases obey the same law" , . J 
 of compressibility. Secondly, Equal volumes of all true gases 
 expand equally on the same increase of temperature. Chem. 
 Phys. (262). Now according to our theory these peculiar 
 relations of the aeriform condition of matter can only be ex- 
 plained on the assumption that Equal volumes of all gases con- 
 tain the same number of molecules. It can easily be seen that 
 the properties just enumerated would be a necessary conse- 
 quence of this fact, and this important theoretical deduction 
 lies at the basis of our modern theories of Chemistry. This 
 peculiar molecular condition, however, is only found in the gas, 
 for it is only in this state that the molecules are sufficiently 
 separated from each other to be freed from the mutual action 
 of those molecular forces which give rise to far more com- 
 plicated relations in both liquid and solid bodies. Moreover, 
 with our ordinary gases (in the degree of condensation in 
 which they exist under the pressure of the atmosphere), the 
 molecules are not yet sufficiently far apart to be wholly freed 
 from the effects of their mutual action, and hence the theo- 
 retical condition is not absolutely fulfilled ; and in vapors, 
 where the molecules are still closer together, the variation 
 from the theory is quite large. In proportion as the gas ex- 
 2 ; 
 
18 MOLECULES. 
 
 pands, the theoretical condition is approached, and, when in a 
 state of great expansion, equal volumes of all gases would 
 undoubtedly contain exactly the same number of molecules. It 
 is only then that we reach the condition of what we have called 
 above the true gas, and this is our criterion of its state, that 
 it obeys absolutely the law of Mariotte. A very important 
 corollary follows at once from the principle we have just de- 
 duced. 
 
 The molecular weight of all substances is directly propor- 
 tioned to their specific gravities in the state of gas. 
 
 We have adopted in this book hydrogen gas as our unit of 
 specific gravity for aeriform substances, and were we also to take 
 the molecule of hydrogen as our unit of molecular weight, then 
 the number which expresses the specific gravity of a gas would 
 express also its molecular weight. But for reasons which will 
 appear hereafter, we have selected the half hydrogen molecule 
 as our unit, and hence the molecular weight of any substance 
 in terms of this unit is always twice its specific gravity in the 
 state of gas. In Table III. we have given, according to the 
 most accurate experimental data, the Sp. Gr. (referred to 
 hydrogen) of all the best known gases and vapors, and in a 
 parallel column we have also given the Half-molecular Weights 
 of the same substances determined by chemical analysis, in a 
 manner which will be hereafter described. It will be seen 
 that the numbers in the second column are almost precisely 
 the same as those in the first, and the slight differences 
 which will be noticed, either arise from the fact that the 
 vapors, under the conditions in which alone their Sp. Gr. 
 can be accurately determined, are not true gases, that is, do 
 not exactly obey Mariotte's law ; or in other cases, where 
 the differences are more considerable, may be referred to a 
 partial decomposition of the substance itself in the process of 
 the experiment. In solving the problems of this book, and 
 generally in most chemical problems, the Half-molecular weight 
 may be taken as the true Sp. Gr. The logarithms of these 
 values given in the last column of the table will be found useful 
 in this connection. Although only given to four places of 
 decimals, they exceed in accuracy the experimental data. The 
 values in the column of Sp. ()C. referred to air, are given, as 
 a rule, to one decimal place beyond the limit of error. 
 
, ' 
 MOLECULES. 19 
 
 Questions and ProNe 
 
 1. Are the qualities of a molecule of any substance, the same as 
 those which distinguish the substance itself? 
 
 2. What is the distinction between cohesion and adhesion ? 
 
 3. When the barometer stands at 76 c. m., with what weight in 
 grammes is the air pressing against each square centimetre of sur- 
 face? Sp. Gr. of mercury 13.596. Ans. 1033. 
 
 4. To what difference of pressure does a difference of one centi- 
 metre in the barometric column correspond ? 
 
 Ans. 13.596 grammes. 
 
 5. When a mercury barometer stands at 76 c. m. how high would 
 a water barometer stand ? Also, how high would barometers stand 
 filled with alcohol or sulphuric acid, disregarding in each case the 
 tension of the vapor? Sp. Gr. of alcohol 0.81 ; Sp. Gr. of sulphuric 
 acid 1.85. Ans. 1033; 1275 and 558.2 c. m. 
 
 6. A volume of hydrogen gas was found to be 200 c. m. 3 The 
 height of the barometer observed at the same time, was 74 c. m. 
 What would have been the volume if observed when the barometer 
 stood at 76 c. m. Ans. 194.7 cTm: 3 
 
 7. A volume of nitrogen standing in a bell-glass over a mercury 
 pneumatic trough measured 250 c. m. 8 The barometer at the time 
 stood at 75.4 c. m., and the level of the mercury in the bell was 
 found by measurement to be 6.5 above the surface of the mercury 
 in the trough. Required to reduce the volume to standard pressure. 
 
 Ans. The pressure of the air on the surface of the mercury in the 
 trough (measured at 75.4 c. m.) was balanced first by the 
 column of mercury in the bell, and secondly by the tension 
 of the confined gas. Hence the pressure to which the gas 
 was exposed was equal to 75.4 6.5 = 68.9 c. m. and we 
 have 76 : 68.9 = 250 : x = 226.7 cTm. B 
 
 8. What would be the answer to the same problem, had the 
 trough been filled with water ? 
 
 Ans. The water column in the bell exerts a pressure which is as 
 much less than the pressure of the mercury column in the 
 previous problem, as the Sp. Gr. of water is less than the 
 Sp. Gr. of mercury. Hence we have 13.6 : 1 = 6.5 : 0.48, 
 also 75.4 0.48 = 74.92, and 76 : 74.92 = 250 : x = 246.4 
 cTmT 3 
 
 9. A closed vessel, which displaces one litre of air, is poised on a 
 balance with weights, whose volume is inconsiderable when com- 
 pared with that of the vessel. The balance is in equilibrium when 
 
20 MOLECULES. 
 
 the barometer stands at 76 c. m. If the barometer falls to 73 c. m. 
 how much weight must be added to restore the equilibrium ? 
 
 Ans. 85 milligrammes. 
 
 10. Given the weight of one litre of dry air under the normal 
 conditions as 14.42 criths, what will be the weight of one litre of 
 dry air at the normal temperature, but under a pressure of 72 c. m. ? 
 
 - \, 1 ^ Ans. 13.67 criths. 
 
 11. A volume of gas measures 500 c. m. 3 at 15 what will be its 
 volume at 288. 2 ? In this and the next three problems the pressure 
 4S assumed to-be, constant. Ans. 1000 cTUT: 3 
 
 " 
 
 ^ b G* ' C" 
 
 12*. To' what temperature must an open vessel be heated before 
 one quarter of the air which it contains at is driven out ? 
 
 Ans. 9P.07. -' 
 
 13. An open vessel is heated to 8 19. 6. What portion of the air 
 which the vessel contained at remains in it at this temperature ? 
 
 f 4 (n J t tjjj? ~ y] Ans - \- 
 
 14. A closed glass vessel, which at 13 was filled with air having 
 a tension of 76 c. m. is heated to 559.4. Determine the tension of 
 the heated air. c Ans. 3 atmospheres. 
 
 15. Reduce the following volumes of gas measured at the tem- 
 peratures and pressure annexed to and 76 c. m. 
 YvVvjio> 
 
 1. 210 cTm. 3 H=57c. m. t = 136.6 Ans. 70 c^f. 3 
 
 2. 320 c7W. s H=95c.m. i= 91.l Ans. 192 UTm. 8 
 
 3. 480 cTni; 3 H= 38 c. m. t= 68.3 Ans. 96 cTm. 8 
 
 16. What is the weight of dry air contained in a glass globe of 
 640 c. m. 3 capacity at the temperature 546.4 and under a pressure 
 of 71.25 c. m. Ans. 0.2583 grammes. 
 
 General Solution. In order to make the solution general we 
 will represent the capacity of the globe, the temperature and the 
 height of the barometer by V, t and H respectively. We can also 
 easily find from Table III. that one cubic centimetre of dry air at 
 0, and when the barometer sfands at 76 c. m., weighs 14.42 criths 
 or 0.001292 grammes. To find what one cubic centimetre would 
 weigh when the barometer stands at H centimetres, we make use 
 of proportion [6], whence we derive 
 
 w 0.001292 . 
 
 7o 
 
 the weight of one cubic centimetre at and under a pressure of 
 H centimetres. To find what one cubic centimetre would weigh 
 
MOLECULES. 21 
 
 under the same pressure but at t , it must be remembered that one 
 cubic centimetre at becomes (1 -f- t 0.00366) cubic centimetres 
 at t [7] ; therefore at t and at H centimetres of the barometer 
 
 (1 -[- t 0.00366) cTm: 3 weigh 0.00129 . ^ grammes. By equating 
 these two terms we obtain 
 
 (1 + * 0.00366) =0.00129 . 5, 
 whence 
 
 1 = - M129 - 
 
 the weight of one cubic centimetre at t and under a pressure of 
 H centimetres. The weight of V cubic centimetres (w) is evidently 
 
 , = 0.00129 V. 1 + ^. 00366 . g. [10 a] 
 
 Thus far in this solution we have neglected the change in capacity 
 of the glass globe due to the change of temperature. This causes 
 no sensible error when the change of temperature is small, but 
 when the change of temperature is quite large the change of ca- 
 pacity of the globe must be considered. If the capacity is V c. m. 8 
 at it becomes at t V (1 -f t 0.00003). (See Chem. Phys. 
 241 - 244.) Introducing this value for V into the above equa- 
 tions we obtain 
 
 W = 0.00129 V (1 + t 0.00003) . l + t l Mm . . [10 6] 
 
 1 7. Required a general method for determining the gm. (g>. of - 
 a vapor. 
 
 Solution. The specific gravity of a vapor has been defined as its 
 weight compared with the weight of the same volume of hydrogen 
 gas under the same conditions of temperature and pressure, but 
 .practically it is most convenient to determine the m. (S>r. with 
 reference to air, and subsequently to reduce the result to the 
 hydrogen standard. 
 
 To find, then, the m. (J$r. of a vapor, we must ascertain the 
 weight of a known volume, V, at a known temperature, t , and under 
 a known pressure, H, and divide this by the weight of the same 
 volume of air at the same temperature, and under the same pressure. 
 The method may best be explained by an example. Suppose, 
 then, that we wish to ascertain the gp. (Jtfa. of alcohol vapor. 
 We take a light glass globe having a capacity of from 400 to 500 
 cmr. 3 , and draw the neck out in the flame of a blast lamp, so as to 
 leave only a fine opening, as shown in the figure at a. The first 
 
MOLECULES. 
 
 step is now to ascertain the weight of the glass globe when com- 
 pletely exhausted of air. As this cannot readily be done directly, 
 
 we weigh the globe full of air, and 
 then subtract the weight of the air, 
 ascertained by calculation from the 
 capacity of the globe, and from the 
 temperature and pressure of the 
 air, by means of equation (10 a). 
 Call the weight of the globe and air 
 W, and the weight of the air w, then 
 W w is the weight of the globe 
 exhausted of air. The second step 
 is to ascertain the weight of the 
 globe filled with alcohol vapor at 
 a known temperature, and under a 
 known pressure. For this purpose 
 we introduce into the globe a few 
 
 grammes of pure alcohol, and mount it on the support represented 
 in the accompanying figure. By loosening the screw, r, we next 
 sink the balloon beneath the oil contained in the iron vessel, V, and 
 secure it in this position. We now slowly raise the temperature of 
 the oil to between 300 and 400, which we observe by means of the 
 thermometer, T. The alcohol changes to vapor, and drives out the 
 air, which, with the excess of vapor, escapes at a. When the bath 
 has attained the requisite temperature, we close the opening a, by 
 suddenly melting the end of the tube at a with a mouth blowpipe, 
 and as nearly as possible at the same moment observe the tempera- 
 ture of the bath and the height of the barometer. We have now 
 the globe filled with alcohol vapor at a known temperature, and 
 under a known pressure. Since it is hermetically sealed, its weight 
 cannot change, and we can therefore allow it to cool, clean it, and 
 weigh it at our leisure. This will give us the weight of the globe 
 filled with alcohol vapor at a known temperature, Z', and under a 
 known pressure, H'. Call this weight W'. The weight of the 
 vapor is W' W -}- w. The third step is to ascertain the weight 
 of the same volume of air at the same temperature and under the 
 same pressure. This can easily be found by calculation from equa- 
 tion (10 I). The last step is to find the capacity of the globe, which, 
 although we have supposed it known, is not actually ascertained 
 experimentally until the end of the process. For this purpose we 
 break off the tip of the tube (a), under mercury, which, if the ex- 
 periment has been carefully conducted, rushes in and fills the globe 
 completely. We then empty this mercury into a carefully gradu- 
 ated glass cylinder, and read off the volume. We find then the 
 
MOLECULES. 23 
 
 gm. (g> ^ by dividing the weight of the vapor by the weight of the 
 air. The formulae for the calculation are then 
 
 Weight of the globe and air, W. 
 
 air, " = 0- 001292Y - 1+ , 0.00366- I" 
 
 globe exhausted of air, W w. 
 
 " filled with vapor at a temperature t' and 
 
 under a pressure H', W. 
 
 vapor, W W + w. 
 
 air at t' and under a pressure H', = 
 
 0.001292 V (1 + t 0.00003) . l + ^^ . *'. 
 
 W'-W + w 
 
 g c = 
 
 0.001292 V (1 + t' 0.00003) . 
 
 1. Ascertain the m. (Jfo. of alcohol vapor from the following 
 data: 
 
 Weight of glass globe, W 50.804 grammes. 
 
 Height of barometer, H 74.75 centimetres. 
 
 Temperature, t 18 
 
 Weight of globe .and vapor, W 50.824 grammes. 
 
 Height of barometer, H' 74.76 centimetres. 
 
 Temperature, t 167 
 
 Volume, V 351.5 cubic centimetres. 
 
 Ans. 1.575. 
 
 2. Ascertain the Pjp. (gfr. of camphor vapor from the following 
 data : 
 
 Weight of glass globe, W 50.134 grammes. 
 
 Height of barometer, H 74.2 centimetres. 
 
 Temperature, t 13.5 
 
 Weight of globe and vapor, W 50.842 grammes. 
 
 Height of barometer, H' 74.2 centimetres. 
 
 Temperature, t' 244 
 
 Volume, V 295 cubic centimetres. 
 
 Ans. 5.371. 
 
CHAPTER IV. 
 
 -.MWS- 
 
 ATOMS. 
 
 18. Definition. The atomic theory assumes that so long 
 as the identity of a substance is preserved its molecules remain 
 undivided ; but when, by some chemical change, its identity is 
 lost, and new substances are formed, the theory supposes that the 
 molecules themselves are broken up into still smaller particles, 
 which it calls atoms. Indeed it regards this division of the 
 molecules as the very essence of a chemical change. 
 
 The word atom is derived from a, privative, and re/^o> (I 
 cut), and recalls a famous controversy in regard to the infinite 
 divisibility of matter, which for many centuries divided the 
 philosophers of the world. But chemistry does not deal with 
 this metaphysical question. It asserts nothing in regard to the 
 possible divisibility of matter ; but its modern theories claim 
 that, practically, this division cannot be carried beyond a certain 
 extent, and that we then reach particles which cannot be fur- 
 ther divided by any chemical process now known. These are 
 the chemical atoms, and the atom is simply the unit of the 
 chemist, just as the molecule is the unit of the physicist, or the 
 stars the units of the astronomer. The molecule is a group of 
 atoms, and is a unit in the microcosm, of which it is a part, in 
 the same sense that the solar system is a unit in the great stel- 
 lar universe. The molecule has been defined as the smallest 
 particle of any substance which can exist by itself, and the 
 atom may be now defined as the smallest mass of an element 
 that exists in any molecule. 
 
 When a molecule breaks up, it is not supposed that the atoms 
 fall apart like grains of sand ; but simply that they arrange 
 themselves in new groups, and thus give rise to the formation 
 of new substances. Indeed, as a rule, the atoms cannot exist 
 in a free state, and with few exceptions every molecule consists 
 of at least two atoms. This is thought to be true, even of the 
 chemical elements. The difference between the molecules of 
 
ATOMS. 25 
 
 an elementary substance and those of a compound, according 
 to the theory, is merely this, that while the first are formed by 
 the union of atoms of the same kind, the last comprise atoms 
 of different kinds. The molecules of oxygen gas are atomic 
 aggregates as well as those of water, only the molecules of 
 oxygen consist of oxygen atoms alone, while the molecules of 
 water contain both oxygen and hydrogen atoms. Such at least 
 is the constitution of most elementary substances. Nevertheless, 
 in the case of mercury, zinc, cadmium, and some other me- 
 tallic elements, the facts compel us to believe that the molecule 
 consists of but one atom, or, in other words, that in these cases 
 the molecule and the atom are the same. 
 
 19. Atomic Weights. There must be evidently as many 
 kinds of atoms as there are elementary substances ; and, since 
 these substances always unite in definite proportions, it must 
 be also true that the elementary atoms have definite weights. 
 This once assumed, the law of multiple proportions, as well 
 as that of definite proportions, becomes an essential part of our 
 atomic theory ; for, since the atoms are by definition indivis- 
 ible, the elements can only combine atom by atom, and must 
 therefore unite either in the proportion of the atomic weights 
 or in some simple multiples of this proportion. We have dis- 
 covered no means of measuring even approximately the ab- 
 solute weight of an atom ; but, after we have determined, from 
 considerations hereafter to be discussed, what must be the num- 
 ber of atoms of each kind in one molecule of any substance, 
 we can easily calculate their relative weight from the results of 
 analysis. A few examples will make the method plain. 
 
 1. The analysis of water, given on page 6, proves that in 
 100 parts it contains 11.112 parts of hydrogen and 88.888 
 parts of oxygen. Every molecule of water, then, must contain 
 these two elements in just these proportions. Now we have 
 good reason for believing that each molecule of water is a 
 group of three atoms, two of hydrogen and one of oxygen. 
 Then, since (11.112) : 88.888 = 1:16, it follows that the 
 oxygen atom must weigh 1 6 times as much as the hydrogen 
 atom ; and, if we make the hydrogen atom the unit of our atom- 
 ic weight, then the weight of the oxygen atom, estimated in 
 these units, must be 16. 
 
 2. The analysis of hydrochloric acid gas proves that it con- 
 
26 ATOMS. 
 
 tains in 100 parts 2.74 parts of hydrogen and 97.26 of chlorine. 
 Moreover, we have reason to believe that each molecule of the 
 acid is a group of two atoms, one of hydrogen and one of 
 chlorine. Hence the atom of chlorine must weigh 35.5 times as 
 much as that of hydrogen. Its atomic weight is then 35.5. 
 
 3. The analysis of common salt, page 6, proves that it con- 
 tains in 100 parts 60.68 parts of chlorine and 39.32 parts of 
 sodium, and we believe that each molecule of salt is a group of 
 two atoms, one of chlorine and one of sodium. Then, since 
 60.68 : 39.32 = 35.5 : 23, it follows that the atomic weight 
 of sodium is 23. In like manner the atomic weights of all the 
 chemical elements have been determined, and the numbers are 
 given in Table II. These numbers are the fundamental data 
 of chemical science, and the basis of almost all the numerical 
 calculations which-the chemist has to make. The elements of 
 a compound body are always united either in the proportions, 
 by weight, expressed by these numbers, or else in some simple 
 multiples of these proportions ; and whenever, by the breaking 
 up of a complex compound, or by the mutual action of different 
 substances on each other, the elements rearrange themselves, 
 and new compounds are formed, the same numerical propor- 
 tions are always preserved. 
 
 The atomic weights evidently rest on two distinct kinds of 
 data ; first, on the results of chemical analysis, which are facts 
 of observation, and in regard to which the only question can be 
 as to their greater or less accuracy ; secondly, on our conclu- 
 sions in regard to the number of atoms in each molecule of the 
 substance analyzed. This conclusion again is based chiefly on 
 two classes of facts, whose bearing on the subject we must 
 briefly consider. 
 
 1 . In the first place we carefully compare together all the 
 compounds of the element we are studying, with the view of 
 discovering the smallest weight of it which enters into the com- 
 position of any known molecule ; for this must evidently be the 
 atomic weight of the element. An example will make the 
 course of reasoning intelligible. 
 
 In the following table we have a list of a number of the 
 most important compounds containing hydrogen, all of which 
 either are gases, or can easily be changed into vapor by heat, 
 
ATOMS. 27 
 
 so that their specific gravities in the state of gas can be readily 
 determined. From these specific gravities we learn the weights 
 of the .molecules (compare 17) which are given in the second 
 column of the table. In the third column we have given the 
 weight of hydrogen contained in the molecules, referred, of 
 course, to the same unit as the weight of the molecules 
 themselves : 
 
 Weight of Molecule 
 
 referred to Weight of Hydrogen 
 
 Compounds of Hydrogen. Hydrogen Atom. in the Molecule. 
 
 Hydrochloric Acid 36.5 1 
 
 Hydrobromic Acid 81.0 1 
 
 Hydriodic Acid 128.0 1 
 
 Hydrocyanic Acid 27.0 1 
 
 Hydrogen Gas 2*0 2 
 
 Water 18.0 2 
 
 Sulphuretted Hydrogen 34.0 2 
 
 Seleniuretted Hydrogen 81.5 2 
 
 Formic Acid 46.0 2 
 
 Ammonia 1 7.0 3 
 
 Phosphuretted Hydrogen 34.0 3 
 
 Arseniuretted Hydrogen 78.0 3 
 
 Acetic Acid 60.0 4 
 
 Olefiant Gas 28.0 4 
 
 Marsh Gas 16.0 4 
 
 Alcohol 46.0 6 
 
 Ether 74.0 10 
 
 Assuming now, as has been assumed in this table, that a 
 molecule of hydrogen gas weighs 2, it appears that the 
 smallest mass of hydrogen which the molecule of any known 
 substance contains, weighs just one half as much, or 1. We 
 infer, therefore, that this mass of hydrogen cannot be divided 
 by any chemical means, or, in other words, that it is the hydro- 
 gen atom. The molecule of hydrogen gas contains then two 
 hydrogen atoms, and this atom is the unit to which we refer all 
 molecular and atomic weights. 
 
 If now, in like manner, we bring into comparison all the 
 volatile compounds of oxygen, we shall find that the smallest 
 mass of oxygen which exists in the molecule of any known 
 substance weighs 16, the atom of hydrogen weighing 1, 
 and hence we infer that this mass of oxygen is the oxygen atom. 
 Moreover it will appear that a molecule of oxygen gas weighs 
 
28 ATOMS. 
 
 32, and hence it follows that each molecule of oxygen gas, like 
 the molecule of hydrogen, is formed by the union of two atoms. 
 A similar comparison would show that, while the molecule of 
 nitrogen gas weighs 28, the atom weighs 14, so that here again 
 the molecule consists of two atoms. This method of investiga- 
 tion can be extended to a large number of the chemical ele- 
 ments, and the conclusions to which it leads are evidently le- 
 gitimate, and cannot be set aside, until it can be shown that 
 some substance exists whose molecule contains a smaller mass 
 of any element than that hitherto assumed as the atomic weight, 
 or, in other words, until the old atom has been divided. 
 
 2. The second class of facts on which we rely for determin- 
 ing the number of atoms in a given molecule is based on the 
 specific heat of the elements (compare 16). It would appear 
 that the specific heat is the same for all atoms, and, if this is 
 true, we might expect that equal amounts of heat would raise 
 to the same extent the temperatures of such quantities of the 
 various elementary substances as contain the same number of 
 atoms, provided, of course, that these atomic aggregates are 
 compared under the same conditions. Now we can determine 
 accurately the number of units of heat required to raise the 
 temperature of equal weights of the elementary substances one 
 degree, and the results, which we call the specific heat of the 
 elements, are given in works on physics. Chem. Phys. (232). 
 Evidently, if our principle is true, these values must be pro- 
 portional in every case to the number of atoms of each element 
 contained in the equal weights compared. Representing then 
 by S and S 1 the specific heat of two elementary substances, by 
 m and m' the weights of the corresponding atoms, and by unity 
 the equal weights compared, we shall have, in any case, 
 
 S : S' = ~ : i,, or mS = m'S', [1 1] 
 
 nr in ' L -J 
 
 m m 
 
 that is, The product of the atomic weight of an elementary sub- 
 ' stance l)y its specific heat is always' a constant quantity. 
 
 Taking now the atomic weights obtained by the method first 
 given, and the specific heats of the elements as they have been 
 determined by experimenting on these substances in the solid 
 state, we find that, with only three exceptions, our inference is 
 >f^^i^ ) 4j7->;. /* . 
 
ATOMS. 29 
 
 correct ; and this principle not only frequently enables us to fix 
 the atomic weight of an element, when the first method fails, 
 but it also serves to corroborate the general accuracy of our 
 results. It is true, owing undoubtedly to many causes which 
 influence the thermal conditions of a solid body, that this prod- 
 uct is not absolutely constant. It varies between 5.7 and 6.9, 
 the mean value being about 6.34 (see Table IV). But the 
 variation is riot important, so far as the determination of the 
 atomic weights is concerned. This determination, as we have 
 seen, rests chiefly on the results of analysis. The question al- 
 ways is only between two or three possible hypotheses, and as 
 between these the specific heat will decide. For example, an 
 analysis of chloride of silver proves that each molecule contains 
 for one atom, or 35.5 parts of chlorine, 108 parts of silver. 
 Now, 108 parts of silver may represent one, two, three, or four 
 atoms, or it may be that this quantity only represents a fraction 
 of an atom. To determine, we divide 6.34 by 0.057, the specific 
 heat of silver. The result is 111, which, though not the exact 
 atomic weight, is near enough to show that 108 is the weight 
 of one atom, and not of two or three. The exceptions to this 
 rule referred to above are carbon, boron, and silicon. But the 
 specific heat of these elements varies so very greatly with 
 the differences of physical condition the so-called allotropic 
 modifications which these elements present, Chem. Phys. 
 (234), that the exceptions are not regarded as invalidat- 
 ing the general principle. The law simply fails in these cases, 
 and we can see why it fails. 
 
 This important law, whose bearing on our subject we have 
 briefly considered, was first discovered by Dulong and Petit, and 
 was subsequently verified by the very careful experiments of 
 Regnault. More recently it has been found, by Voestyn and 
 others, that its application extends, in some cases at least, to 
 chemical compounds ; for it would seem that the atoms retain, 
 even when in combination, their peculiar relations to heat, so 
 that the product of the specific heat of a substance by its molec- 
 ular weight is equal to as many times 6.3 as there are atoms in 
 the molecule. Thus the specific heat of common salt, multiplied 
 by its molecular weight, gives 0.214 X 58.5 = 12.52, which is 
 very nearly equal to 6.3 X 2 ; while in the case of corrosive 
 sublimate the corresponding product, 0.069 X 271 18.70, is 
 
30 ATOMS. 
 
 nearly equal to 6.3 X 3, results which are in accordance 
 with our views in regard to the number of atoms in the mole- 
 cules of these substances. 
 
 We have here, then, an obvious method by which we might 
 determine the number of atoms in the molecule of any solid, 
 and which would be of the very greatest value in investigating 
 the atomic weights, could we rely on the general application 
 of our law. We do not expect mathematical exactness. We 
 know very well that the specific heat of solid bodies varies 
 very greatly with the temperature, as well as from other phys- 
 ical causes, and that it is impossible to compare them under 
 precisely the same conditions, as would be required in order to 
 secure accuracy. But, unfortunately, the discrepancies are so 
 great, and we are so ignorant of their cause, that as yet we 
 have not been able to place much reliance on the specific heat 
 as a means of determining the number of atoms in the mole- 
 cules of a compound. 
 
 3. Lastly, assuming that both of the means we have consid- 
 ered fail to give satisfactory evidence in regard to the number 
 of atoms in the molecule of a given substance (which we may 
 have analyzed for the purpose of determining some atomic 
 weight), we may frequently, nevertheless, reach a satisfactory, 
 or at least a probable conclusion, by comparing the substance 
 we are investigating with some closely allied substance whose 
 constitution is known. Thus, if the molecule of sodic chlo- 
 ride (common salt) contains two atoms, it is probable that 
 the molecules of sodic iodide, as well as those of potassic 
 chloride and potassic iodide, qpntain the same number ; for 
 all these compounds not only have the same crystalline form 
 and the same chemical relations, but also they are composed 
 of closely allied chemical elements. Nevertheless it is true, in 
 very many cases, that our conclusion in regard to the number 
 of atoms which a molecule may contain is more or less hypo- 
 thetical, and hence liable to error and subject to change. This 
 uncertainty, moreover, must extend to the atomic weights of 
 the elements, so far as they rest on such hypothetical conclu- 
 sions. 
 
 If we change the hypothesis in any case, we shall obtain a 
 different atomic weight; but then the new weight will be 
 
ATOMS. 31 
 
 some simple multiple of the old, and will not alter the impor- 
 tant relations to which we first referred. These fundamental 
 relations are independent of all hypothesis, and rest on well- 
 established laws. 
 
 The atomic weights are the numerical constants of chem- 
 istry, and in determining their value it is necessary to take 
 that care which their importance demands. The essential part 
 of the investigation is the accurate analysis of some compound 
 of the element whose atomic weight is sought. The compound 
 selected for the purpose must fulfil several conditions. It must 
 be one which can be prepared in a condition of absolute purity. 
 It must be one the proportions of whose constituents can be 
 determined with the greatest accuracy by the known methods 
 of analytical chemistry. It must contain a second element 
 whose atomic weight is well established. Finally, it should be 
 a compound whose molecular condition is known, and it is best 
 that this should be as simply as possible. When they are once 
 thus accurately determined, the atomic weights become essen- 
 tial data in all quantitative analytical investigations. 
 
 am _ f 
 
 Questions and Problems. T2, ^ I \ ^7* 
 
 1. Does the integrity of a substance reside in its molecules or in f~\ t 
 its atoms ? 
 
 2. We find by analysis that in 100 parts of potassic chloride C 
 there are 52.42 parts of potassium and 47.58 parts of chlorine. l( 1 
 Moreover, we know from previous experiments that the atomic 1 O ^ 
 weight of chlorine is 35.5, and we have reason to believe that every ~ 
 molecule of the compound consists of two atoms, one of potassiuhpl i 
 
 and one of chlorine. What is the atomic weight of potassium ? /_*t 4 
 
 ^Ans. 39.1. | ? \ 
 
 3. We find by analysis that in 100 parts of phosphoric anhydride tj^j 
 there are 43.66 parts of phosphorus and 56.34 parts of oxygen. 
 Moreover, we know that the atomic weight of oxygen is 16 ; and we 
 have reason to believe that every molecule of the compound consists 
 
 of seven atoms, 2 of phosphorus and 5 of oxygen. What is the 
 atomic weight of phosphorus ? Ans. 31. 
 
 4. In Table III. the student will find the molecular weights of the 
 following oxygen compounds ; and we give below, following the 
 name, the weight of oxygen (estimated like the molecular weight 
 in hydrogen atoms) which each contains. From these data it is 
 
32 ATOMS. 
 
 required to determine the atomic weight of oxygen. Oxygen Gas, 
 32 ; Water, 16 ; Sulphurous Anhydride, 32, Sulphuric Anhydride, 
 48; Phosphoric Oxychloride, 16; Carbonic Oxide, 16; Carbonic 
 Anhydride, 32 ; Osmic Anhydride, 64 ; Nitrous Oxide, 16 ; Nitric 
 Oxide, 16 ; and Nitric Peroxide, 32. Ans. 16. 
 
 5. We give below the weight of chlorine in one molecule of 
 several of its most characteristic volatile compounds. It is required 
 to deduce the atomic weight of chlorine on the principle of the last 
 problem. Chlorine gas, 71; Phosphorous Chloride, 106.5; Phos- 
 phoric Oxychloride, 106.5; Arsenious Chloride, 106.5; Phosgene 
 Gas, 71 ; Stannic Chloride, 142 ; Stanno-triethylic Chloride, 35.5 ; 
 and Hydrochloric Acid, 35.5. Ans. 35.5. 
 
 6. Review the steps of the reasoning by which the atomic weights 
 have been deduced in the last two problems, and show that the 
 " molecular weight " and " the weight of the element in one molecule " 
 are actual and independent experimental data. 
 
 7. Analysis shows that in 100 parts of mercuric chloride there are 
 73.80 parts of mercury and 26.20 parts of chlorine. The specific 
 heat of mercury is 0.032. What is the probable atomic weight of 
 mercury, that of chlorine being 35.5 '? Also, how many atoms of 
 each element does one molecule of the compound contain ? 
 
 Ans. Atomic weight of mercury, 200. Each molecule consists 
 ( of one atom of mercury and two of chlorine. 
 
 'i Analysis shows that in 100 parts of ferric oxide there are 70 
 parts of iron and 30 parts of oxygen. The specific heat of iron is 
 0.514. What is the probable atomic weight of iron, that of oxygen 
 being 16 ? and also, how many atoms of each element does one 
 molecule of the oxide contain ? 
 
 Ans. Atomic weight of iron, 56. One molecule of ferric oxide 
 contains 2 atoms of iron and 3 of oxygen. 
 
 9. The molecular weight of silicic chloride is 1 70, and its specific 
 heat, 0.1907. How many atoms does one molecule of the compound 
 probably contain ? Ans. 5. 
 
 10. The molecular weight of mercuric iodide is 454, and its 
 specific heat, 0.042. How many atoms does one molecule of the 
 compound probably contain ? Ans. 3. 
 
CHAPTER V. 
 
 CHEMICAL NOTATION. 
 
 20. Chemical Symbols. The atomic theory has found ex- 
 pression in chemistry in a remarkable system of notation, which 
 has been of the greatest value in the study of the science. In 
 this system, the initial letter of the Latin name of an element 
 is used as the symbol of that element, and represents in every 
 case one atom. Thus stands for one atom of Oxygen, N for 
 one atom of Nitrogen, H for one atom of Hydrogen. When 
 several names have the same initial, we add for the sake of dis- 
 tinction a second letter. Thus O stands for one atom of Car- 
 bon, Gl for one atom of Chlorine, Ca for one atom of Calcium, 
 Ou for one atom of Cuprum (copper), Or for one atom of 
 Chromium, Co for one atom of Cobalt, Gd for one atom of 
 Cadmium, Gs for one atom of -Caesium, and Ge for one atom 
 of Cerium. The symbols of all the elements are given in 
 Table II. Several atoms of the same element are generally 
 indicated by adding figures, but distinguishing them from alge- 
 braic exponents by placing them below the letters. Thus Sn 2 
 stands for two atoms of Stannum (tin), S 3 for three atoms 
 of Sulphur, and I 5 for five atoms of Iodine. Sometimes, how- 
 ever, in order to indicate certain relations, we repeat the symbol 
 with or without a dash between them, thus H-H represents a 
 group of two atoms of Hydrogen, Se=Se a group of two atoms 
 of Selenium. We can now easily express the constitution of 
 the molecule of any substance by simply grouping together the 
 symbols of the atoms of which the molecule consists. This 
 group is generally called the symbol of the substance, and 
 stands in every case for one molecule. Thus Na Gl is the sym- 
 bol of common salt, and represents one molecule of salt. ff 2 
 is the symbol of water, and represents, as before, one molecule. 
 So in like manner H Z N stands for one molecule of ammonia 
 gas, JJ 4 O for one molecule of marsh gas, KNO Z for one mole- 
 cule of saltpetre, H 2 S0 4 for one molecule of sulphuric acid, 
 3 
 
34 CHEMICAL NOTATION. 
 
 C 2 H 4 2 for one molecule of acetic acid, H-H for one 
 molecule of hydrogen gas. We do not, however, always 
 write the symbols in a linear form, but group the letters in such 
 a way as will best indicate the relations we are studying. 
 When several molecules of the same substance take part in a 
 chemical change, we represent the. fact by writing a numerical 
 coefficient before the molecular symbol. A figure so plaoed 
 always multiplies the whole symbol. Thus H-NO Z stands 
 for four molecules of nitric acid, 3 C 2 H 6 for three molecules 
 of alcohol, Q0=0 for six molecules of oxygen gas. When 
 clearness requires it, we enclose the symbol of the molecule in 
 parentheses, thus, 4(H^N), or (ff 3 =N) 4 . The precise mean- 
 ing of the dashes will hereafter appear. They are used, like 
 punctuation marks, to point off the parts of a molecular sym- 
 bol, between which we wish to distinguish. 
 
 21. Chemical Reactions. These chemical symbols give at 
 once a simple means of representing all chemical changes. As 
 these changes almost invariably result from the reaction of one 
 substance on another, they are called Chemical Reactions. Such 
 reactions must necessarily take place between molecules, and 
 simply consist in the breaking up of the molecules and the rear- 
 rangement of the atoms in new groups. In every chemical re- 
 action we must distinguish between the substances which are 
 involved in the change and those which are produced by it. 
 The first will be termed the factors and the last the products of 
 the reaction. As matter is indestructible, it follows that TJie 
 sum of the weights of the products of any reaction must always 
 be equal to the sum of the weights of the factors, and, further, 
 that The number of atoms of each element in the products must 
 be the same as the number of atoms of the same kind in the 
 factors. This statement seems at first sight to be contradicted 
 by experience, since wood and many other combustibles are 
 consumed by burning. In all such cases, however, the apparent 
 annihilation of the substance arises from the fact that the prod- 
 ucts of the change are invisible gases ; and, when these are col- 
 lected, their weight is found to be equal, not only to that of the 
 substance, but also, in addition, to the weight of the oxygen from 
 the air consumed in the process. As the products and factors 
 of every chemical change must be equal, it follows that A 
 chemical reaction may always be represented in an equation 
 
CHEMICAL NOTATION. 35 
 
 by writing the symbols of the factors in the first member and 
 those of the products in the second. Thus, the following equa- 
 tion expresses the reaction of dilute sulphuric acid on zinc, by 
 which hydrogen gas is commonly prepared. The products are 
 a solution of zinc sulphate and hydrogen gas. 
 
 Xn + (H 2 S^ + Aq) = (ZnS0 4 + Aq)+m-IE. [12] 
 
 The initial letters of the Latin word Aqua are here used 
 simply to indicate that the substances enclosed with it in pa- 
 rentheses are in solution. The symbol Zll is printed in " full- 
 faced " type to indicate that the metal is used in the reac- 
 tion in. its well-known solid condition ; while the symbol of 
 the molecule of hydrogen is printed in skeleton type to indi- 
 cate the condition of gas. This usage will be followed through- 
 out the book; but, generally, when it is not important to indicate 
 the condition of the materials involved in the reaction, ordinary 
 type will be used. The molecule of hydrogen gas consists of 
 two atoms, as our reaction indicates, and this is the smallest 
 quantity of hydrogen which can either enter into or be formed 
 by a chemical change. The molecule of zinc is known to 
 consist of only one atom. When the molecular constitution 
 of an element is not known, we simply write the atomic symbol 
 in the reaction. 
 
 Among chemical reactions we may distinguish at least three 
 classes. First, Analytical Reactions, in which a complex mole- 
 cule is broken up into simpler ones. Thus, when sodic bisul- 
 phate is heated, it breaks up into sodic sulphate and sulphuric 
 anhydride, 
 
 S0 3 . [13] 
 
 So, also, by fermentation grape sugar or glucose breaks up into 
 alcohol and carbonic anhydride, 
 
 CtHu 6 = 2 C 2 ff & + 2 00 r [14] 
 
 Secondly, Synthetical Reactions, in which two molecules 
 unite to form a more complex group. Thus baryta burns 
 in an atmosphere of sulphuric anhydride, and forms baric 
 sulphate, 
 
 [15] 
 
36 CHEMICAL NOTATION. 
 
 In like manner ammonia enters into direct union with hydro- 
 chloric acid to form ammonic chloride, 
 
 HJf + HCl = HJfOl [16] 
 
 Thirdly, Metathetical Reactions, in which the atoms of one 
 molecule change place with the dissimilar atoms of another, 
 one atom of one molecule replacing one, two, three, or more 
 atoms of the other, as the case may be. Thus, when we add a 
 solution of common salt to a solution of argentic nitrate, we ob- 
 tain a white precipitate l of argentic chloride, while sodic nitrate 
 remains in solution. The result is obtained by a simple in- 
 terchange between an atom of silver and an atom of sodium, 
 as the following reaction shows : 
 
 (Na Cl+ AgNO* + Ag) = (NaNO, + Aq) + AgCl. [17] 
 
 In the next example, one atom of barium changes place with 
 two atoms of hydrogen. Baric chloride and sulphuric acid 
 yield hydrochloric acid and insoluble baric sulphate, which is 
 precipitated from the solution in water as the reaction in- 
 dicates, 
 
 (Ba C1 2 + H 2 SO, + Aq) = (ZHCl + Aq) + BaSO 4 . [18] 
 
 Of the three classes of chemical reactions the last is by far 
 the most common, and many chemical changes which were for- 
 merly supposed to be examples of simple analysis or synthesis 
 are now known to be the results of metathesis. In very many 
 cases, -however, a chemical reaction cannot be explained in 
 either of these ways alone, but seems to consist in a primary 
 union of two or more molecules and a subsequent splitting up 
 of this large group. Indeed, this is the best way of conceiving 
 of. all metatheticdl reactions, for we do not suppose that in any 
 case there is an actual transfer of atoms from one molecule to 
 the other. The word metathesis is merely used to indicate the 
 result of the process, not the manner in which the change takes 
 place, and the same is true of the words analysis and synthesis. 
 
 i The separation of a solid or sometimes of a liquid substance in a fluid 
 menstruum, as the result of a chemical reaction, is called precipitation, and 
 the material which separates, a precipitate ; and this, too, even when the ma- 
 terial, being lighter than the fluid, rises instead of falls. 
 
CHEMICAL NOTATION. 37 
 
 The common method of preparing carbonic anhydride is to 
 pour a solution of hydrochloric acid on small lumps of marble 
 (calcic carbonate), 
 
 CaO 3 + (2ff& + Ag) = (CaC0 3 ff,Cl 2 + [19] 
 Aq) (OaCl 2 + H^O + Aq) 
 
 We may suppose that the molecules of the two substances are, 
 in the first place, drawn together by the force which manifests 
 itself in the phenomena of adhesion, 1 but that, as they approach, 
 a mutual attraction between their respective atoms comes into 
 play, which, the moment the molecules come into collision, 
 causes the atoms to arrange themselves in new groups. The 
 groups which then result are determined s by many causes 
 whose action can seldom be fully traced ; but there are two 
 conditions which, when the substances are in solution, have a 
 very important influence on the result. These conditions may 
 be thus stated : 
 
 1. Whenever a compound can be formed, which is insoluble 
 in the menstruum present, this compound always separates as 
 a precipitate. 
 
 2. Whenever a gas can be formed, or any substance which 
 is volatile at the temperature at which the experiment is made, 
 this volatile product is set free. 
 
 The reactions 17 and 18 of this section are examples of 
 the first, while the reactions 12 and 19 are examples of the 
 second of these conditions. The facts just stated illustrate 
 an important truth, which must be carefully borne in mind in 
 the study of chemistry. A chemical equation differs essen- 
 tially from an algebraic expression. Any inference which 
 can be legitimately drawn from an algebraic equation must, in 
 some sense, be true. It is not so, however, with chemical sym- 
 bols. These are simply expressions of observed facts, and, 
 although important inferences may sometimes be drawn from 
 the mere form of the expression, yet they are of no value 
 whatever unless confirmed by experiment. Moreover, the facts 
 
 1 We find it convenient to distinguish between the force which holds to- 
 gether different molecules and that which unites the atoms of the molecules. 
 To the last we give the name of chemical affinity, while we call the first co- 
 hesion or adhesion, according as it is exerted between molecules of the same 
 kind or those of a different kind. 
 
38 CHEMICAL NOTATION. 
 
 which are expressed in this peculiar system of notation are 
 as purely materials for the memory as if they were described 
 in common language. 
 
 22. Compound Radicals. In many chemical reactions the 
 elementary atoms change places, not with other elementary 
 atoms, but with groups of atoms, which appear to sustain rela- 
 tions to the compounds they leave or enter similar to those of 
 the elements themselves. Thus, if we add to a solution of ar- 
 gentic nitrate a solution of ammoiiic chloride, we get the reac- 
 tion expressed by the equation 
 
 AgNO & + NHf Cl = NH,-NO & + Ag CL [20] 
 
 Here the group NH^ has taken the place of Ag. So, also, 
 in the reaction of hydrochloric acid on common alcohol, the 
 group C 2 H 5 in the molecule of alcohol changes places with the 
 atom of hydrogen in the molecule of hydrochloric acid, 
 
 C 2 ff 5 -0-ff-\- HCl = H-0-H-\- C,H :r Cl * [21] 
 
 Alcohol. Ethylic Chloride. 
 
 We write the symbols in this peculiar way in order to make 
 it evident to the eye that such a substitution has taken place. 
 Lastly, in the reaction of chloroform on ammonia, the group 
 Cffof the first changes places with the three atoms of hydro- 
 gen of ammonia gas, 
 
 Off* C1 3 + ff 3 N= BHCl + CH-=N. [22] 
 
 Chloroform. Hydrocyanic Acid. 
 
 Such groups as these are called compound radicals. Like 
 the atoms themselves, they cannot, as a rule, exist in a free 
 state ; but aggregates of these radicals may exist, which sus- 
 tain the same relation to the radicals that elementary substances 
 hold to the atoms. Thus, as we have a gas chlorine consisting 
 of molecules, represented by Cl-Cl, so there is a gas cyanogen 
 consisting of molecules, represented by CN-CN , where CNis 
 a compound radical called cyanogen. Again, the important 
 radicals CO, S0 2 , and PCI& are also the molecules of well- 
 known gases. These radical substances correspond to the ele- 
 mentary substances previously mentioned, in which the mole- 
 cule is a single atom. 
 
 But with few exceptions the radical substances have never 
 
CHEMICAL NOTATION. 89 
 
 been isolated, and the radicals are only known as groups of 
 atoms which pass and repass in a number of chemical reac- 
 tions. Indeed, in the same compound we may frequently 
 assume several radicals. The possible radicals of a chemi- 
 cal symbol correspond in fact almost precisely to the possi- 
 ble factors of an algebraic formula, and in writing the sym- 
 bol we take out the one or the other, as the chemical change 
 we are studying requires. A number of these radicals have 
 received names, and among those recognized in mineral com- 
 pounds a few of the most important are 
 
 Hydroxyl HO Sulphuryl S0 t 
 
 Hydrosulphuryl HS Carbonyl CO 
 
 Ammonium H^N Phosphoryl PO 
 
 Amidogen H Z N Nitrosyl NO 
 
 Cyanogen CN Nitryl NO Z . 
 
 The radicals recognized in organic compounds are very 
 numerous, and will be tabulated hereafter. 
 
 Questions and Problems. 
 1. For what do the following symbols stand ? 
 
 N-, Ca 2 ; H-H-, 7/ 4 <7; 4fiN0 8 ; (O 2 H 4 2 ) 
 
 2. For what do the following symbols stand ? 
 C7; S 3 -, 0-0-, 
 
 3. For what do the following symbols stand ? 
 
 0-, # 5 ; Se=Se-, Nad; J? 2 0; 
 
 4. Analyze the following reaction. Show that the same number 
 of atoms are represented on each side of the equation, and state the 
 class to which it belongs. 
 
 Fe + (2//C7 + Ag) = (FeCl 2 + Aq) + 2HU. 
 
 Hydrochloric Acid Ferrous Chloride. 
 
 5. Analyze the following reaction: Show in what the equality 
 consists, and state the class to which the reaction belongs. 
 
 Ammonic Nitrate. Water. Nitrous Oxide. 
 
 6. Analyze the following reactions. Show in what the equality 
 consists, and state the class to which the reaction belongs. 
 C+ 0-0 = GO* 
 
 Carbon. Oxygen. Carbonic Anhydride. 
 
40 CHEMICAL NOTATION. 
 
 7. Analyze the following reaction. Show in what the equality 
 consists, and state the class to which the reaction belongs. 
 
 2H-0-H+ Na-Na = ZNa-0-H+ H-H. 
 
 Water. Sodium. Sodic Hydrate. 
 
 8. The following reaction may be so written as to indicate that 
 the products are formed by a metathesis between two similar mole- 
 cules. It is required to show that this is possible. 
 
 = 3H-ff + JST-N. 
 
 Ammonia gas. Hydrogen gas. Nitrogen gas. 
 
 9. Write the reactions [17] and [18] so as to indicate the manner 
 in which the metathesis is supposed to take place. 
 
 10. State the conditions which determine the metathesis in the 
 various reactions given in this chapter so far as these conditions are 
 indicated. 
 
 11. Write the reactions [17] and [18] so as to indicate the manner 
 in which the metathesis is supposed to take place. 
 
 12. Analyze the following reaction. Show what determines the 
 metathesis and also what is meant by a compound radical. 
 
 ( 
 
 P 
 
 Pb-(N0 3 ) 2 
 
 lumbic Nitrate. Ammonic Chloride. 
 
 Aq) 
 
 Plumbic Chloride. Ammonic Nitrate. 
 
 13. Compare with [22] the following reaction and point out the 
 two radicals, which, as we may assume, hydrocyanic acid contains. 
 
 (Ag-NO, + ff-CN + Aq} = Ag-CN + (H-NO, + Aq) 
 
 Argentic Nitrate. Hydrocyanic Acid. Argentic Cyanide. Nitric Acid. 
 
 14. When sulphuric anhydride (S0 3 ) is added to water (H^O) a 
 violent action ensues and sulphuric acid is formed. The reaction 
 may be written in two ways, and it is required to explain the different 
 views of the process, which the following equations express. 
 
 ff 2 0+ S0 3 = ff 2 SO, 
 or 2H-0-H + SOfO = HfO./S0 2 + HfO. 
 
 15. State the distinction between a chemical element and an 
 elementary substance. Give also the distinction between a com- 
 pound radical and a radical substance. 
 
 16. Give the names of the following radicals. 
 
 HO-, HS-, NH^ NH 2 ', S0. 2 ; CO-, PO-, N0 &c. 
 
CHAPTER VI. 
 
 X STOCHIOMETRY. 
 
 /> 
 
 23. Stochiometry. The chemical symbols enable us not 
 only to represent chemical changes, but also to calculate ex- 
 actly the amounts of the substances required in any given pro- 
 cess as well as the amounts of the products which it will yield. 
 Each symbol stands for a definite weight of the element it rep- 
 resents, that is, for the weight of an atom ; but, as only the rela- 
 tive values of these weights are known, they are best expressed 
 as so many parts. Thus H stands for 1 part by weight of 
 hydrogen, the unit of our system. In like manner stands 
 for 16 parts by weight of oxygen, N for 14 parts by weight 
 of nitrogen, G for 12 parts by weight of carbon, C 5 for 60 parts 
 by weight of carbon, and so on for all the symbols in Table II. 
 The weight of the molecule of any substance must evidently 
 be the sum of the weights of its atoms, and is easily found, 
 when the symbol is given, by simply adding together the 
 weights which the atomic symbols represent. Thus ff 2 
 stands for 2 + 16= 18 parts of water, Jf 8 NfoT 3 -f 14 = 17 
 parts of ammonia gas, and (7 2 ^0 2 for 24 -\- 4 -[- 32 = 60 
 parts of acetic acid. 1 
 
 Having then given the symbol of a substance, it is very easy 
 to calculate its percentage composition. Thus, as in 60 parts of 
 acetic acid there are 24 parts of carbon, in 100 parts of the 
 acid there must be 40 parts of carbon, and so for each of the 
 other elements. The result appears below ; and in the same 
 way the percentage composition both of alcohol and ether has 
 been calculated from the accompanying symbol. 
 
 1 In this book " the molecular weight of a substance " will always mean the 
 sum of the atomic weight of the atoms composing one molecule, and we shall 
 use the phrase, " the molecular weight of a symbol," or " the total atomic weight 
 of a symbol," to denote the sum of the atomic weights of all the molecules which 
 the symbol represents. 
 
42 STOCHIOMETRY. 
 
 Acetic Acid Alcohol Ether 
 
 Carbon 40.00 52.18 64.86 
 
 Hydrogen 6.67 13.04 13.52 
 
 Oxygen 53.33 34.78 21.62 
 
 100.00 100.00 100.00 
 
 The rule, easily deduced, is this : As the weight of the mole- 
 cule is to the weight of each element, so is one hundred parts to 
 the percentage required. 
 
 On the other hand, having given the percentage composition, 
 it is easy to calculate the number of atoms of each element in 
 the molecule of the substance. This problem is evidently the 
 reverse of the last, but it does not, like that, always admit of a 
 definite solution ; for, while there is but one percentage compo- 
 sition corresponding to a given symbol, there may be an infinite 
 number of symbols corresponding to a given percentage com- 
 position. For example, the percentage composition of acetic 
 acid corresponds not only to the formula C 2 ff 4 2 , given above, 
 but also to any multiple of that formula, as can easily be seen 
 by calculating the percentage composition of Cff 2 0, C 3 ff 6 3 , 
 O 4 ff 8 0^ &c. They will all necessarily give the same result, 
 and, before we can determine the absolute number of atoms of 
 each element present, we must have given another condition, 
 namely, the sum of the weights of the atoms, or, in other 
 words, the molecular weight of the substance. When this is 
 known, the problem can at once be definitely solved. 
 
 Suppose we have given the percentage composition of alco- 
 hol, as above, and also the further fact that its molecular weight 
 is 46. We can then at once make the proportion 
 
 100 : 52.18 = 46 : x = 24 the weight of the atoms of carbon, 
 100 : 13.04 = 46 : x = 6 " " " " " " hydrogen, 
 100 : 34.78 = 46 : x = 1 6 " " " " " " oxygen. 
 
 Then it follows that 
 
 J = 2 the number of atoms of carbon in one molecule, 
 e. _ g u hydrogen in one molecule, 
 -| = 1 " " " " " oxygen in one molecule. 
 
 It is evident from this example, that, in order to determine 
 
STOCHIOMETRY. 43 
 
 exactly the symbol of a compound, we must know its molecular 
 weight. When the substance is a gas, or is capable of being 
 changed into vapor, we can easily determine its molecular 
 weight by the principle on page 15. The molecular weight is 
 simply twice its specific gravity referred to hydrogen. For all 
 the problems given in this book, which deal only with the com- 
 mon gases and vapors, the molecular weight can be at once 
 taken from Table III. If we are dealing with a new substance, 
 we must determine its specific gravity experimentally by one of 
 the methods which will hereafter be described. 
 
 When, on account of the fixed nature of the substance, the 
 last mode of investigation is impossible, we can still frequently 
 determine with great probability the molecular weight, by study- 
 ing the chemical reactions into which the substance enters, and 
 connecting, by careful quantitative experiments, the molecular 
 weight sought with that of some substance whose molecular 
 weight is known. The methods used in such cases will be in- 
 dicated hereafter ; but even when all such means fail, we can 
 nevertheless always find which of all possible symbols ex- 
 presses the composition of the substance we are studying in 
 the simplest terms, in other words, with the fewest number of 
 atoms in the molecule. Suppose the substance to be cane sugar, 
 which cannot be volatilized without decomposition, and of which 
 no reaction is known which gives any definite clew to its mole- 
 cular weight. Peligot's analysis, cited on page 6, shows that it 
 contains, in 100 parts, 42.06 parts of carbon, 6.50 parts of 
 hydrogen, and 51.44 parts of oxygen. Assume for the mo- 
 ment that the molecular weight is equal to 100 then 
 
 ^- = 3.50 the number of atoms of carbon. 
 ^ 6.50 " " hydrogen. 
 
 - 1 '* 4 = 3.22 " " oxygen. 
 
 This would be the number of atoms of each element if the 
 sum of the atomic weight, that is, the molecular weight, of 
 sugar, were equal to 100. As, from the very definition, frac- 
 tional atoms cannot exist, these numbers are impossible, but 
 any other possible number of atoms must be either a multiple 
 or a submultiple of the numbers found ; and we can easily dis- 
 
44 STOCHIOMETRY. 
 
 cover the fewest number of whole atoms possible, by seeking for 
 the three smallest whole numbers which stand to each other 
 in the relation of 3.50 : 6.50 : 3.22, a proportion which is very 
 nearly satisfied by 12 : 22 : 11. Hence, the simplest possible 
 symbol is O^H^ U , and this has been adopted by chemists as 
 the symbol of cane sugar, although, from anything we as yet 
 know, the symbol may be a multiple of this. If now, taking 
 this symbol as our starting-point, we calculate the percentage 
 composition which would exactly correspond to it, we obtain 
 the following results, which we have arranged in a tabular 
 form, so that the student may compare the theoretical compo- 
 sition with the numbers Peligot obtained by actual analysis. 
 
 Composition of Cane Sugar, 
 
 QA4i. 
 
 Peligot's Analysis. Theoretical. 
 
 Carbon 42.06 42.11 
 
 Hydrogen 6.50 6.43 
 
 Oxygen 51.44 51.46 
 
 100.00 100.00 
 
 The difference between the two is now seen to be within the 
 probable errors of analysis, and this example illustrates the 
 method of arranging analytical results generally adopted by 
 chemists. 
 
 From the above discussion we can easily deduce a simple 
 arithmetical rule for finding the symbol of a compound when 
 its percentage composition is known. But this rule may be best 
 expressed in an algebraic formula, which will show to the eye 
 at once the relation of the quantities involved in the calcula- 
 tion, and enable us to extend our method to the solution of 
 many classes of problems which we might not otherwise foresee. 
 Let us then represent 
 
 By M the weight of any chemical compound in grammes. 
 " m the molecular weight of the compound in hydrogen 
 
 atoms. 
 " W the weight of any constituent of that compound, whether 
 
 element or compound radical, in grammes. 
 " w the total atomic weight of element or radical in one 
 
 molecule. 
 
STOCHIOMKTRY. 45 
 
 Then 
 
 = proportion by weight of the constituent in the compound, 
 
 and 
 
 M = weight of constituent in M grammes of compound, or 
 
 W=M-. [23] 
 
 m L J 
 
 Any three of these quantities being given, the fourth can, of 
 course, be found. Thus we may solve four classes of problems. 
 
 1. We may find the weight of any constituent in a given 
 weight of a compound, when we know the molecular weight of 
 the compound^and the total atomic weight of the constituent in 
 one molecule. 
 
 Problem. It is required to find the weight of sulphuric 
 anhydride S0 8 in 4 grammes of plumbic sulphate PbO, S0 3 . 
 Here, w = 32 + 3 X 16 = 80, m = 207 + 16 + 80 = 303, 
 and M = 4. Ans. 1.056 grammes. \J 
 
 2. We can find the weight of a compound which can be 
 produced from, or corresponds to, a given weight of one of its 
 constituents, when the same quantities are known as above. 
 
 Problem. How many grammes of crystallized green vitriol, I 
 FeSO. 7ff 2 0, can be made from 5 grammes of iron? Here, 
 w = 56, m = 278, JF= 5. Ans. 24.821. 
 
 3. We can find the molecular weight of a compound when 
 we have given the weight of one constituent in a given weight 
 of the compound, and the total atomic weight of that constitu- 
 ent in the molecule. 
 
 Problem. In 7.5 grammes of ethylic iodide, there are 6.106 
 grammes of iodine; the total atomic weight of iodine in one 
 molecule is 127. What is the molecular weight of ethylic 
 iodide? Ans. 156. 
 
 4. We can find the total atomic weight of one constituent of 
 a molecule when the molecular weight is given, and also the 
 weight of the constituent in a known weight of the compound. 
 
46 STOCHIOMETRY. 
 
 Problem. The molecular weight of acetic acid is 60, the 
 per cent of carbon in the compound 40. What is the total 
 atomic weight of carbon in one molecule ? Ans. 24. 
 Whence number of carbon atoms in one molecule, 2. 
 
 The last problem is essentially the same as that of finding 
 the symbol of a compound when its percentage composition is 
 given, while the first corresponds to the reverse problem of 
 deducing the percentage composition from the symbol. By a 
 slight change the formula can be much better adapted to this 
 class of cases. For this purpose we may put M = 1 00, since 
 we are solely dealing with per cents, and also put w = na, 
 a standing for the atomic weight of any element, and n for the 
 number of atoms of that element in one molecule of the 
 compound we are studying. We then have 
 
 
 JP= 100 - and ra = - - [24] 
 
 m 100 a 
 
 The first of these forms is adapted for calculating the per cent 
 of each element of a compound when the molecular weight, 
 the number of atoms of each element in one molecule, and the 
 several atomic weights, are known ; and it is evident that all 
 these data are given by the chemical symbol of the compound. 
 The second of these forms enables us to calculate the number 
 of atoms of each element present in one molecule of a com- 
 pound when the percentage composition, the molecular weight, 
 and the several atomic weights, are known, and illustrates the 
 principle before developed, that the molecular weight is an 
 essential element of the problem. 
 
 . Stochiometrical Problems. The principles of the pre- 
 section apply not only to single molecular formulae, but 
 obviously may also be extended to the equations which repre- 
 sent chemical changes. Since the molecular symbols which 
 are equated in these expressions represent known relative 
 weights, it must be true in every case that we can calculate the 
 weight of either of the factors or products of the chemical 
 change it represents, provided only that the weight of some one 
 is known. If we represent by w and m the total atomic weight 
 of any two symbols entering into the chemical equations, and 
 by JFand M the weight in grammes of the factors or products 
 
STOCHIOMETRY. 47 
 
 which these symbols represent, then the simple algebraic 
 formulas of the last section will apply to all stochiometrical 
 problems of this kind, as. well as to those before indicated. 
 These formulae, however, are merely the algebraic expression 
 of the familiar rule of three, and all stochiometrical problems 
 are solved more easily by this simple arithmetical rule. Using 
 the word symbol to express the sum of the atomic weights it 
 represents, we may state the rule as applied to chemical prob- 
 lems in the following words, which should be committed to 
 memory. 
 
 Express the reaction in the form of an equation ; make then 
 the proportion, As the symbol of the substance given is to the sym- 
 bol of the substance required, so is the weight of the substance 
 given to x, the iveight of the substance required ; reduce the 
 symbols to numbers, and calculate the value of x. 
 
 This rule applies equally well to all problems, like those of 
 the' last section, in which the elements or radicals of the same 
 molecular symbol are alone involved ; only in such cases there 
 is of course no equation to be written. A few examples will 
 illustrate the application of the rule. 
 
 Problem 1. We have given 10 kilogrammes of common salt, 
 and it is required to calculate how much hydrochloric acid gas 
 can be obtained from it by treating with sulphuric acid. The 
 reaction is expressed by the equation 
 
 (2Na 01 + ff 2 S0 4 + Aq) = (Na^SO^ + Aq) + 2IS(^, 
 whence we deduce the following proportion, 
 
 117 73 
 
 2Na Cl : 2ffCl = W:x = Ans. 6.239 kilogrammes. 
 
 Problem 2. It is required to calculate how much sulphuric 
 acid and nitre must be used to make 250 grammes of the 
 strongest nitric acid. The reaction is expressed by the 
 equation 
 
 KNO, + & 2 SO, == K, ffS0 4 + HNO Z1 
 whence we get the proportions 
 
 f,3 98 
 
 ffN0 3 : N 2 S0 4 =250:x = Ai\s. 1. 388.9 grammes sulphuric 
 acid. 
 
 63 101.1 
 
 250 : x = Ans. 2. 401.2 grammes nitre. 
 
48 
 
 STOCHIOMETBT. 
 
 The student should also solve by the same rule the problems 
 given in the last section. 
 
 25. Gay-Lussac's Law. This eminent French chemist was 
 the first to state clearly the important truth, that, when gases or 
 vapors react on each other, the volumes both of the factors and 
 of the products of the reaction always bear to each other some 
 very simple numerical ratio. This truth is generally known as 
 the law of Gay-Lussac, but, since the principle is a direct con- 
 sequence of the atomic theory, it is best studied in that relation. 
 It is, as we have seen, a fundamental postulate of the theory that 
 equal volumes of all substances, when in the aeriform condition, 
 contain the same number of molecules. Hence it follows, that 
 the volumes of all single molecules are the same, and, if we take 
 this common volume as our unit of measure, it follows, further, 
 that the total molecular volume represented by any symbol is 
 always equal to the number of molecules. We are thus led to 
 a most important fact, which gives an additional meaning to our 
 chemical symbols, for it appears that Every chemical equation, 
 when properly written, represents not only the relative weights, 
 but also the relative volumes of its factors and products y when in 
 the state of gas. 
 
 This principle is illustrated by the following equations : 
 
 + 
 
 Marsh Gas. 
 
 Carbonic Anhydride. Aqueous Vapor 
 
 Nitric Oxide Gas. 
 
 Hydrogen Gas. 
 
 Ammonia Gas. 
 
 Aqueous Vapor. 
 
 The squares which here serve to indicate equal volumes, 
 and to impress on the mind the meaning of the symbols, are 
 evidently unnecessary and will not be used hereafter. 
 
 It is a great advantage of the crith, which has been proposed 
 as a unit of weight in chemistry (see 2), that it stands in the 
 same relation to the French unit of volume, the litre, in which 
 the weight of the hydrogen molecule stands to the common 
 volume of all molecules, the unit of molecular volume. The 
 
STOCHIOMETRY. 49 
 
 volume of a given mass of any gas is always equal to the 
 weight in criths divided by its specific gravity referred to 
 hydrogen [3]. In like manner, the molecular volume rep- 
 resented by any symbol is equal, to one half ( 17) the total 
 atomic weight of that symbol divided by the specific gravity of 
 the gas it represents. In other words, the weight in criths of 
 any mass of gas stands in the same relation to its volume in 
 litres as that in which one half the total atomic weight of any 
 symbol stands to the total molecular volume, or, what amounts 
 to the same thing, to the number of molecules which the symbol 
 represents. This relation must, of course, hold in every chem- 
 ical equation, and hence, with a simple modification, the rule of 
 the last section may be extended to the many cases in which 
 it is desired to calculate the volumes of gas or vapor involved 
 in a chemical change. The rule so modified may be stated 
 thus : 
 
 Express the reaction in an equation ; make then the propor- 
 tion, As one half of the symbol of the first substance is to the 
 number of molecules of the second, so is the weight in criths of 
 the first to the volume in litres of the second ; reduce the symbol 
 to numbers, and calculate the value of the unknown quantity. 
 
 This rule has the same general application as the first, and 
 a few examples will illustrate the use of it. 
 
 Problem 1. How much chlorate of potash must be used to 
 obtain one litre of oxygen gas ? The reaction is expressed by 
 the equation 
 
 whence we get the proportion 
 
 122.6 
 
 (2K C10 3 ) :3 = x:l. x = 40.9 criths, 
 40.9 X 0.0896 = Ans. 3.664 grammes. 
 
 Problem 2. How many litres of oxygen gas can be obtained 
 from 500 grammes of chlorate of potash ? The reaction is the 
 same as before, but in this case the grammes must first be 
 reduced to criths. The proportion will then be written 
 
 122.6 KAA 
 
 KCIO Z '. 3 = -^- : x = Ans. 136.6 litres. 
 
50 STOCHIOMETRY. 
 
 Problem 3. How many litres of ammonia gas NH 3 are con- 
 tained in 20 grammes of ammonic chloride, NH Z -HCI? Here 
 we require no equation ; for the symbol itself gives at once the 
 proportion 
 
 1 == : x = Ans. 8.343 litres. 
 
 In applying the rules of this chapter to the solving of 
 stochiometrical problems, the student should carefully bear in 
 mind, first, that the rule of (24) applies to all those cases in 
 which the weight of one substance is to be calculated from the 
 weight of another ; secondly, that when volume is to be deduced 
 from volume the answer can be found by mere inspection of 
 the equation according to the principles stated in (25), and 
 thirdly, that the rule of page 49 applies only to those problems 
 in which volume is to be calculated from weight, or the reverse. 
 In using this last rule it must be remembered that the " first 
 substance " is always the one whose weight is given or sought, 
 while the " second substance " is always the one whose volume 
 is given or sought. 
 
 Questions and Problems. 
 
 1. What is the molecular weight of plumbic sulphate, Pb=0 2 =SO z ? 
 f calcic phosphate, Co 3 |0 6 l(PO) 2 ? Of ammonia alum, 
 
 (NH 4 \, (AlJiO B -(SOJ v 24# 2 0? Ans. 303, 310, and 906.8. 
 
 2. What are the molecular weights of the symbols 
 
 3<? 2 # 4 2 ; 5(FeSO. 1R,0) and 7K 2 =0 2 =CO? 
 
 Ans. 180, 1390, and 967.4. 
 
 3. Are the total atomic weights of the two members of the follow- 
 ing reaction equal ? 
 
 Fe + (N 2 S0 4 + Ag) = (FeS0 4 + Aq) + H-H. 
 Ans. The total weight of each member of the equation is 154. 
 
 4. Calculate the percentage composition of ammonic chloride, 
 NH^CL Ans. Nitrogen, 26.17; Hydrogen, 7.48; Chlorine, 66.35. 
 
 5. Calculate the percentage composition of nitrobenzoel, C 6 H.N0 2 . 
 Ans. Carbon, 58.53; Hydrogen, 4.07 ; Nitrogen, 11.39 ; Oxygen, 
 26.01. 
 
STOCHIOMETRY. 51 
 
 6. Given the percentage composition of chloroform as follows : 
 Carbon, 10.04 ; Hydrogen, 0.83 ; Chlorine, 89.13. Required the 
 symbol, knowing that the Sp. Gr. of chloroform vapor equals 59.75. 
 
 Ans. CHCl y 
 
 1. Given the percentage composition of stanno-diethylic bromide 
 as follows: Tin, 35.13; Carbon, 14.29; Hydrogen, 2.97; Bromine, 
 47.61. Required the symbols, knowing that the Sp. Gr. of the 
 vapor equals 168. Ans. SnC 4 H lo Br 2 . 
 
 8. Given the percentage composition of ethylene chloride as fol- 
 lows : Carbon, 24.24 ; Hydrogen, 4.04 ; Chlorine, 71.72. Required 
 the symbol, knowing that the Sp. Gr. of the vapor equals 49.5. 
 
 Ans. 
 
 9. Given the percentage composition of cream of tartar as fol- 
 lows: Potassium, 20.79; Hydrogen, 2.66; Carbon, 25.52; Oxygen, 
 51.03. Required the simplest symbol possible. Ans. 
 
 10. Given the percentage composition of crystallized ferrous sul- 
 phate as follows: Iron, 2Q.15 ; Sulphur, 11.51; Oxygen, 23.02; 
 Water, 45.32. Required the simplest symbol possible. 
 
 Ans. Estimating the number of molecules of water (H 2 0), as 
 if water were a fourth element with an atomic weight of 18, we get 
 FeSO,. 7H,0. 
 
 11. The percentage composition of morphia according to Liebig's 
 analysis is Carbon, 71.35 ; Hydrogen, 6.69 ; Nitrogen, 4.99 ; Oxy- 
 gen (by loss), 16.97. What is the symbol of this alkaloid, and how 
 closely does this symbol agree with the results of analysis ? 
 
 Ans. The symbol C 17 H 19 NO S would require 71.58 Carbon, 6.66 
 Hydrogen, 4.91 Nitrogen, and 16.85 Oxygen. 
 
 12. It is required to find the. weight of phosphorus in 155 kilos. 
 of calcic phosphate (Ca 3 P 2 ^ 8 )' -^ ns - 31 kilos. 
 
 13. It is required to find the weight of sulphuric anhydride (/S0 3 ) 
 in 284 kilos, of sodic sulphate, Na 2 S0 4 . Ans. 80 kilos. 
 
 14. How many grammes of plumbic sulphate (P&S0 4 ) can be 
 made from 2.667 grammes of sulphuric anhydride (S0 3 ) 
 
 Ans. 30.3 grammes. 
 
 15. How many grammes crystallized cupric sulphate (CuSO t . 
 6#2<9) will yield 317 grammes of copper ? Ans. 1337 grammes. 
 
 16. Required the total molecular weight of crystallized sodic 
 phosphate, knowing that 71.6 parts of the salt contain 9.2 parts of 
 sodium, and that the total atomic weight of sodium in one mole- 
 cule of the compound is 46. s Ans. 358. 
 
 A 
 
52 STOCHIOMETRY. 
 
 17. The molecular weight of potassic nitrate is 101.1, and 2.359 
 grammes of the salt contain 1.120 grammes of oxygen. What is 
 the total atomic weight of oxygen, and also the number of oxygen 
 atoms in one molecule ? 
 
 Ans. Total atomic weight 48. No. of oxygen atoms 3. 
 
 18. How much nitric acid (HN0 3 ) is required to dissolve 3.804 
 grammes of copper (Cu) and how much cupric nitrate (CuN^O^ 
 and how much nitric oxide (NO) will be formed in the process V 
 The reaction is expressed by the equation 
 
 3Cu+ (SHN0 3 + Aq) = (3 Cuff a 0, + H, +Aq) + SSF. 
 
 Ans. 10.08 grammes of nitric acid; 11.244 grammes of cupric 
 nitrate and 0.60 grammes of nitric oxide. 
 
 19. How much common salt (NaCl) must be added to a solution 
 containing 30 grammes of argentic nitrate (AgNO s ) in order to 
 throw down the whole of the silver, and how much argentic chloride 
 (AgCl) will be thus precipitated ? 
 
 (AgNO* + Na Cl + Aq) = AgCl + (NaN0 8 + Aq). 
 Ans. 9,75 grammes of salt and 23.92 grammes argentic chloride. 
 
 20. How many litres of ammonia gas (SSFHIj) and how many of 
 chlorine gas OKSIl are required to make one litre of nitrogen gas 
 SS >E SST ? How many litres of hydrochloric acid gas (IHO1) are 
 also formed ? 
 
 301-01 = 
 
 Ans. 2 litres of ammonia gas ; 3 litres of chlorine gas, and 6 
 litres of hydrochloric acid gas. 
 
 21. How many litres of hydrochloric acid gas (IHO1) and how 
 many of oxygen gas (=) can be obtained from one litre of 
 aqueous vapor (IHa), and how many litres of chlorine gas 
 (O1-O1) must be used in the process ? 
 
 25H 2 + 2O1-O1 = 43SO1 + <fi>. 
 
 Ans. 2 litres of hydrochloric acid gas, litre of oxygen gas, and 
 1 litre of chlorine gas. 
 
 22. How many litres of oxygen gas ((o>(D) are required to burn 
 completely (i. e. to combine with) one litre of alcohol vapor 
 COsHIs)) and how many litres of carbonic anhydride (0(0)2) and 
 how many of aqueous vapor 0H 2 ) are formed by the process ? 
 The chemical reaction which takes place when alcohol burns is 
 expressed by the equation 
 
STOCHIOMETRY. 53 
 
 3 = 2 (oJ 2 + 3 HI 2 . 
 
 Ans. 3 litres of oxygen gas ; 2 litres of carbonic anhydride, and 
 3 litres of aqueous vapor. 
 
 23. How many litres of oxygen gas are required to burn one 
 litre of arseniuretted hydrogen (IH 3 ^s), and how many litres of 
 arsenious acid vapor (^s 3 ) and how many of aqueous vapor are 
 formed in the process V 
 
 4m 3 ^s + 9= = 4^s 3 + 6IH 2 . 
 
 Ans. 2 litres of oxygen gas ; 1 litre arsenious acid vapor and l 
 litres of aqueous vapor. 
 
 24. How many litres of chlorine gas can be made with 19.49 
 grammes of manganic oxide (MnO%) ? 
 
 ]HllO 2 + (4HCl+Aq) = (Mn Cl 2 + 2ff 2 0+Aq) +@1-L 
 
 Ans. 5 litres. 
 
 25. How many grammes of chalk (CaC0 3 ) are required to yield 
 one litre of carbonic anhydride ? 
 
 CaCOa + (2HCI + Aq) = ( Ga C1 2 + H 2 0+Aq) + CO* 
 
 Ans. 4.48 grammes. 
 
 26. How many litres of hydrochloric acid gas (HCF) can be made 
 with 8.177 kilogrammes of common salt (NaCl) ? 
 
 (2Na Cl + ff z SOt + Aq) = (Na 2 S0 4 + Aq) + 2 SIOL 
 
 Ans. 5000. 
 
 27. How many grammes of ferrous sulphide (FeS) are required 
 to yield 568 crm. 8 of sulphuretted hydrogen (# 2 S) ? 
 
 + (ff,S0 4 + Aq) = (FeS0 4 + Aq) + SlaS. 
 
 Ans. 2.24 grammes. 
 
CHAPTER VII. 
 
 CHEMICAL EQUIVALENCY. 
 
 26. Chemical Equivalents. If in' a solution of argentic 
 sulphate we place a strip of metallic copper, we find after a 
 short time that all the silver has separated from the solution, 
 and that a certain quantity of copper has dissolved in its place. 
 
 (AfrS0 4 + Ag) + Cu = ( CuSOt + Aq) + Aft, [25] 
 
 If now we pour off the solution of cupric sulphate, and place 
 in this solution a strip of metallic zinc, the metallic copper in 
 its turn will all separate, and to replace it a certain amount of 
 zinc will dissolve. 
 
 (CuSOt + Aq) + Zn = (ZnSOt + Ag) + Cu. [26] 
 
 Lastly, if we pour off the solution of zincic sulphate, and 
 place in this a strip of metallic magnesium, the zinc will in like 
 manner be replaced by magnesium. 
 
 (ZnSO, + .Aq) + OTEg = (MgSO + Aq) + Zn. [27] 
 
 In experiments like these, we can by proper analytical 
 methods determine the relative quantities by weight of the 
 several metals which thus replace each other, and we find that 
 they are always the same. Thus, if our first solution contained 
 108 milligrammes of silver, the amount of each metal suc- 
 cessively dissolved and precipitated would be, of copper, 
 31.7 m. g., of zinc, 32.6 m. g., of magnesium, 12 m. g. More- 
 over, if, instead of using in our experiments a metallic sulphate, 
 we take a metallic chloride, nitrate, acetate, or any other com- 
 pound of the metals, we find that the same definite ratios are 
 preserved, at least in every case where the substitution is pos- 
 sible. It would appear then that these relative quantities of 
 the several metals exactly replace each other in all such cases. 
 They are, therefore, regarded as the chemical equivalents of 
 
CHEMICAL EQUIVALENCY. 55 
 
 each other, in the sense that they are capable of filling each 
 other's place. 
 
 In a strict sense, two quantities of different elements can 
 be said to be equivalent to each other only when they are 
 actually capable of replacing each other in some known chem- 
 ical reaction, but formerly the word was used with a much 
 wider significance, and quantities of two different elements 
 were said to be equivalent to each other if they had been 
 proved to be equivalent to the same quantity of some third 
 element which served as a link of connection. In this way 
 an equivalency may be established between all the chemical 
 elements, and the system of chemistry still used in many text- 
 books is based on a system of equivalency so determined. If 
 the table of chemical equivalents on this old system is com- 
 pared with a table of atomic weights on the new, it will be 
 found that the numbers of the one are either the same as those 
 of the other, or else some very simple multiples of them. The 
 one set of numbers can be used in all stochiometrical calcula- 
 tions in the same way as the other, and on the old system the 
 symbols stand for equivalents, as in the new they stand for 
 atomic weights. The equivalents have this advantage, that 
 they are the result of direct experiments, and are based on no 
 hypothesis in regard to the molecular constitution of matter. 
 But this hypothesis is necessary, in order to correlate a large 
 number of facts which modern chemical investigation has 
 brought to light, and when once made, the rest of the system 
 follows as a necessary consequence. 
 
 27. Quantivalence and Atomicity of the Elements. If now, 
 starting with the atomic weights as they have been determined 
 or assumed in Table II., we compare together the different 
 elements from the point of view taken in the last section, it 
 will be found, that, while in some cases one atom of one ele- 
 ment is the equivalent of one atom of another in other cases, 
 it may be the equivalent of two, three, or four atoms. Since 
 in the system of this book the symbols always stand for atomic 
 weights, the relation here referred to is made evident whenever 
 any metathetical reaction is expressed in the form of an equa- 
 tion. A few examples will illustrate the point, and make 
 clear what is meant. The reaction of aqueous hydrochloric 
 acid on a solution of argentic nitrate is expressed by the 
 equation, 
 
56 CHEMICAL EQUIVALENCY. 
 
 + HOI + Aq) = (HNO, + Aq) + AgCl, [28] 
 
 and here evidently Ag changes places with H, and hence one 
 atom of silver is equivalent to one atom of hydrogen. Take 
 now the reaction of dilute sulphuric acid on zinc, which is 
 expressed by the equation, 
 
 Zn + (ff a S0 4 + Aq) = (ZnSOt + Aq) + gHH, [29] 
 
 and it will be seen that Zn has changed places with /7 2 > and 
 hence that one atom of zinc is the equivalent of two atoms of 
 hydrogen. Lastly, in the reaction of water on phosphorous 
 trichloride, expressed by the equation, 
 
 ni 
 IT 3 ff 3 3 + PCl 3 = 3HCl+ff 3 P0 3 , [30] 
 
 Phosphorous Acid. 
 
 it is equally evident that P has changed places with ff 3j and 
 hence in this reaction one atom of phosphorus is equiva- 
 lent to three atoms of hydrogen. 
 
 This relation of the elements to each other is called by 
 Hofmann quantivalence ; and selecting here, as in the system of 
 atomic weights, the hydrogen atom as our standard of reference, 
 the atoms of different elements are called wm'valent, divalent, 
 frtvalent, or quadrivalent, according as they are in the sense 
 already indicated equivalent to one, two, three, or four atoms 
 of hydrogen. These terms are very appropriate, since they 
 are all derived from the same root as our common English 
 word equivalent, which best expresses the fundamental idea 
 that underlies the whole subject. We shall therefore adopt 
 them in this book, and, as Hofmann recommends, designate 
 the quantivalence, whenever important, by a Roman numeral 
 placed over the atomic symbol thus, 
 
 i ii in iv 
 <7/, 0, tf, O. 
 
 In most cases, however, the quantivalence is indicated with 
 sufficient clearness by the dashes, which are also used in this 
 book to separate the parts of a molecular symbol. The num- 
 ber of these dashes is always the same as the quantivalence 
 of the atoms, or groups of atoms, on either side. 
 
CHEMICAL EQUIVALENCY. 57 
 
 With these additions to our notation we are able to express 
 by our symbols all that was valuable in the old system of 
 equivalents, and at the same time all that is peculiar to our 
 modern theories. 
 
 Precisely the same relations of quantivalence are manifested 
 even more fully by the compound radicals, whenever in a 
 chemical reaction they change places with elementary atoms, 
 and their replacing value is indicated in the same way. Thus, 
 in the following reaction, 
 
 c 2 ff 3 o-a+ff-o-ir=ji-a+ff-o-c 2 H s 6, pi] 
 
 Acetyl chloride. Water. Acetic Acid. 
 
 the radical C 2 H& 0, named acetyl, changes places with one atom 
 of hydrogen, and is therefore -umvalent, while in the next, 
 
 ni in 
 
 GHz (7/3 + ff 3 N= 3HCI + CH-=N, [32] 
 
 Chloroform. Hydrocyanic Acid. 
 
 the radical Cffis as evidently trivalent. 
 
 The quantivalence of an element or radical is shown, not only 
 by its power of replacing hydrogen atoms, but also by its power 
 of replacing any other atoms whose quantivalence is known. 
 Moreover, what is still more important, the quantivalence of an 
 element or radical is shown, not only by its replacing power, but 
 also by what we may term its atom-fixing power, that is, by its 
 power of holding together other elements or radicals in a mole- 
 cule. We may take as examples the molecules of four very 
 characteristic compounds, namely, hydrochloric acid, water, 
 ammonia, and marsh gas, whose symbols may be written thus, 
 
 i n in iv 
 
 H-Cl H,H-0 H,H,H=-N ff, ft H, H^C. 
 
 Hydrochloric Acid. Water. Ammonia. Marsh Gas. 
 
 By these symbols it appears, that, while the univalent atom of 
 chlorine can hold but one atom of hydrogen, the bivalent atom 
 of 'oxygen holds two, the trivalent atom of nitrogen three, and 
 the quadrivalent atom of carbon four atoms of the same ele- 
 ment. It appears, then, that the Roman numerals or dashes, 
 which represent the replacing power of the atoms or radicals, 
 represent also the atom-fixing power of the same, measured 
 in each case by the number of atoms of hydrogen, or their 
 
58 CHEMICAL EQUIVALENCY. 
 
 equivalents, with which these atoms or radicals can combine 
 to form a single molecule. On account of the importance of 
 this principle we will extend our illustrations to a number of 
 other compounds, and the student should carefully compare 
 in each case the quantivalence on the two sides of the dash 
 or dashes, which mark the atom-fixing power of the dominant 
 atom in the molecule. 
 
 ii ii ii ii 
 
 Na-Cl K-I O 2 ff 5 -Br K-CN-, 
 
 Sodic Chloride. Potassic Iodide. Ethylic Bromide. Potassic Cyanide. 
 
 i ii i H n i ii i i ii i 
 
 K-O-H Pb-0 N-0-N0 2 H-O-C^O-, 
 
 Potassic Hydrate. Plumbic Oxide. Nitric Acid. Acetic Acid. 
 
 i i i m i mil im 
 
 H,H,C,HfN (C 2 ff^P CH ?J ,C,H,,C 5 H^N. 
 
 Ethylamine. Triethyl phosphine. Methyl-ethyl-amyl-amine. 
 
 The quantivalence of the chemical elements, especially as 
 indicated by their atom-fixing power, is by no means always 
 the same. They constantly exhibit under different conditions 
 an unequal atom-fixing power. Thus we have 
 
 SnCla and SnCl 4J P01 3 and PCl s , NJT 3 and NHCl. 
 
 Each element, however, has a maximum power, which it never 
 exceeds. This we shall call its atomicity, and we shall distin- 
 guish the elements as monads, dyads, triads, &c., according to 
 the number of univalent atoms or radicals they are able at 
 most to bind together. Thus nitrogen is a pentad, although 
 it is more commonly trivalent, and lead is a tetrad, although 
 it is usually bivalent. Again, sulphur is a hexad, although 
 in most of its relations it is, like lead, bivalent. In like 
 manner with other elements, one of the few possible con- 
 ditions is generally much more common and stable than the 
 rest, and this prevailing quantivalence of an element is a 
 more characteristic property than its maximum quantiva- 
 lence or atomicity. A classification of the elements based on 
 their atomicity alone would contravene their most striking 
 analogies, while one based on the prevailing quantivalence 
 very nearly satisfies all natural affinities. Moreover, it should 
 be added, that, while the prevailing quantivalence of the ele- 
 ments is generally well established, their atomicity is frequently 
 
CHEMICAL EQUIVALENCY. 59 
 
 still in doubt ; for the first can generally be discovered by study- 
 ing the simple compounds of the elements with chlorine or hy- 
 drogen, while the last is often only manifested in those more 
 complex combinations, in regard to which a difference of opin- 
 ion is possible. 
 
 The possible degrees of quantivalence of an elementary 
 atom are related to each other by a very simple law. They 
 are either all even or all odd. Thus the atom of sulphur may 
 be sextivalent, quadrivalent and bivalent, but is never triva- 
 lent or univalent ; and on the other hand the atom of nitrogen 
 may be quinquivalent, trivalent and univalent, but not quad- 
 rivalent or bivalent. Atoms like those of sulphur, whose quan- 
 tivalence is always even, are called artiads, while those like 
 nitrogen, whose quantivalence is always odd, are called 
 
 28. Atomicity or Quantivalence of Radicals. When in the 
 molecule of any compound the dominant or central atom is 
 united to as many other atoms as it can hold of that kind, the 
 molecule is said to be saturated; thus 
 
 HO, H 2 0, HJir, H,O 
 
 are all saturated molecules ; for, although nitrogen is a pentad, 
 it cannot without the intervention of some other atom or radical 
 hold more than three atoms of hydrogen. While on the other 
 hand the molecules 
 
 IT n n 
 
 GO, PCl 3 znd SnCl 2 
 
 are not saturated, for they can combine directly with more 
 oxygen or chlorine, forming thus the saturated molecules 
 
 CO* PCl 5 *ndSnCl 4 . 
 
 If now from a saturated molecule we withdraw one or more 
 atoms of hydrogen, or their equivalents, the residue may be re- 
 garded as a compound radical with an atomicity equal to the 
 number of hydrogen atoms, or their equivalents, withdrawn. 
 Thus, if from the saturated molecule of marsh gas H 4 we 
 withdraw one atom of hydrogen, we get the radical methyl 
 H z C, which is a monad ; if we withdraw two atoms, we have 
 
60 CHEMICAL EQUIVALENCY. 
 
 the radical, ff 2 C, which is a dyad; if we withdraw three, 
 there results HG, which is a triad ; and lastly, if we with- 
 draw all four, we fall back on the tetrad atom of carbon. Again, 
 if from the saturated molecule of nitric anhydride N 2 5 we 
 withdraw one atom of the dyad oxygen 0, it falls into two 
 atoms of N0 2 each of which is a monad. If now we with- 
 draw from NO Z one of its remaining atoms of oxygen, we 
 have left NO, which is a triad. Lastly, a molecule of sulphuric 
 anhydride S0 3 , which is saturated, gives, by withdrawing one 
 atom of oxygen, SO.^ which acts as a bivalent radical. These 
 considerations lead us to a simple rule, first stated by Wurtz, 
 which in almost every case will enable us to infer the atomicity 
 of any given radical. The atomicity l of a compound radical 
 is always equal to the number of hydrogen atoms, or their equiva- 
 lents, which the radical may be regarded as having lost. 
 
 It must not be supposed, however, that all such radicals are 
 possible compounds. In a few cases only these residues, of 
 which we have been speaking, form non-saturated molecules, 
 which are capable of existing in a free state, like those of car- 
 bonic oxide, nitric oxide and sulphurous acid. At other times 
 they are compound radicals, which, by doubling, form molecules 
 that can exist in a free state, as those of cyanogen gas, and 
 perhaps also of some hydrocarbons. Again, they appear as 
 compound radicals, which pass and repass in so many chemical 
 reactions as to almost force upon us the belief that they have 
 a real existence, and represent the actual grouping of the 
 atoms in the compounds of which they seem to be an in- 
 tegral part. Still again, and even more frequently, they can 
 only be regarded as convenient factors in a chemical equation. 
 
 1 The quantivalence of a compound radical is always the same as its 
 atomicity. 
 
CHEMICAL EQUIVALENCY. 61 
 
 Questions and Problems* 
 
 1. Analyze the following metathetical reactions, showing in each 
 case how many parts of the several elements are equivalent to one 
 part by weight of hydrogen, and also to how many atoms of hydro- 
 gen one atom of each of the interchanging elements corresponds. 
 For the atomic weights refer to Table II. 
 
 2ff-0-C 2 ff 5 + K-K = 2K-0-C 2 ff 5 + H-H. 
 
 Alcohol. Potassium. Potussic Ethylate. 
 
 2H-0-H+ Mg Mg-0 2 =H 2 + H-H. 
 
 Water. Magnesic Hydrate. 
 
 = SbCl 3 + 3N-0-H. 
 
 Antimonious Hydrate. Antimonious Chloride. 
 
 H-0-H + SiCl 4 fffO/Si + HCL 
 
 Silicic Chloride. Silicic Acid. 
 
 2 Make out a table of chemical equivalents so far as the reactions 
 of this chapter will enable you to deduce them from the atomic 
 weights given in Table II. 
 
 3. Analyze the following metathetical reactions, showing in each 
 case how the quantivalence of the several compound radicals in- 
 volved in the metathesis, is indicated. 
 
 H- 0-H+ ( 2 H S Oy 0-( 2 ff a )=( 2 ff 3 0)- 0-ff+ff- 0- 
 
 Water. Acetic Ether. Acetic Acid. Alcohol. 
 
 %K-(CN) + (OAY-Br, = (0 2 ff,)-(ON) 2 + ZKBr. 
 
 Potassic Cyanide. Ethylene Bromide. Ethylene Cyanide. Potassic Bromide. 
 
 sff-on + (C,ff 5 y-ai s = (c 3 H 5 )-=OfH 3 + sffa 
 
 Water. Glyceryl Chloride. Glycerine. Hydrochloric Acid. 
 
 The names of the radicals are as follows : C Z H 3 0, Acetyl ; 
 Ethyl ; C Z H V Ethylene ; C 3 # 5 , Glyceryl ; CN, Cyanogen. 
 
 4. What is the atom-fixing power or quantivalence of the differ- 
 ent atoms and radicals in the following symbols ? 
 
 H,Na - 2 = CO (NH^- -NO' 
 
 Potassic Sulphantimonite. Add Sodic Carbonate. Ammonic Nitrite. 
 
 fffNf0 2 2 (HO),(H,N)=( 
 
 Oxamide. Succinamic Acid. Tartar Emetic (dried). 
 
 5. If H 2 ; C 2 # 6 ; C Z H 6 S (alcohol) ; COCl, (phosgene gas) ; 
 C Z H+0 2 (acetic acid) and C Z H Z (oxalic acid) are saturated mole- 
 cules, what is the atomicity of the radicals HO (hydroxyl) ; C 2 H & 
 (ethyl) ; C z Ht (ethylene) ; C 2 H,0 (aldehyde) ; CO (carbonyl) ; 
 C Z H 3 (acetyl) and C 2 O 2 (oxalyl). 
 
CHAPTEE VIII. 
 
 CHEMICAL TYPES. 
 
 29. Types of Chemical Compounds. There are three 
 modes or forms of atomic grouping, to which so large a num- 
 ber of substances may be referred, that they are regarded as 
 molecular types, or patterns, according to which the atoms of 
 a molecule are grouped together. These types may be repre- 
 sented by the general formulae : 
 
 ii iin ini 
 
 R-R R,R-R or R-R-R [33] 
 
 i i i in ii in i 
 
 R, R, R=R or R, R-R-R. 
 
 It will be noticed, that in the first of these types a single uni- 
 valent atom or radical 1 is united to another single univalent 
 atom, that in the second a bivalent atom binds together two 
 univalent atoms or their equivalents, and that in the third a 
 trivalent atom binds together three univalent atoms, or their 
 equivalents. The dashes are used to separate what has been 
 called the central, the dominant, or the typical atom from those 
 which it thus unites into one molecular whole, and serve at 
 the same time to point out the parts of the symbol to which 
 its affinities are directed. Commas are used to separate the 
 subordinate atoms so united. It will be further noticed, that 
 in each case the quantivalence of the dominant atom is equal 
 to the sum of the quanti valences of the subordinate atoms, or 
 radicals, on either side ; and the peculiarity in each case consists 
 solely in the relations of the parts of the molecule which we 
 thus attempt to indicate by the symbol. The three compounds, 
 hydrochloric acid, water, and ammonia, 
 
 ii iin iiim 
 H-Cl, H,H=0, H,H,H--N, 
 
 1 Here, as elsewhere through the book, we use the symbol R for any 
 
 ii in 
 
 univalent, R for any bivalent, and R for any trivalent atom or radical. More- 
 over, to avoid unnecessary repetition, we shall for the future conform to the 
 general usage, and speak of the atoms of a radical as well as of those of an 
 element, and use the word " atom " as applying to both, although the usage 
 frequently involves an obvious solecism. 
 
CHEMICAL TYPES. 63 
 
 are generally taken as representatives of these types, and sub- 
 stances are described as belonging to the type of hydrochlo- 
 ric acid, to the type of water, or to the type of ammonia, as 
 the case may be. These substances, however, are regarded as 
 types in no other sense than that their molecules present the 
 same mode of grouping which is indicated above by the more 
 general symbols. Substances belonging to the same type may 
 have widely different properties. To the type of water be- 
 long the strongest alkalies and the most corrosive acids known. 
 In what, then, it may be asked, does the type outwardly con- 
 sist, or in what is it manifested ? for the grouping of the atoms 
 can only be a matter of inference. The answer is, that the 
 type of the molecules of a substance is manifested solely by 
 its chemical reactions. Substances belonging to the same type 
 are simply those whose reactions may be classed together ac- 
 cording to some one general plan. Thus water, alcohol, and 
 acetic acid are classed in the same type, because, when submit- 
 ted to the action of the same or similar reagents, they undergo 
 a like transformation, which seems to point to a similarity of 
 atomic grouping. 
 
 H, H-0 + PCI, = PC1 3 + H-Cl + H-Cl 
 
 Water. Phosphoric Chloride. Hydrochloric Acid. 
 
 H, 0,H 5 =0 + PG1 5 = PCkO + H-d+ C a ff,-a [34] 
 
 Alcohol. Phosphoric Oxz-chloride. Ethyl Chloride. 
 
 ff, G 9 ffnO=0 + PC1 5 = PC1 3 + H-a 
 
 Acetic Acid. Acetyl Chloride. 
 
 On studying these reactions, it will be seen that both the man- 
 ner in which the three compounds break up, and the probable 
 constitution of the products formed, point to the conclusion, that, 
 in each, one bivalent atom holds together two univalent atoms 
 or radicals. It will be found, in the first place, that in all three 
 cases the reaction consists primarily in the substitution of two 
 atoms of chlorine for one of oxygen in the original molecule. 
 It will appear, in the next place, that as soon as this dominant 
 atom, which holds together the parts of the molecule, is taken 
 away, each of the three molecules splits up into two others of a 
 similar type ; and lastly, it is evident from the third example 
 that one of the oxygen atoms of acetic acid stands in a very 
 different relation to the molecule from the other. All this 
 
64 CHEMICAL TYPES. 
 
 points to the inference just made. At least, these 'and a vast 
 number of similar reactions are best explained on this hypoth- 
 esis, and herein its only value lies and its probability rests. 
 In section 27 we have already given the symbols of a number 
 of chemical compounds so printed that they can be at once re- 
 ferred to one or the other of the three types here alluded to, 
 and it will not, therefore, be necessary to multiply examples in 
 this place. 
 
 30. Condensed Types. In the same way that a bivalent 
 atom may bind together two univalent atoms or their equiva- 
 lents, so, also, it may serve to bind together two molecules, and, 
 in like manner, a trivalent atom may bind together three mole- 
 cules into a more complex molecular group ; and thus are 
 
 formed what are called condensed types. We may represent 
 
 i n i 
 
 a double molecule of the type of water thus, RfRfR* but 
 it must be borne in mind that such a symbol stands for two 
 molecules, since, by the very definition, two molecules of the 
 same kind cannot chemically combine. We can, however, 
 
 solder them, as it were, into one molecular whole by substituting 
 
 i n 
 
 for the two univalent atoms R 2 a single bivalent atom R, 
 
 when we obtain a mode of molecular grouping represented by 
 
 inn 
 R 2 =R 2 =jR, [35] 
 
 which may be called the type of water doubly condensed. The 
 constitution of common sulphuric acid is best represented after 
 this type by the symbol, 
 
 H 2 =0 2 =S0 2 . [36] 
 
 n 
 The soldering atom is here the bivalent radical S0 2 . In like 
 
 manner, by using a trivalent atom, we can solder together 
 three molecules of the same water-type, as in the general 
 symbol, 
 
 i n m rQ7T 
 
 RfRfR, 
 
 which represents the type of water trebly condensed. In the 
 same way we may derive the symbol, 
 i i m n 
 
 
CHEMICAL TYPES. 65 
 
 which represents the type of ammonia doubly condensed. The 
 substance urea, one of the most important of the animal secre- 
 tions, is best represented by a symbol after this last type, 
 
 m ii 
 U 2 ,ff^N 2 -CO [39] 
 
 where the soldering atom is the bivalent radical carbonyl. 
 
 Chemists have also been led to admit the existence of what 
 are called mixed types, which are formed by the union of mole- 
 cules of different types soldered together by a single multiva- 
 lent atom or radical as before. Thus, the molecules of sul- 
 phurous acid may be regarded as formed of a molecule of water 
 soldered to a molecule of hydrogen by an atom of sulphuryl, 
 
 S0 2 ; thus, H-0-Hfm& H-H, united by S0 2 give 
 
 ff-0-S0 2 -H. [ 4 ] 
 
 So, also, the composition of a complex organic compound 
 called sulphamide, or sulphamic acid, is most simply expressed 
 when regarded as formed by the union of water and ammonia 
 soldered together by the same radical sulphuryl ; thus, from 
 
 in n m n 11 
 
 H, H=N-H, an* H- 0-H we have R, ff-N-S0 2 - 0-ff. [41] 
 
 Lastly, if we bind together on the same principle molecules 
 of the type of hydrochloric acid, we shall simply reproduce 
 the types of water and of ammonia, thus showing that all the 
 types are only condensed forms of the simplest. We must not, 
 therefore, attach to the idea of a chemical type any deeper sig- 
 nificance than that indicated above. It is simply a conven- 
 ient mode of classifying certain groups of chemical reactions, 
 and a help in representing them to the mind; and we may 
 regard the same substance as formed on one type or on the 
 other, as will .best he^ us to explain the reactions we are study- 
 ing. Moreover, it is frequently convenient to assume other types 
 besides those here specially mentioned. 
 
 31. Substitution. When cotton-wool is dipped in strong 
 nitric acid (rendered still more active by being mixed with 
 twice its volume of concentrated sulphuric acid), and after- 
 wards washed and dried, it is rendered highly explosive, and, 
 5 
 
CHEMICAL TYPES. 
 
 although no important change has taken place in its outward 
 aspect, it is found on analysis to have lost a certain amount of 
 hydrogen and to have gained from the nitric acid an equivalent 
 amount of nitric peroxide N0 2 in its place. 
 
 6 (ff lo ) O s ' becomes CJ[ff 7 (NO a ) 8 ) 5 . 
 
 Cotton. Gun-Cotton. 
 
 Under the same conditions glycerine undergoes a like change, 
 and is converted into the explosive nitre-glycerine, 
 
 3 (ff 8 )0 3 becomes C S (H,(NO^}0 3 . 
 
 Glycerine. Nitro-glycerme. 
 
 So, also, the hydrocarbon naphtha, called benzole, is changed 
 into nitro-benzole, 
 
 C B H Q becomes C 6 (H 5 ,N0 2 ). 
 
 Benzole. Nitro-benzole. 
 
 The last compound is not explosive, and the explosive nature 
 of the first two is in a measure an accidental quality, and is 
 evidently owing to the fact that into an already complex struc- 
 ture there have been introduced, in place of the indivisible atoms 
 of hydrogen, the atoms of a highly unstable radical rich in oxy- 
 gen. The point of chief interest for our chemical theory is that 
 this substitution does not alter, at least profoundly, the outward 
 aspect of the original compound. Every one knows how closely 
 gun-cotton resembles cotton-wool. In like manner nitro-glycer- 
 me is an oily liquid like glycerine, and nitro-benzole, although 
 darker in color, is a highly aromatic volatile fluid like benzole 
 itself. Products like these are called substitution products, and 
 they certainly suggest the idea that each chemical compound 
 has a certain definite structure, which may be preserved even 
 when the materials of which it is built are in part at least 
 changed. If in the place of firm iron girders we insert weak 
 wooden beams, a building, while retaining all its outward as- 
 pects, may be rendered wholly insecure, and so the explosive 
 nature of the products we have been considering is not at all 
 incompatible with a close resemblance, in outward aspects and 
 internal structure, to the compounds from which they were 
 derived. 
 
 The idea that each body has a definite atomic structure is 
 
CHEMICAL TYPES. 67 
 
 even more forcibly suggested by another class of substitution 
 products first studied by Dumas, in which atoms of chlorine, 
 bromine, or iodine have taken the place of the hydrogen atoms 
 of the original compound. Thus, if we act upon acetic acid 
 with chlorine gas, we may obtain three successive products, as 
 shown in the following table, although only the first and the 
 last have been fully investigated. 
 
 i n i 
 Acetic acid Cy^Oj or (C 2 H 3 0)-0-H 
 
 Chloracetic acid C 2 (H 3 CI)0 Z (C 2 H z Clb)-0-H 
 
 Dichloracetic acid C Z (H Z CI Z }0 Z (CfC$)-O-H 
 
 Trichloracetic acid C 2 (HCI S )0 Z (C Z C1 3 0)-0 -H 
 
 We cannot, however, replace the fourth atom of hydrogen 
 by chlorine ; and this fact seems to prove that there is a real 
 difference between this atom of hydrogen and the other three, 
 and gives an additional ground for the distinction we make 
 when we write the symbol of acetic acid after the type of water, 
 as in the second column. The three atoms of hydrogen in the 
 radical placed on the left-hand side of the dominant atom may 
 all be replaced by chlorine, but the single atom of hydrogen 
 placed on the right cannot. These products all resemble 
 acetic acid in that they form with the alkalies crystalline 
 salts, when the fourth atom of hydrogen is replaced by an 
 atom of sodium or potassium, as the case may be. 
 
 It was the study of these and similar substitution products 
 which first led to the conception of chemical types, and the 
 word as first used was intended to convey the idea of a definite 
 structure, although perhaps as yet unknown ; but as the theory 
 was extended more and more, and to widely different chemical 
 compounds, it was found that the first definite conception could 
 not be maintained, and the idea gradually assumed the shape we 
 have given it in the last section. Still, the facts from which 
 the original conception was drawn remain, and they point no 
 less clearly now than they did before to the existence of a def- 
 inite structure in all chemical compounds as the legitimate ob- 
 ject of chemical investigation. 
 
68 CHEMICAL TYPES. 
 
 32. Isomorphism. Closely associated with the facts of the 
 last section, which find their chief manifestation in substances 
 of organic origin, are the phenomena of isomorphism, which 
 are equally conspicuous among artificial salts and native min- 
 Fig. i. erals. There seems to be an intimate 
 
 connection between chemical composition 
 and crystalline form, and two substances 
 which under a like form have an anal- 
 ogous composition are said to be isomor- 
 phous. Thus the following minerals all 
 crystallize in rhombohedrons (Fig. 1,) 
 which have very nearly the same inter- 
 facial angles, and, as the symbols show, 
 they have an analogous composition. They are therefore 
 isomorphous. 
 
 Calcite or calcic carbonate 
 Magnesite or magnesic carbom 
 
 A j> /"<4= 
 
 \\ $1 n n n 
 
 iate(\ fv\ Mg^OfCC 
 
 ^J /Vk ^ __ _ 
 
 n n 
 
 Chalybdite or ferrous " ^ K^ ; Fe=0,=CO 
 
 '-_ n n n 
 
 Diallogite or manganous " ^ Mn=O z =CO 
 
 v* ^ n ii n 
 Smithsonite or zincic Zn=O^CO 
 
 The most cursory examination of these symbols will show 
 that they differ from each other only in the fact that one me- 
 tallic atom has been replaced by another. It is not, however, 
 every metallic atom which can thus be put in without altering 
 the form. This is a peculiarity that is cpnfined to certain 
 groups of elements, which for this reason are called groups of 
 isomorphous elements. Moreover, as a rule, there is a close re- 
 semblance between the members of any one of these groups in 
 all their other chemical relations. These facts, like those of the 
 last section, tend to show that the molecules of every substance 
 have a determinate structure, which admits of a limited substi- 
 tution of parts without undergoing essential change, but which 
 is either destroyed or takes a new shape when in place of one 
 of its constituents we force in an unconformable element. A 
 well-known class of artificial salts, called the alums, affords even 
 a more striking illustration of the principles of isomorphism 
 than the simpler example we have chosen ; but all the bearings 
 
 U- 
 
CHEMICAL TYPES. 69 
 
 of the subject cannot be understood without a knowledge of 
 crystallography, and we must therefore refer for further details 
 to works on mineralogy. 
 
 33. Rational Symbols. Chemical formula, like those of 
 the last few sections, which endeavor, by grouping together the 
 elementary symbols, to illustrate certain classes of reactions, 
 and to illustrate the manner in which a complex molecule may 
 break up, are called rational symbols, and are to be distinguished 
 from the simpler symbols used earlier in the book, which ex- 
 press only the relative proportions in which the elements are 
 combined, and which, since they are simply expressions of the 
 results of analysis on a concerted plan, are called empirical 
 symbols. Whether these rational symbols can be regarded in 
 any sense as indicating the actual grouping of the material 
 atoms is very doubtful, although facts like those stated above 
 would seem to indicate that such may be the case, at least to a 
 limited extent. It is difficult, for example, to resist the con- 
 clusion that in alcohol and its congeners the atoms C%H 5 are 
 grouped together in some sense apart from the rest of the 
 molecule ; but then we have no evidence of this grouping apart 
 from the reactions of these compounds, and, until greater cer- 
 tainty is reached, it is not best to attach a significance to our 
 symbols beyond the truths they are known to illustrate. 
 
 It is objected to the use of rational symbols that they bias 
 the judgment on the side of some theory, of which they are 
 more or less the exponents. But when they are used in the 
 sense stated above, this objection has no force, for the reactions 
 they prefigure are no less facts than the definite proportions they 
 conventionally represent, and we employ one mode of grouping 
 the symbols or another, as will best indicate the reactions we 
 are studying. Moreover, as science advances, we have every 
 reason to believe that we shall gain more and more knowledge 
 of the actual relations between the parts of a material molecule, 
 and as has already been intimated, there can hardly be a 
 doubt that in some cases our rational symbols do express even 
 now actual knowledge of this sort, however crude and partial 
 it may be. Our present typical symbols are indeed the ex- 
 pressions of partial generalizations, which, however imperfect, 
 have an element of truth. Hence it is that they have pointed 
 out new lines of investigation, have led to new discoveries, and 
 
70 CHEMICAL TYPES. 
 
 have been of the greatest value to science. They will doubt- 
 less soon be superseded by other rational symbols, expressing 
 other partial generalizations, to serve the same purpose in their 
 turn and be likewise forgotten. We must not, however, de- 
 spise these temporary expedients of science. They are not only 
 useful, but necessary, and cannot mislead the student if he re- 
 members that all such aids are merely the scaffoldings around 
 the science, on which the builders work. It is from this point 
 of view alone that we are to look at the whole idea of chemi- 
 cal atoms, which lies at the basis of our modern chemical 
 philosophy. That this idea is actually realized in the concrete 
 form which it takes in some minds, can hardly be believed. 
 The true chemical idea of the atom is more nearly represented 
 by the corresponding Latin word individuum. The atom is 
 the chemical individual, the uAit/m which the mind seeks to 
 repose for the time the indrfi^iality of that as yet undivided 
 substance we call an element. X \ 
 
 34. Graphic Symbols. A more graphic method of repre- 
 senting the relations between the atoms of a molecule than 
 that of our ordinary rational symbols has been contrived by 
 Kekule, and has a similar value in aiding the conceptions, and 
 thus facilitating the study of chemistry. In describing this 
 system we shall speak of the possibilities of combinations of 
 any polyad atom with monad atoms as so many centres of at- 
 traction or points of attachment, and, also, as so many affinities. 
 Kekule represents a monad atom, with its single centre, thus, 0, 
 while the symbols (T"7), C 7 Q, ( Q, &c., represent 
 polyad atoms of different atomicities. When the several affini- 
 ties are satisfied, the points are exchanged for lines pointing 
 
 in the direction of the attached atoms. Thus, the symbol >rJ< 
 
 represents a dyad atom with its two affinities satisfied by two 
 
 ii 
 monad atoms, as, for example, in a molecule of water H-Q-H. 
 
 In like manner the symbol 
 
 sents a molecule of nitric anhydride N. 2 O 5 , -and the symbol 
 
 (11 ii IU a molecule of sulphuric anhydride S0 3 . Mole- 
 
 .cules like these, in which all the affinities are satisfied, are said to 
 
CHEMICAL TYPES. 71 
 
 v 
 be saturated or closed, while the atomic group NO.^ represented 
 
 by > ^ ^N has one point of attraction still open, and, 
 
 ' i ' ) 
 therefore, acts as a monad radical. So, also, the molecular 
 
 group S0 2 represented by | PTiTT)' acts as a d ^ ad radi " 
 
 cal. 
 
 These graphic symbols enable us to illustrate several impor- 
 tant principles which could not readily be understood without 
 their aid. 
 
 First. In the examples given in this section thus far, the 
 quantivalence of a group of atoms of the same element is 
 
 equal to the sum of the quantivalences of all the atoms of the 
 
 v ii 
 group. Thus, in the molecule N. 2 5 , the group of two pentad 
 
 atoms presents ten affinities, and is saturated by the group of 
 five dyad atoms, which presents the same number of affinities 
 in return. So, also, in the molecule S0 3 , a group of three 
 dyad atoms just saturates the single hexad atom S. Such, how- 
 ever, is not necessarily the case, for it frequently happens that 
 the similar atoms of such groups are united among them- 
 selves, and that a portion of the affinities (necessarily always 
 an even number) are thus satisfied. For example, although 
 C is a tetrad atom, the hydrocarbons, G^H^ O 2 ff 4 , and G^H.^ are 
 all saturated molecules, as is shown by the following graphic 
 symbols, 
 
 and it is evident that in the first the two carbon atoms have 
 been united by two, in the second by four, and in the third by 
 six, of their eight affinities, while a corresponding number of 
 points to which hydrogen atoms might otherwise have been at- 
 tached are thus closed. 
 
 In like manner we have a well-known series of hydrocar- 
 bons, whose symbols are 
 
 GH^ GtiHfy G^H^ CH m C^H^ O 6 If u , &c., 
 
 the molecule of each one differing from that of the last by the 
 group OH 2 . In all these compounds the carbon atoms are 
 
72 
 
 CHEMICAL TYPES. 
 
 united among themselves at the smallest possible number of 
 points, as is shown, in a single case, by the following graphic 
 symbol, 
 
 and by constructing the graphic symbols of the other members 
 of the series, it will be easily seen that the number of affinities 
 thus closed is in every case equal to 2 n 2, while the number 
 remaining open is 4 n (2 n 2) = 2 n -f- 2, where n 
 stands for the number of carbon atoms in the molecule. Hence, 
 while the groups just mentioned form saturated molecules, the 
 atomic groups 
 
 Off 3 
 
 Methyl. 
 
 Ethyl. 
 
 C 3 ff, 
 
 Propyl. 
 
 Butyl. 
 
 AmyL 
 
 i &c., 
 
 act as univalent radicals. 
 
 :\ 
 
 The graphic symbol of ethyl is 
 , and in a similar way the graphic symbols of 
 
 the other radicals may be easily constructed. In like manner 
 may be also constructed the graphic symbols of the following 
 important compound radicals,* which forms a series parallel to 
 the first, and are all evidently dyads : 
 
 2 ff 4 
 
 Ethylene. 
 
 C 4 ff 8 
 
 Propylene. Butylene. 
 
 &c. 
 
 Amylene. 
 
 Here again the graphic symbols enable us to explain a remark- 
 able fact. These last atomic groups act not only as compound 
 radicals, but also form the molecules of definite hydrocarbons 
 (the first in the series being the well-known olefiant gas), and 
 the difference in these two conditions may be represented to 
 the eye, in the case of amylene, for example, as below : 
 
 Radical C S H 10 . 
 
 Hydrocarbon C 5 H 10 . 
 
 The molecule in the first case is open, and presents two points 
 of attraction, while in the second case it is closed. 
 
CHEMICAL TYPES. 73 
 
 The members of the two classes of hydrocarbon radicals 
 mentioned above are the characteristic constituents of an im- 
 portant class of compounds called alcohols, and hence they are 
 usually called alcohol radicals. If, in these atomic groups, we 
 substitute oxygen for a portion of the hydrogen, one atom of 
 oxygen always taking the place of two atoms of hydrogen, we 
 obtain still other series of radicals, which are the characteristic 
 constituents of several important organic acids, and belong to 
 the class of acid radicals, which will be defined in the next 
 chapter. Among the most important of the radicals thus de- 
 rived are those of the following series : 
 
 CHO C 2 H 3 3 H 5 G,H 7 C 5 H 8 
 
 Formyl. Acetyl. Propionyl. Butyryl. Valeryl. 
 
 and the student should construct the graphic symbol of each. 
 
 The compounds ' of carbon have been selected to illustrate 
 the apparent change of atomicity which frequently accompa- 
 nies the grouping together of similar atoms, because this ele- 
 ment is peculiarly susceptible of such a mode of combination, 
 and in fact the almost infinite variety of its compounds may be 
 traced to this circumstance. The same phenomenon, however, 
 is presented, although to a less marked degree, by other ele- 
 ments. Thus arises the remarkable fact that a group of two 
 atoms of a bivalent element has not unfrequently only the same 
 quantivalence as a single atom. For example, there are two 
 compounds of mercury and chlorine Hg=Cl 2 represented graphi- 
 
 cally by >y< and [_Hg^\ = C1 2 represented by ^?^y So also 
 
 we have Cu=0 and \_Gu^\=0 2 . We also frequently meet with 
 another illustration of the same principle in an important class 
 of tetrad elements whose atoms readily pair together, forming 
 an atomic group which is sextivalent. Thus are formed the 
 well-known compounds 
 
 When these same elements enter into combination by single 
 atoms, they are almost invariably bivalent, and thus we have, 
 in several cases, two very distinct classes of compounds, the 
 one formed with the single and the other with the double atom 
 of the element ; for example, 
 
Fe=Cl 2 and \_Fe^\lCl 6 ' Fe--0 and [Fe. 2 li0 3 
 
 It will be noticed that although in the compounds of the 
 second class the quantivalence of the single atoms is twice as 
 great as it is in the first, yet their atom-fixing power is only 
 increased by one half, and hence the name of sesqui -oxides 
 or sesqui-chlorides, &c., which is frequently applied to them. 
 
 In order to distinguish the groups of similar atoms whose 
 affinities are all open, from those groups where the affinities are 
 in part closed by the union of the atoms among themselves, we 
 may, as above, enclose the symbols of the last in brackets ; and 
 this rule will generally be followed. In most cases, however, 
 the relations of the parts of the symbol are sufficiently evident 
 without this aid. 
 
 Secondly. The graphic symbols illustrate another important 
 theoretical principle, which, although almost self-evident, might 
 be overlooked if not dwelt upon specially ; namely, that 
 on the multivalence of one or more of its atoms depends the 
 integrity of every complex molecule. According to our pres- 
 ent theories, no molecule can exist as an integral unit unless its 
 parts are all bound together by such atomic clamps. More- 
 over, the whole virtue of a compound radical consists in the 
 circumstance that it is an incomplete structure of the same sort, 
 and its quantivalence is in every case equal to the number of 
 univalent atoms (or their equivalents) which are required to 
 complete it, or which it may be regarded as having lost. 
 Hence the law of Wurtz finds a perfect expression in this sys- 
 tem of graphic notation. 
 
 Thirdly. The graphic symbols illustrate most forcibly the 
 relations of the parts of a complex molecule. Thus, for ex- 
 ample, the symbols of alcohol and acetic acid given below show 
 that in these compounds the dominant 
 atom of oxygen acts as a bond uniting 
 a complex radical to a single monad 
 atom. They also show how it is 
 possible that three of the atoms of 
 hydrogen in acetic acid may stand in 
 a very different relation to the mole- 
 cule from the fourth (31). Again 
 they show that the molecule of acetic A^tkAcid. 
 
CHEMICAL TYPES. 75 
 
 fact that one dyad atom has taken the place of two monad 
 atoms; and, lastly, they give form to the idea of chemical 
 types, so far as it has any real significance. When the com- 
 position of a compound is represented in this way, all the 
 accidental or arbitrary divisions of our ordinary notation dis- 
 appear, and only those are preserved which are fundamental. 
 We gain thus more accurate conceptions of molecular struc- 
 ture. We understand better the relations of 'the various com- 
 pound radicals (compare 28), and, above all, we thus realize 
 the full meaning of the fundamental tenet of our new philoso- 
 phy, which holds that each chemical molecule is a completed 
 structure bound together in all its parts by a system of mutual 
 attractions. 
 
 There is another system of graphic symbols, frequently used 
 in works on modern chemistry, which has some advantages 
 over the one just described. In this system the atoms are 
 represented by small circles circumscribing the ordinary sym- 
 bol, and the atomicity is indicated by dashes radiating from 
 these circles. A few examples will sufficiently illustrate the 
 application of this method. 
 
 
 
 ll l II 
 
 -- ---- ---- 
 
 Water I I I 
 
 Alcohol. Acetic Acid. 
 
 C 2 H 5 -0-H. C z H a O.O-H. 
 
 It is obvious, however, that the circles here used 'are not es- 
 sential, and if we omit them, and only use dashes between the 
 dominant atoms, and also, for convenience in printing, bring the 
 whole expression into a linear form, using commas to separate 
 disconnected atoms, and such other signs as may be necessary to 
 avoid ambiguity, we have at once the ordinary system of nota- 
 tion adopted in this book. The graphic symbols last described 
 are merely an expansion of this system. Nevertheless, the prac- 
 tice of developing the ordinary symbols into either of the more 
 graphic forms will tend to impress the full meaning of the 
 symbols on the mind of the student, and will thus greatly aid 
 him in acquiring a clear conception of the theory of modern 
 chemistry. 
 
76 CHEMICAL TYPES. 
 
 We may, however, extend the use of dashes so as to indicate 
 the relations of all the parts of a complex molecule by our or- 
 dinary notation. Thus we may write the symbol of alcohol 
 
 or that of acetic acid 
 
 and these expanded symbols may frequently be used to ad- 
 vantage in place of the graphic forms. When thus developed, 
 the symbol indicates the quantivalence of each of the atoms of 
 the molecule, and in every case, if the symbol is correctly 
 written, the number of dashes will be one half of the total 
 quantivalence of all the atoms which are thus grouped together, 
 for each dash evidently represents two affinities. 
 
 The remarks at the close of the last section apply, of course, 
 still more forcibly to such bold and material conceptions as 
 these graphic symbols appear to represent, and when we re- 
 call the hooked atoms of an elder philosophy, we cannot but 
 , smile to think how closely our modern science has reproduced 
 what we once considered as strange and grotesque fancies. But, 
 absurd as such conceptions certainly would be, if we supposed 
 them realized in the concrete forms which our diagrams em- 
 body, yet, when regarded as aids to the attainment of general 
 truths, which in their essence are still incomprehensible, even 
 these crude and mechanical ideals have the very greatest value, 
 and cannot well be dispensed with in the study of science. 
 
 Questions and Problems. 
 
 1. To what types may the following symbols be referred, and what 
 is the quantivalence of the different compound radicals here distin- 
 guished ? Study with the same view the symbols already given in 
 the previous chapter. 
 
 Benzole. Oil of Bitter Almonds. Ethylene. Glycollic Acid. 
 
 H-0-(C 7 H.O) L 
 
 Phenic Acid. ' Benzoic Acid. Glycol. Oxalic' Acid. 
 
 Aniline. ^ Benzamide. 
 
 Ethylene diamine. Oxamide. 
 
CHEMICAL TYPES. 77 
 
 H, H-N-( C 2 H 2 0)-0-H H, H--N-( C 2 2 )- 0-H 
 
 Glycocol. Oxamic Acid. 
 
 ff, (C 7 H 5 0)-N-(C 2 H 2 0)-0-H H, H=N-(C 2 2 )-0-(C 2 ff 5 ) 
 
 Hippuric Acid. Oxamethane. 
 
 2. Analyze the following reactions, and show that by comparing 
 the reactions in each group, the typical structure of the various 
 compounds may be inferred. 
 
 Cl-Cl + JJ-H = ffCl + HCl 
 
 Chlorine gas. Hydrogen gas. Hydrochloric Acid. Hydrochloric Acid. 
 
 Cl-Cl + (C 7 H 5 0)-H = (C 7 H 5 0)-Cl + HCl 
 
 Oil of Bitter Almonds. Benzoyl Chloride. 
 
 ff-Cl + K-O-H = KOI + H-O-H 
 
 Potassic Hydrate. Potassic Chloride. Water. 
 
 ff-Cl + (C Z H 6 }-0-H = (C 2 H 5 )-Cl + H-O-H 
 
 Alcohol. Ethylic Chloride. 
 
 H,H-S + Pi 07, = P-=C1 3 ,S + HOI + HCl 
 
 Sulphohydric Acid. Phosphoric Chloride. 
 
 H, ( C 2 H, 0)-S + Pi Cl & = Pi (74, S + ( C 2 H S 0)- 01 + HCl 
 
 Thiacetic Acid. Acetyl Chloride. 
 
 KrOfHi + ((70), H*N = K 2 =0 2 =(CO) + H, H, 
 
 Potassic Hydrate. Cyanic Acid. Potassic Carbonate. Ammonia. 
 
 *- ^^- 
 
 Cyanic Ether. Ethylamine. 
 
 3. What would be the symbols of cyanic acid and cyanic ether (see 
 last problem), on the supposition that they contain the radical cyan- 
 ogen, and are formed after the water type ? Is the following reaction 
 compatible with that last given ? 
 
 K-O-H + (CJT 6 )-0-(CN) = (C 2 H 5 )-0-H+ K- 
 
 Cyanetholine. Alcohol. Potassic Cyanate. 
 
 and if not, what conclusion must you draw in regard to the two 
 compounds cyanic ether and cyanetholine ? 
 
 4. What bearing have the phenomena of substitution on the doc- 
 trine of chemical types ? Does the circumstance that the proper- 
 
 1 This product in the actual process is decomposed by the excess of potash 
 into potassic carbonate and ammonia. 
 
78 CHEMICAL TYPES. 
 
 ties of the substitution products are frequently quite different from 
 those of the original substance invalidate the doctrine ? 
 
 5. How does the action of chlorine on acetic acid indicate that 
 this compound is fashioned after a determinate type ? On what 
 particular fact does this evidence chiefly rest V 
 
 6. What bearing have the phenomena of isomorphism on the doc- 
 trine of types ? Enforce the argument by some familiar illustra- 
 tion. 
 
 7. The radical allyl C S H 5 is univalent in oil of garlic (C 3 H,).=S, 
 and in allylic alcohol (C^H^-O-H, but atrivalent in glycerine 
 (C 3 H & )=OfH 3 . Moreover, this radical when set free doubles, forming 
 a volatile hydrocarbon oil, which has the composition (C 3 F 5 )=(C 3 ^T 5 ), 
 and which combines directly with bromine, the resulting product hav- 
 ing the symbol (C 3 /Z 5 )-(C 3 F 5 )i J Br 4 . Represent these symbols by the 
 graphic method, and thus explain the different relations of the 
 radical. 
 
 8. Represent the symbols of phenic acid and benzoic acid by the 
 second graphic method, and explain why the radical phenyl (C 6 Z-) 
 and benzoyl (C 7 77 5 0) are only univalent. 
 
 9. Why is it that the addition of the atoms CH Z does not change 
 the atomicity of a radical ? 
 
 10. What is the quantivalence of At in the symbol [Al-Al~]iCl 6 f 
 Is there any difference in the quantivalence of Fe in the two com- 
 pounds Fe =OfCO and [Fe-.Fe]10JS0 a ? Answer the questions by 
 the aid of graphic symbols. 
 
 11. Is there any difference in the quantivalence of nitrogen in 
 potassic nitrite K-O-NO and potassic nitrate K-0-NO Z f 
 
 12. Represent by graphic symbols the difference between cyanic 
 ether and cyanetholine (see problems 2 and 3 above). 
 
 13. The symbol [Hg 9 "]Cl t represents a single molecule, while 
 Na^CL represents two molecules, and would be more properly writ- 
 ten 2NaCl. What is the difference in the two cases ? 
 
 14. Represent by the graphic method the symbols of potassic car- 
 bonate Kf0 2 =(CO) and potassic oxalate #=0=(C 2 2 ), and show 
 that both form a perfect molecular unit. 
 
 15. Represent by the graphic method the following symbols ; 
 
 fffOf( O s ff 6 ) (Propyl Glycol.) ; 
 Hf 2 =( C S H0) (Lactic Acid.) ; 
 -> &<! 
 
CHEMICAL TYPES. 79 
 
 ff z = Of( G Z E Z 2 ) (Malonic Acid) ; 
 S 2 = 2 =( C 3 3 ) (Unknown), 
 
 and thus show that they are formed after the same type. 
 
 16. What is the atom-fixing power or .quantivalence of the ele- 
 ments and radicals, which appear in the various symbols given in 
 this chapter ? Develop these symbols, and show that they repre- 
 sent in each case a single perfect molecule. 
 
 N. B. The student should practice developing the ordinary mole- 
 cular symbols into the graphic forms described above, until he is per- 
 fectly familiar with the method, and has acquired a clear conception 
 of the different types of molecular structure. 
 
 y 
 
 & J 
 
 (J-f i 
 
 ~ I 
 
 t H . ' J t)^~4.^ \ m,tk H 
 
 / ' ' 
 
 SJL&* 
 
 C- 
 
 s? 
 
 M^V- ^ ^Lr^ ^r; 
 ^^vvw ^^ ^ 
 
 a //r^ <xr -^ c "^ 
 
CHAPTER IX. 1 
 
 BASESi ACIDS, AND SALTS. 
 
 35. Hydrates, Alkalies, Bases. It is not unfrequently the 
 case that the technical terms of a science remain in use long 
 after they have lost their original meaning. This is peculiarly 
 true of those which we have placed at the head of this section. 
 They have, with the exception of the first, come down to us 
 from the period of alchemy, and are still retained in the lan- 
 guage of trade and in many works on practical science, with a 
 peculiar meaning which they have acquired during the last 
 hundred years under the teaching of the dualistic theory. 
 Since they, in many cases at least, suggest erroneous concep- 
 tions in regard to the constitution of chemical compounds, it 
 would be well if they could be discarded altogether ; but, as 
 this is impracticable, we must endeavor to give to them as 
 definite a meaning as possible. 
 
 The term " hydrate " is applied to a class of compounds which 
 were formerly supposed to contain water as such, but which are 
 now believed to have no closer relation to water than is indi- 
 cated by the circumstance that they have the same type, and 
 may be formed from water by replacing one of its hydrogen 
 atoms with some metal. Thus, by acting on water with potas- 
 sium, we obtain potassic hydrate ; or, if we use ^sodium, we ob- 
 tain sodic hydrate. 
 
 2ff-0-H + K-K = ^K-O-H + H-H 
 
 Water. Potassium. Potassic Hydrate. Hydrogen Gas. 
 
 [42] 
 2ff-0-H+Na-Na = 2 Na-O-H + HH 
 
 Water. Sodium. Sodic Hydrate. Hydrogen Gas. 
 
 Both of these hydrates, and also those of the very rare but 
 closely allied metals, lithium, caesium, and rubidium, are very 
 
 1 In studying this chapter the student should endeavor to remember the 
 names and symbols of the different compounds mentioned. Hitherto we 
 have been chiefly employed with the forms of the symbols, and this exercise 
 of the memory has not been expected. 
 
BASES, ACIDS, AND SALTS. 81 
 
 soluble in water, and yield solutions which corrode the skin, and 
 convert the fats into soaps. To all the substances known to 
 them which possessed these caustic qualities the alchemists 
 gave the name of alkalies, and this term is now applied to the 
 five hydrates just enumerated. The first two of these are 
 commercial products, and have important applications in the 
 arts. They all differ from the hydrates of other metals in that 
 they cannot be decomposed by heat alone. 
 
 Again, if* we act on water with calcium or magnesium, we 
 obtain calcic or magnesic hydrate ; but the double atom of 
 water is then decomposed by these bivalent metals. 
 
 H: 2 =0 2 =If 2 + Ca = Ca=0 2 =K 2 + H-H 
 
 Water. Calcium. Calcic Hydrate. Hydrogen Gas. 
 
 fff0 2 =H 2 J^Mg Mg=0,=ff 2 + H-H 
 
 Water. Magnesium. Magnesic Hydrate. Hydrogen Gas. 
 
 These two hydrates, as well as those of the allied metals, 
 barium and strontium, although much less soluble in water 
 than the alkalies, still dissolve in this common solvent to a 
 limited extent, and manifest decided caustic qualities. When 
 dry they have an earthy appearance, and hence are frequently 
 known as the alkaline earths. They also differ from the true 
 alkalies in the fact that they are readily decomposed by heat ; 
 and since they are then resolved into water and a metallic 
 oxide, as the following reaction shows, the opinion formerly 
 entertained in regard to their composition was not unnatural. 
 
 Mff-=0 2 =Jff 2 = MgO + H 2 [44] 
 
 When heated. 
 
 Moreover, when the anhydrous oxides are mixed with water, 
 they enter into direct union with a portion of the liquid. This* 
 combination is usually attended with the evolution of great 
 heat, and the process is known as slaking. 
 
 Ca + ff 2 = Car 2 =ff 2 . [45] 
 
 There are many other metallic hydrates which are still more 
 
 readily decomposed by heat. These, as a rule, cannot be 
 
 formed by the direct union of the corresponding metallic oxide 
 
 and water, but may be obtained by adding to a solution of 
 
 6 
 
82 BASES, ACIDS, AND SALTS. 
 
 a salt of the metal one of the soluble hydrates mentioned 
 above. Thus, 
 
 ( Cu (7/ 2 + ZNa-O-H-}- Aq) = ( Cu- 2 =H 2 + 2Na Cl + Aq) 
 
 Cupric Chloride. Cupric Hydrate. Sodic Chloride. 
 
 [46] 
 
 (ZnCl,_ + 2K-0-H+ Aq) (Zn-OfH,_ + 2KCI + Aq) 
 
 Zincic Chloride. Zincic Hydrate. Potassic Chloride. 
 
 Ferric Chloride. Ferric Hydrate. Baric Chloride. 
 
 The hydrates are regarded by some chemists as compounds 
 of the metal with the compound radical hydroxyl, and their 
 symbols are then written after a simpler type, thus, 
 
 m?" 
 
 Ca=(ffO), Fe-(HO) 2 
 
 Calcic Hydrate* Ferrous Hydrate. Chromic Hydrate. 
 
 Ammonia. Closely allied to these metallic hydrates is a 
 very remarkable compound, formed by dissolving ammonia 
 gas, NH%, in water. Although the product resembles, in many 
 of its physical relations, a simple solution of gas in water, yet 
 the compound in all its chemical relations acts like a metallic 
 hydrate, / 
 
 NHj +/ H,0 = NH.-O-H 
 
 Ammonia Gas. Water. Ammonic Hydrate. 
 
 which has led chemists to write its symbol after the type of 
 water, and to assume the existence of a univalent compound 
 
 radical NH, to which has been given the name of ammonium. 
 Metallic Oxides or Basic Anhydrides. Closely allied to 
 the metallic hydrates, in the relation we are now considering, 
 are many of the simple compounds of the metals with oxygen 
 "which are called in general metallic oxides. Such compounds 
 as 
 Ca-0 Ba-0 Pl-0 Fe-0 Ou=0 Ag?0 
 
 Calcic Oxide. Baric Oxide. Plumbic Oxide. Ferrous Oxide. Cupric Oxide. Argentic Oxide. 
 
 may be regarded as formed from one or more molecules of water, 
 by replacing all the atoms of hydrogen with those of some metal ; 
 and these oxides as well as the hydrates before mentioned are 
 frequently classed together under the common title of bases, 
 although it would be best to confine this term to the metallic 
 
BASES, ACIDS, AND SALTS. 83 
 
 hydrates alone, and to distinguish the basic oxides as basic 
 anhydrides. (37) 
 
 Salts. The atoms of hydrogen still remaining in a metallic 
 hydrate may be replaced with the atoms of a well-defined class 
 of non-metallic elements and compound radicals ; and, for a 
 reason which will soon appear, the replacing atoms are called 
 acid or negative radicals. 1 
 
 From this replacement results a new class of compounds we 
 call salts. Thus, 
 
 K-O-H gives K-O-Cl, also K~0-N0 2 and K-0~(C 2 ff s O) 
 
 Potassic Hydrate. Potassic Hypochlorite. Potassic Nitrate. Potassic Acetate. 
 
 Ca=0,=ff 2 gives Ca=OfSO a Ca=0 2 =CO Ca=0 2 =(O 2 ff 3 0) 2 
 
 Calcic Hydrate. Calcic Sulphate. Calcic Carbonate. Calcic Acetate. 
 
 36. Acids. Opposed in chemical properties to the so- 
 called bases is another very important class of compounds 
 called acids. They derive their name from the fact that they 
 are generally soluble in water and have a sharp or sour taste, 
 although there are many exceptions to the rule. Like the 
 bases, they all contain hydrogen ; but this hydrogen can no 
 longer be replaced by non-metallic elements or negative radi- 
 cals, but only by metallic elements and positive radicals, and it 
 is herein that the chief distinction lies. Moreover, the opposi- 
 tion of these two classes of compounds also appears in the fact 
 that, while in bases the replaceable hydrogen atoms are united 
 to a metallic atom or positive radical, which for this reason we 
 frequently call a basic radical, in the acids, on the other hand, 
 
 1 The word radical, as used in chemistry, stands for any atom or group of 
 atoms, which is, for the moment, regarded as the principal constituent of the 
 molecules of a given compound, and which does not lose its integrity in the 
 ordinary chemical reactions to which the siibstance is liable. The distinc- 
 tion between basic and acid radicals (or positive and negative radicals as they 
 are more frequently called) will become clear as we advance. It is sufficient 
 for the present to state that, although these terms imply an opposition of rela- 
 tions rather than a difference of qualities, yet, as a general rule, the metallic 
 atoms are basic radicals, while the non-metallic atoms are acid radicals. 
 Moreover it may be added, that among compound radicals those consisting of 
 cafbon and hydrogen alone are usually basic, and those containing also oxy- 
 gen usually acid; and, further, that of the two most important radicals con- 
 taining nitrogen, ammonium (JV77 4 ) is strongly basic, and cyanogen ( CN) as 
 decidedly acid. In this book, with few exceptions, the basic radicals are 
 always placed on the left-hand, and the acid radicals on the right-hand side, 
 of the molecular symbols. 
 
84 BASES, ACIDS, AND SALTS. 
 
 these same hydrogen atoms are united as a rule to a non- 
 metallic atom or negative radical, frequently, also, called as 
 above an acid radical. In most cases there is a vinculum 
 which unites the two parts of the molecule ; and both in acids 
 and in bases this vinculum consists usually of one or more 
 oxygen atoms, although in a large class of acids the hydrogen 
 atoms are united directly to the radical without any such con- 
 nection. The acids of this class have by far the simplest 
 constitution ; and we will give examples of these first, adding 
 in each case a reaction to illustrate the acid relations of the 
 compound. In studying these reactions, it must be borne in 
 mind that the evidence of acidity is in each case to be found in 
 the fact that one or more of the hydrogen atoms of the com- 
 pound may be replaced by positive radicals or metallic atoms. 
 This replacement may be obtained in one of four ways, by 
 acting on the acid, either with the metal itself, or with a metallic 
 oxide, or with a metallic base, or with a metallic salt. 
 
 (2HCI + Aq) + NaNa = (2 Na Cl + Aq) + IS-SS 
 
 Hydrochloric Acid. Sodium. Sodic Chloride. 
 
 (ZHCl + Aq) + ZnO = (ZnCl 2 + H.,0 + Aq) 
 
 Zincic Oxide. Zincic Chloride. 
 
 [47] 
 (HBr + K-O-H + Aq) = (KBr + 
 
 Hydrobromic Acid. Potassic Hydrate. Potassic Bromide. 
 
 = Agl + (ff-0-NO, 
 
 Hydriodic Acid. Argentic Nitrate. Argentic Iodide. Nitric Acid. 
 
 We will next give examples of more complex acids, in which 
 the two parts of the molecule are united by a vinculum of oxy- 
 gen atoms. 
 
 (H-0-(C Z H,0) + Na-0-H+ Aq) = (Na-0-(C 2 H 3 0) + H, O+Aq) 
 
 Acetic Acid. ' Sodic Hydrate. Sodic Acetate. 
 
 (HfOfSO a -\-Aq) 4- CuO = (Cu=OfSO t 
 
 Sulphuric Acid. Cupric Oxide. Cupric Sulphate. 
 
 (HfOfPO + 3K-0-H 4- Aq) = (KfOfPO-\ 
 
 Phosphoric Acid. Potassic Hydrate. Potassic Phosphate. 
 
 Such acids as these are called oxygen acids. Like the 
 hydrates, they may be regarded as compounds of hydroxyl, 
 but with negative instead of positive radicals, thus : 
 
BASES, ACIDS, AND SALTS. 85 
 
 ffO-N0 2 (ffO) 2 =SO, 
 
 Nitric Acid. Sulphuric Acid. Phosphoric Acid. 
 
 This mode of writing the symbols is not only frequently con- 
 venient, but has been of real value by bringing out unex- 
 pected and important relations. It does not, however, indicate 
 any fundamental difference of opinion in regard to the consti- 
 tution of these hydrates, and this at once appears when the 
 symbols are put into the graphic form. 
 
 When an acid, like acetic acid, contains but one atom of hy- 
 drogen, which is replaceable by a metallic atom or a positive 
 radical, it is called monobasic ; when, like sulphuric acid, it con- 
 tains two such hydrogen atoms, it is called dibasic ; when, like 
 phosphoric acid, it contains three, it is tribasic, &c. Moreover, 
 one evidence of this difference of basicity is found in the fact 
 that whereas a monobasic acid can only form one salt with a 
 univalent radical, a bibasic acid can form ' two, and a tribasic 
 three. Thus, while we have only one sodic nitrate, there are 
 two sodic sulphates and three sodic phosphates. 
 
 Sodic Nitrate. Acid Sodic Phosphate. 
 
 ffJTcrOfSOt HNofOfPO 
 
 Acid Sodic Sulphate. Neutral Sodic Phosphate. 
 
 Neutral Sodic Sulphate. Basic Sodic Phosphate. 
 
 There* is, however, but one calcic sulphate, for, since the cal- 
 cium atoms are bivalent, a single one is sufficient to replace 
 both of the hydrogen atoms in the acid. 
 
 37. Acid Anhydrides. Besides the acids properly so called, 
 all of which contain hydrogen, there is another class of com- 
 pounds which bear the same relation to the true acids which the 
 metallic oxides bear to the true bases. To avoid confusion, com- 
 pounds of this class have been distinguished as anhydrides^ and 
 they may be regarded as one or more molecules of water in 
 which all the hydrogen has been replaced by negative or acid 
 radicals. As among the most important of these we may 
 enumerate Sulphuric Anhydride SOfO or SO& Nitric Anhy- 
 
 1 More precisely acid anhydrides, but as the basic anhydrides are usually 
 called simply metallic oxides, the qualifying term is seldom added. 
 
86 BASES, ACIDS, AND SALTS. 
 
 dride (N0 2 ) 2 =0 or N. 2 5 , Carbonic Anhydride 00=0 or C0 2 , 
 
 i , 
 
 Phosphoric Anhydride (P0. 2 ) 2 = or P 2 5 , and Silicic Anhy- 
 
 IV 
 
 dride Si^0 2 . Most of the anhydrides unite directly with 
 water to form acids, and several of the acids, when heated, 
 give off water and are resolved into anhydrides. [Compare 
 44 and 45.] 
 V- ^ H,0 -f SO, = R 2 =0./S0 2 
 
 ^ -3R 2 + P 2 5 = Zff^OfPO 
 
 [49] 
 ff/O/Si = SiO, + 
 
 Silicic Acid. SUicic Anhydride. 
 
 v ZfffOfB = R 2 3 + 
 
 Boric Acid. Boric Anhydride. 
 
 Moreover in many cases these anhydrides will combine di- 
 rectly with the metallic oxides to form salts ; and the reac- 
 tions are best indicated by a rational formula, which represents 
 the oxide and anhydride as radicals in the resulting compound. 
 Thus, baric oxide burns in the vapor of sulphuric anhydride, 
 yielding baric sulphate ; and lime also unites directly with the 
 same anhydride, although with less energy, forming calcic sul- 
 phate. 
 
 BaO + S0 3 = BaO, S0 3 and CaO + S0 3 = CaO, S0 3 
 
 We are thus led to the old formulas of the dualistic. system, 
 according to which the metallic oxides were the only true 
 bases, the anhydrides were the only true acids, and the two 
 were regarded as paired in all true salts. But, although in 
 its modern theories our science has fortunately left the ruts to 
 which the dualistic ideas for so long limited its progress, yet it 
 must be remembered, that, according to our present definitions, 
 these dualistic formulae are perfectly legitimate, and still give 
 the simplest exposition of a large number of important facts. 
 
 38. Salts. The definition of the term " salt " has been clearly 
 implied in the definitions of " base " and " acid " already given. 
 It is any acid in which one or more atoms of hydrogen have 
 been replaced with metallic atoms or basic radicals ; it is any 
 base in which the hydrogen atoms have been more or less re- 
 placed by non-metallic atoms or acid radicals ; or it may be the 
 
BASES, ACIDS, AND SALTS. 87 
 
 product of the direct union of a metallic oxide and an anhy- 
 dride. A neutral salt is, properly speaking, one in which all 
 the hydrogen atoms, whether of base or acid, have been re- 
 placed as just stated. A basic salt is one in which one or 
 more of the hydrogen atoms of the base remain undisturbed, 
 and therefore still capable of replacement by acid radicals. An 
 acid salt is one in which one or more of the hydrogen atoms of 
 the acid remain undisturbed, and therefore capable of replace- 
 ment by basic radicals. 
 
 But, besides the basic and acid salts, which come under these 
 definitions, there are also others which can be most simply de- 
 fined as consisting of several atoms of the metallic oxide to one 
 of anhydride, or of several atoms of anhydride to one of the 
 metallic oxide. 
 
 As an example of acid salts of the second class we have, be- 
 sides the two sodic sulphates mentioned on page 61, also a 
 third, which may be written Na 2 0, 2S0 3 . This is easily ob- 
 tained by simply heating the acid sulphate. 
 
 , Na=0 2 =S0 2 ) = Na 2 0, 2S0 3 + IH 2 (o) [50] 
 
 Acid Sodic Sulphate. Sodic Bisulphate. Water. 
 
 If heated to a still higher temperature, one atom of the anhy- 
 dride is set free, and the salt falls back into the neutral sul- 
 phate. 
 
 Na*0 9 2S0 3 = Na 2 0,S0 3 + 
 
 Bisulphate. Neutral Sulphate. Anhydride. 
 
 This reaction justifies the dualistic form given to the symbol ; 
 but other relations of the bisulphate may be better expressed 
 by the following typical formula, 
 
 fSOt + S0 3 
 
 Sodic Bisuphate. Neutral Sulphate. Anhydride. 
 
 in which a group of two atoms of 80%, soldered together by 
 one atom of oxygen, acts as a bivalent radical. 
 
 As an example of a basic salt of the second class we have, 
 in addition to the two plumbic acetates of the normal type, 
 
 Pb- Of( 2 ff 3 0) 2 and PI- Of( O 2 H 3 0), H 
 
 Neutral Plumbic Acetate. Basic Plumbic Acetate. 
 
88 BASES, ACIDS, AND SALTS. 
 
 a third salt containing three times as much lead, 
 
 (P&-0-Pb-O-A)*Of(G&tyx [51] 
 
 Triplumbic Acetate. 
 
 in which a group of three atoms of lead, soldered together by 
 two atoms of oxygen, acts as a bivalent radical. It is evident 
 that, theoretically, any number of multivalent radicals might be 
 united in this way, and also that the complex radical thus 
 formed will have a quanti valence easily determined by esti- 
 mating the number of bonds which remain unsatisfied ; but, 
 practically, the grouping cannot be carried to a very great ex- 
 tent, for the stability of the radical diminishes with its com- 
 plexity, and a condition is soon reached when it can no longer 
 sustain, if we may so express it, its own weight. Moreover, 
 while some radicals, like the atoms of lead, copper, mercury, 
 and iron, are prone to group themselves in this way, the larger 
 number show but little tendency to this mode of union. 
 
 The symbols of these acetates may also be written on the 
 dualistic type, which represents them as compounds of plumbic 
 oxide, Pb 0, and acetic anhydride, G 4 H 6 3 . We have, then, 
 
 PbO, O,ff G 3 and 3PbO, C 4 ff0 3 ' [52] 
 
 Neutral Plumbic Acetate. Triplumbic Acetate. 
 
 and we may thus best illustrate the important fact that the 
 second compound is prepared by combining/Vith the first an 
 additional quantity of plumbic oxide. 
 
 It will appear on reviewing the symbols of the acids, bases, 
 and salts given in this section, that, in by far the greater num- 
 ber, the two parts of the molecule are held together by one or 
 more atoms of oxygen, which act as a vinculum. Such com- 
 pounds are called oxygen salts, using the word salt, as is fre- 
 quently done, to stand for acids and bases, as well as for the 
 true metallic salts; and in fact they all belong to the same 
 type of chemical compounds. Since oxygen plays so impor- 
 tant a part in terrestrial nature, we might well expect that 
 these oxygen compounds would hold a very conspicuous place 
 in our chemical science, and such is indeed the fact. Dur- 
 ing the dualistic period the study of chemistry was almost 
 wholly confined to the oxygen compounds, and, even now, 
 they occupy by far the largest share of a chemist's attention. 
 
BASES, ACIDS, AND SALTS. 89 
 
 There is, however, another element, namely, sulphur, which 
 is capable of filling the place occupied by oxygen in many 
 of its compounds, and thus may be formed a distinct class of 
 bodies which are called sulphur salts. These compounds are 
 not nearly so numerous as the oxygen salts, and have not been 
 so well studied, so that a few examples will be sufficient to 
 illustrate their general composition, and the relations which 
 they bear to the corresponding oxygen compounds. 
 
 Oxygen Salts. Sulphur Salts. 
 
 H-O-H H-S-H 
 
 Water or Hydric Acid. Sulphohydric Acid. 
 
 K-O-H K-S-H 
 
 Potassic Hydrate. Potassic Sulphohydrate. 
 
 Potassic Carbonate. Potassic Sulphocarbonate. 
 
 39. Test-Papers. The soluble bases and acids, when dis- 
 solved in water, cause a striking change of color in certain 
 vegetable dyes, and these characteristic reactions give to the 
 chemist a ready means of distinguishing betweeYi these two 
 important classes of compounds. The two dyes chiefly used 
 for this purpose are turmeric and litmus, and strips of paper 
 colored with the dyes are employed in testing. Turmeric 
 paper, which is naturally yellow, is turned brownish red by 
 bases, while litmus paper, which is naturally blue, is turned 
 red by acids, and in both cases the natural color is restored by 
 a compound of the opposite class. 
 
 If to a solution of a strong base, like sodic hydrate, we add 
 slowly and carefully a solution of a strong acid, like sulphuric, 
 we shall at last reach a condition in which the solution affects 
 neither test-paper, and it is then said to be neutral. On evap- 
 orating this solution we obtain a neutral salt, like sodic sulphate, 
 and the presence in the solution of the slightest excess of acid 
 or base beyond the amount required to form this salt would 
 have been made evident by the test-papers. In such cases, we 
 may therefore use these test-papers to distinguish between acid, 
 basic, and neutral salts, but only with great caution ; for we find 
 that when, as in acid-carbonate of soda, a strong base is asso- 
 ciated with a weak acid," the reaction is still basic, although 
 
90 BASES, ACIDS, AND SALTS. 
 
 the acid may be greatly in excess, and, on the other hand, 
 when, as in cupric sulphate, a weak base has been associated 
 with a strong acid, the reaction may be strongly acid even in 
 the basic salts. The explanation of these apparent anomalies 
 is to be found in the fact that these colored reagents are all 
 salts themselves, and the reactions examples of metathesis. 
 The coloring matter of these dyes is an acid which varies its 
 tint according as the hydrogen atoms have or have not been 
 replaced ; and when, for any reason, the acid or base of the salt 
 examined is not in a condition to determine the necessary me- 
 tathesis, the characteristic change of color does not take place. 
 
 Unfortunately, the facts just stated have led to great confu- 
 sion in the use of the words "acid" and "basic" as applied to 
 salts, since these terms sometimes have reference solely to the 
 number of atoms of hydrogen, in the acid or base, which have 
 not been replaced in the formation of the salt, and at other times 
 refer to the reactions of the salt on the colored reagents just 
 described. A confusion of this sort must have been noticed in 
 the names of the three phosphates of soda on page 85. The 
 so called neutral phosphate is theoretically an acid salt, and 
 the basic pltosphate a neutral salt, but the salts give with test- 
 papers the reactions which their names indicate. The theo- 
 retical is the only legitimate use, and the one we shall adhere 
 to in this book, except in regard to names of compounds which 
 cannot be arbitrarily changed. 
 
 40. Alcohols, Fat Acids, Ethers. The hydrocarbon radicals 
 mentioned in 34 yield a very large number of compounds 
 after the type of water, which are closely allied to the hy- 
 drates and anhydrides, both acid and basic, just described. If 
 one of the hydrogen atoms in the molecule of water is replaced 
 by either of the univalent basic radicals, methyl, ethyl, propyl, 
 &c., we obtain a class of compounds, called alcohols, of which 
 our common alcohol is the most important. On the other 
 hand, if the atom of hydrogen is replaced by one of the uni- 
 valent acid radicals, formyl, acetyl, propionyl, &c., we obtain an 
 important class of acid compounds, of which acetic acid (vine- 
 gar) is the best known, but which also includes a large number 
 of fatty substances closely related to our ordinary fats. Hence 
 the name Fat Acids, by which this class of compounds is gen- 
 erally designated. 
 
BASES, ACIDS, AND SALTS. 91 
 
 Basic Hydrates or Alcohols. 
 
 Methylic Alcohol (wood spirits) CH^O-H. 
 
 Ethylic Alcohol (common alcohol) C 2 T 6 -0-ff. 
 
 Propy lie Alcohol C 3 N 7 - -H. 
 
 Butylic Alcohol CJEfr 0-H. 
 
 Amylic Alcohol (fusel oil) C^O-H. 
 
 (With six others already known.) 
 
 Acid Hydrates, Fat Acids. 
 Formic Acid H- 0-CHO. 
 
 Acetic Acid H- 0- C 2 H 3 0. 
 
 Propionic Acid H- 0- C 3 H 5 0. 
 
 Butyric Acid H-Q-0 4 H 7 0. 
 
 Valerianic Acid H- 0- <7 5 # 9 0. 
 
 (With fifteen others already known.) 
 
 If now we replace both of the hydrogen atoms of water by 
 the same basic radicals mentioned above, we obtain a class of 
 compounds called ethers, which correspond to the metallic 
 oxides or basic anhydrids ; and if we replace the two hydro- 
 gen atoms by the corresponding acid radicals, we obtain a 
 similar series of acid anhydrides. Lastly, if we replace one of 
 the hydrogen ' atoms by a basic radical, and the other by an 
 acid radical, we get a class of compounds also called ethers 
 (but distinguished as compound ethers), which correspond to 
 the salts. 
 
 Examples of Anhydrides. 
 
 1. Simple Ethers. 
 
 Methylic Ether CH s -0-Cff s or (CH S ) 2 =0. 
 
 Ethylic Ether (common ether) C 2 H 5 -Q-C 2 H 5 or (C 2 H 5 ) 2 =0. 
 
 2. Mixed Ethers. 
 
 Methyl-ethyl Ether CH f O- O 2 R 5 . 
 
 Ethyl-amyl Ether C 2 H 5 - - C 5 N n . 
 
 * 
 
 3. Compound Ethers. 
 
 Acetic Ether G 2 H & -0~O 2 H 3 0. 
 
 Butyric-methyl Ether CH S -Q-C^H 7 0. 
 
 4. Acid Anhydrides. 
 
 Acetic Anhydride O 2 H 3 0~0~ O 2 H B or ( O 2 R S 0) 2 =0. 
 
 Valerianic Anhydride C 5 H^O-Q-C 5 H g O or 
 
92 BASES, ACIDS, AND SALTS. 
 
 The positive radicals, of which the alcohols consist, hold an 
 intermediate position between the strong basic radicals on the 
 one hand, and the strong acid radicals on the other, and the 
 same is true of the alcohols themselves, which hold a middle 
 place between the strong basic and the strong acid hydrates. 
 This is indicated by the following reactions ; in what way it is 
 left to the student to inquire. 
 
 , o Q 
 
 K-K= ZK-O-CA + E-H 
 2 CH 3 -0-H+ HfOfSOi = (CIQfOfSOi + 2 H,0 
 
 41. Glycols. The class of hydrates described in the last sec- 
 tion belong to the simple type of water. But we have also a class 
 of analogous compounds belonging to the type of water doubly 
 condensed. If in the double molecule of water (H./0./H 2 ) we 
 replace one of the pairs of hydrogen atoms by either of the 
 bivalent positive radicals, ethylene, propylene, butylene, &c., 
 we obtain a series of compounds closely resembling the alco- 
 hols, called glycols, and by substituting the related negative 
 radicals we obtain two series of acid hydrates, which stand in 
 the same relation to the glycols that the fat acids bear to the 
 alcohols. These relations are shown in the following scheme, 
 which, however, includes only the five first members of each 
 of these three series of compounds. It should be noticed in 
 this connection that each of the bivalent positive radicals yields 
 two related negative radicals, while the univalent positive radi- 
 cals of the last section yield only one such negative radical ; 
 and moreover that the acids in the first series, although dia- 
 tomic, are only monobasic, while those in the second series are 
 both diatomic and bibasic (43). 
 
 C,Nf0 2 =H 2 fff 
 
 Ethylic Glycol. Glycolic Acid. Oxalic Acid. 
 
 C 3 ff G =0 2 =H 2 H 2 =0./C 3 
 
 Propylic Glycol. Lactic Acid. 
 
 Propylic Glycol. Lactic Acid. Malonic Acid. 
 
 Butylic Glycol. Acetonic Acid. Succinic Acid. 
 
 CtHtfOfHi H 2 =0 2 =C 5 ff s O fffOfC& 
 
 Amylic Glycol. Lipic Acid. 
 
 Hexyl Glycol. Leucic Acid. Adipic Acid. 
 
BASES, ACIDS, AND SALTS. 93 
 
 Corresponding to these basic and acid hydrates we have 
 also been able to obtain in several cases the basic and acid 
 anhydrides, besides a very large number of compound ethers. 
 
 42. Glycerines and Sugars. In the alcohols one hydrogen 
 atom from the original typical molecule (typical hydrogen) re- 
 mains undisturbed. In the glycols there are two such hydro- 
 gen atoms, and hence these compounds are frequently called 
 diatomic alcohols. Our common glycerine is a triatomic alco- 
 hol, and may be regarded as formed from a molecule of water 
 trebly condensed (JfyOfff 3 ), by replacing one of the groups of 
 hydrogen atoms with the trivalent radical glyceryl (O 2 ff 5 ). It 
 is probable that a large number ofHriatomic alcohols or glycer- 
 ines may hereafter be obtained, but only two are now known. 
 
 Propylic Glycerine (common glycerine) 
 Amylic Glycerine 
 
 From the glycerines we may derive acids, anhydrides, and 
 compound ethers, bearing to each other the same relations as 
 those derived from the alcohols of a lower order, but only a 
 few of the possible compounds which our theory would foresee 
 are yet known. Lastly, it appears probable that our common 
 sugars are also constituted after the type of water greatly con- 
 densed, and are simply alcohols of a very high order of atom- 
 icity. 
 
 43. Atomicity and Basicity of an Acid. By the atom- 
 icity of a compound is meant the number of hydrogen atoms 
 which it retains from the original typical molecule still unre- 
 placed. and the use of this term with reference to the basic 
 hydrates has been already abundantly illustrated in this chap- 
 ter. In the case of the acids a distinction must be made be- 
 tween atomicity and basicity, which is frequently important.' 
 
 The formula of every acid may be written on the type of one 
 or more atoms of hydrochloric acid, as H n 7? n , in which ff n stands 
 for the replaceable atoms of hydrogen, and R n for all the rest 
 of the atoms of the molecule, which may be regarded as forming 
 
 a radical with an atomicity equal to the number of replaceable 
 
 i ii in 
 
 hydrogen atoms. The symbols H-NO & HfSO 4 H 3 =P0 4 are 
 
94 BASES, ACIDS, AND SALTS. 
 
 written on this principle. In each case the acid is said to 
 have the atomicity of the radical. The basicity of the acid, 
 on the other hand, depends, not on the total number of replace- 
 able hydrogen atoms, but on the number which may be 
 replaced by metallic atoms or basic radicals. As a general 
 rule, it is true that the basicity is the same as the atomicity, 
 but this is not always the case. Thus lactic acid is diatomic 
 but monobasic, and the same is true of the other acids homol- 
 ogous with it (page 92). 
 
 7 4 8 ) &<*, (QHrt 
 
 Lactic Acid. Sodic Lactate. Sodic Benzolactate. 
 
 s ) <7 2 # 5 , GM-( C 3 ff 4 3 ) 
 
 Potassic Ethyl-lactate. Diethylic-lactate. 
 
 Only one atom of hydrogen can be replaced by a metallic 
 radical, but a, second may be replaced by either a negative or 
 an alcoholic radical, as in the last three symbols, and in desig- 
 nating the atoms, thus differently related to the molecular struc- 
 ture, it is usual to call the first basic and the other alcoholic 
 hydrogen. 
 
 We might, in like manner, distinguish between the atomicity 
 and the acidity of a base, but this distinction has not been found 
 as yet to be of practical importance. 
 
 44. Water of Crystallization. Among the most striking char- 
 acteristics of the class of compounds we call salts is their sol- 
 ubility in water and their tendency on separating from it, 
 in consequence of either the evaporation or the cooling of 
 the fluid, to assume definite crystalline forms. These crys- 
 tals, as a general rule, are complex crystalline aggregates of 
 molecules of the salt and molecules of water. The water is 
 held in combination by a comparatively feeble force, and may 
 be generally driven off by exposing the salt to the temperature 
 of 100 C., when the crystals fall to powder. Sometimes it es- 
 capes at the ordinary temperature of the air, when the crystals, 
 as before, fall to powder and are said to effloresce. It thus evi- 
 dently appears that the water, although an essential part of the 
 crystalline structure, is not inherent in the chemical molecule, 
 and hence the name Water of Crystallization. The presence of 
 
BASES, ACIDS, AND SALTS. 95 
 
 water of crystallization in a salt is expressed by writing after 
 the symbol of the salt, and separated from it by a period, the 
 number of molecules of water with which each salt molecule 
 is associated. Thus we have 
 
 FeS0 4 .7R 2 
 
 Crystallized Ferrous Sulphate or Green Vitriol. Crystallized Sodic Carbonate or Sal Soda. 
 
 The same salt, when crystallized, at different temperatures 
 not unfrequently combines with different amounts of water of 
 crystallization, the less amounts corresponding to the higher 
 temperatures. Thus manganous sulphate may be crystallized 
 with three different amounts of water of crystallization. We 
 have 
 
 MnSO v lH z O when crystallized below 6 C. 
 MnS0^.5H 2 " " between 7 and 20. 
 
 MnSOAH z O between 20 and 30. 
 
 The crystalline forms of these three compounds are entirely 
 different from each other ; and this fact again corroborates the 
 view that the molecules of water, while a part of the crystalline 
 structure, are not a part of the chemical type of the salt. It 
 will be well to distinguish the molecular aggregate, which the 
 symbols of this section represent, from the simpler chemical 
 molecules by a special term, and we propose to call them crys- 
 talline molecules. While, however, there is little room for 
 difference of opinion in regard to the relations in which the 
 molecules of water stand to the structure of most crystals, there 
 are cases where the condition is apparently far less simple, and 
 where we find the water so firmly bound to the salt itself that 
 it seems to form a part of its atomic structure. 
 
 Questions and Problems. 
 
 1. Analyze reactions [42]. Show what is meant by a metallic 
 hydrate, and define the term alkali. Write the similar reactions 
 which may be obtained with lithium, calcium, and rubidium. Name 
 in each case the class of compounds to which the factors and pro- 
 ducts belong. Also represent these reactions by graphic symbols. 
 
 2. Analyze reactions [43]. State the distinction between an 
 alkaline earth and an alkali, and write the similar reactions which 
 may be obtained with barium and strontium. Name in each case 
 
96 BASES, ACIDS, AND SALTS. 
 
 the class of compounds to which the factors and products belong. 
 Also represent the reactions by graphic symbols. 
 
 3. Analyze reactions [44] and [45], and write the similar reac- 
 tions which may be obtained with either of the metals, calcium, 
 strontium, barium, and magnesium. What theory of the constitution 
 of the metallic hydrates do these reactions suggest ? 
 
 4. In what respects do the hydrates Ca = 2 = J/ 3 and Mg = O a = H z 
 differ from K-O-H and Na-O-H ? 
 
 5. Analyze reactions [46], and show that the principal products 
 must be regarded as hydrates. Name the class of compounds to 
 which the other products and factors belong. 
 
 6. State the third theory which is held in regard to the constitu- 
 tion of the hydrates, and write the symbols of the different hydrates 
 according to this view. Also bring these symbols into comparison 
 with those of the same compounds written after the other two plans, 
 and show by means of graphic symbols how far these forms are arbi- 
 trary, and how far they represent fundamental differences. 
 
 7. In what sense may the solution of ammonia gas in water be 
 regarded as an hydrate ? Write reactions [46], using ammonic hy- 
 drate instead of the hydrates of sodium, potassium, and barium. 
 
 8. In what relation do the metallic oxides stand to the hydrates ? 
 Define the term base. 
 
 es. 
 
 ene te term ase. 
 
 9. Define the term salt, and illustrate your definition by exampl 
 
 10. Define the term acid. How does an acid differ from a me- 
 tallic hydrate ? Is an acid necessarily an hydrate ? What two 
 classes of acids may be distinguished ? 
 
 11. What is the distinction between an acid and a basic radical. 
 How are they related to the two hydrogen atoms of water ? As- 
 suming that there is no difference between these two atoms in the 
 original molecule of water, does not the replacement of one of the 
 atoms by a radical of either class alter the relations of the second ? 
 Is there not an analogy between these phenomena and those of 
 magnetism ? ^ 
 
 12. Analyze reactions [47 et seq.], and point out the evidence of 
 acidity in each case. 
 
 13. Analyze the following reactions. 
 
 K-O-H + HF = KF 
 
 Ca=0 2 =H 2 + EfOfCO = Ca=0.= CO 
 
BASES, ACIDS, AND SALTS. 97 
 
 Nad + H^ 
 
 2NaCl + HffrSOa = Na 2 =0,=S0 2 + 2SK9L 
 
 Point out the different acids and bases. In what does the evidence 
 of their acidity or basicity appear either in these or in reactions pre- 
 viously given ? Show in each case how the replacement of the hy- 
 drogen atoms is obtained, and illustrate the difference between the 
 hydrogen atoms of an acid and those of a base. What two classes 
 of acids may be distinguished ? 
 
 14. Regarding the hydrates as compounds of hydroxyl, how can 
 you define the acids and bases of this class ? 
 
 15. Represent the composition of nitric, sulphuric, and phosphoric 
 acid by graphic symbols, and show that the two modes of writing 
 their symbols embody essentially the same idea. 
 
 16. Hydrochloric acid, acetic acid, nitric acid, hydriodic acid, hy- 
 drobromic acid, sulphuric acid, carbonic acid, and phosphoric acid 
 have what basicity ? Point out, in the various reactions given in 
 this chapter, the evidence in each case, and write the symbols of the 
 possible sodic salts of the different acids. 
 
 1 7. What class of compounds do the symbols S0 3 , N Z 0^ P Z 0^ 
 C0 y and Si0 2 represent ? By a comparison of symbols show how 
 these compounds may be regarded as formed from water, and how 
 they are related to the corresponding acids. To what class of com- 
 pounds do they stand in direct antithesis ? 
 
 18. Define the terms basic and acid hydrate ; basic and acid an- 
 hydride, and compare reactions [49] with [44 and 45]. 
 
 19. Analyze the reaction, BaO -)- SO S = BaO,$O y 
 
 What reason may be urged for writing the symbol of baric sulphate 
 in this way V What was the theory of the dualistic system in 
 regard to such compounds ? Represent the symbol by the graphic 
 method, and seek to determine whether the dualistic form is compat- 
 ible with the theory of molecular unity. 
 
 20. The following symbols represent compounds of what class ? 
 H-O-Hi HfO/P 
 
 K-O-H; Ca-OfH 
 
 Co.? Of Si ; K-0-N0 2 ; 
 
 7 
 
98 BASES, ACIDS, AND SALTS. 
 
 Give in each case the name of the compound so far as you are able 
 to infer it from examples previously given, and show how the sym- 
 bol is related to that of water. 
 
 21. Point out the acid basic and neutral salts among the com- 
 pounds represented by the following symbols : 
 
 Jf,Na=0 2 -CO H,K-0.f(C. 2 0. 2 ) (Hg-O-Hg-0-H g y0.fS0. 2 
 Na 2 = 2 = C Kf 0,=( C, 2 ) 
 
 Cu=0 2 =(N0 2 ),ff 
 2 H fcOfAs K 2 =0./(S0. 2 -0-S0. 2 ). 
 
 What two classes of basic salts may be distinguished ? Convert the 
 symbols into the dualistic form. 
 
 22. Analyze reactions [49 and 50], and show how far they justify 
 the dualistic form given to the symbols. Represent the same reac- 
 tions in the typical form. 
 
 23. What class of compounds do the following symbols represent ? 
 
 Ag^SfAs Ag-S-SIS Ca=S 2 =ff 2 . 
 
 Write the symbols of the corresponding oxygen compounds. 
 
 24. Explain the theory of the colored test papers, and the use of 
 the terms acid and basic in connection with them. To what confu- 
 sion does the double meaning of these terms sometimes lead ? 
 
 25. The members of the series of alcohols stand in what relation 
 to each other ? Does the same relation exist between the members 
 of the series of fat acids, glycols, &c. ? Find a general symbol, 
 which will represent the composition of each of these classes of com- 
 pounds. 
 
 26. In what relations do the alcohols stand to the fat acids, and the 
 glycols to the acids derived from them ? 
 
 27. Select examples from each of the classes of compounds de- 
 scribed in sections 40, 41, and 42, and bring the symbols into com- 
 parison with those of some simple hydrate or anhydride with which 
 they exactly correspond. 
 
 28. We are acquainted with a class of compounds known as con- 
 densed glycols, one of which has the following symbols : 
 
 t- 0- C 2 H,- 0- 24 2 . 
 
 
 
BASES, ACIDS, AND SALTS. ' 99 
 
 To what class of salts does this correspond ? 
 
 29. Judging from the following symbols of a few of the salts of 
 tartaric acid, what conclusion should you reach in regard to the 
 atomicity and basicity of this acid V 
 
 30. What is the atomicity and basicity of the different acids 
 whose symbols have been given in this chapter ? Does the basi- 
 city of the different hydrocarbon acids ( 40 to 43) appear to 
 have any connection with the number of oxygen atoms in the rad- 
 ical ? 
 
 31. How do you explain the state of ycombination of the water 
 which enters into the composition of most crystalline salts ? Show 
 by an example how this mode of combination is represented sym- 
 bolically. What facts may be adduced in support- of the opinion 
 that the molecules of water are not a part of the chemical type of 
 the salt. 
 
CHAPTER X. 1 
 
 CHEMICAL NOMENCLATURE. 
 
 45. Origin of Nomenclature. Previous to the year 1787 
 the names given to chemical compounds were not conformed to 
 any general rules ; and many of these old names, such as oil of 
 vitriol, calomel, corrosive sublimate, red precipitate, saltpetre, 
 sal-soda^ borax, cream of tartar, Glauber's and Epsom salts, are 
 still retained in common use. As chemical science advanced, 
 and the number of known substances increased, it became 
 important to adopt a scientific nomenclature, and the system 
 which came into use was due almost entirely to Lavoisier, who 
 reported to the French Academy on the subject, in behalf of a 
 committee, in the year named above. In the Lavoisierian 
 nomenclature the name of a substance was made to indicate its 
 composition ; and at the time of its adoption, and for fifty years 
 after, it was probably the most perfect nomenclature which 
 any science ever enjoyed. It was based, however, on tho 
 dualistic theory, of which Lavoisier was the father ; and, when 
 at last the science outgrew this theory, the old names lost much 
 of their significance and appropriateness. Within the last few 
 years the English chemists have attempted to modify the old 
 nomenclature so as to better adapt the names to our modern 
 ideas. Unfortunately the result, like most attempts to mend a 
 worn-out garment, is far from satisfactory, although it is prob- 
 ably the best which under the circumstances could be attained. 
 The new nomenclature has not the simplicity or unity of the 
 old, and its rules cannot be made intelligible until the student 
 is more or less acquainted with the modern chemical theories. 
 Fortunately, however, the admirable system of chemical sym- 
 bols supplies the defects of the nomenclature, and for many 
 
 1 In studying this chapter, the student is expected to remember the names 
 corresponding to the different symbols, and also the symbols corresponding 
 to the names. 
 
CHEMICAL NOMENCLATURE. 101 
 
 purposes may be used in its place. We have, therefore, devel- 
 oped this system first, but have also used, meanwhile, the corre- 
 sponding scientific names, so that the student might become 
 familiar with the nomenclature, and gather its rules as he 
 advanced. A brief summary of these rules is all that will be 
 necessary here. 
 
 46. Names of Elements. The names of the elements are 
 not conformed to any fixed rules. Those which ^were known 
 before 1787, such as sulphur, phosphorus, ^j'J^x 
 
 iron, gold, and the other useful metals,^e,tajn their 
 Several of the more recently discovered, ^tentents* 
 named in allusion to some prominent property or some circum- 
 stance connected with their history : as oxygen, from ogvs 
 ycwato (acid-generator) ; hydrogen, from vScop yewcuo (water- 
 generator) ; chlorine, from xXapor (green) ; iodine, from looSq? 
 (violet) ; bromine, from /Spcojuos (fetid odor). The names of the 
 newly discovered metals have a common termination, urn, as 
 potassium, sodium, platinum ; and the names of several of the 
 newly discovered metalloids end in ine, as chlorine, bromine, 
 iodine, fluorine. Equally arbitrary names have been given to 
 the compound radicals ; but, with a few exceptions, they all 
 terminate in yl or ene, as ethyl, acetyl, hydroxyl, and ethylene, 
 acetylene, &c. 
 
 47. Names of Binary Compounds}- The simple compounds 
 of the elements with oxygen are called oxides, and the specific 
 names of the different oxides are formed by placing before the 
 word "oxide" the name of the element, but changing the termi- 
 nation into ic or ous, to indicate different degrees of oxidation, 
 and using the Latin name of the element in preference to the 
 English, both for the sake of euphony and in order to secure 
 more general agreement among different languages. When 
 the same element unites with oxygen in more than two pro- 
 portions, the Latin prepositions or numeral adverbs, sub, per, 
 bis, &c., are prefixed to the .word "oxide," in order to indicate 
 the additional degrees. Formerly these compounds were called 
 oxides of the different elements, the degrees of oxidation being 
 indicated solely by the prefixes ; and, as the old names are still 
 in very general use, they are also given in the following ex- 
 amples : 
 
 1 Compounds, of two elements. 
 
102 
 
 CHEMICAL NOMENCLATURE. 
 
 AgO 
 
 NO 
 NO, 
 FeO 
 
 New Names. 
 
 Argentic Oxide 
 Nitrous Oxide 
 Nitric Oxide 
 Nitric Peroxide 
 Ferrous Oxide 
 Ferric Oxide 
 
 Old Names. 
 Oxide of Silver 
 Protoxide of Nitrogen 
 Deutoxide of Nitrogen 
 Peroxide of Nitrogen 
 Protoxide of Iron 
 Sesquioxide of Iron. 
 
 '-An important exception to the above rules is made in the 
 case of thos*e oxides which, when combined with the elements 
 ^f;^atte ( r,l^rm t acfids: ',As has been already stated, page 61, 
 such compounds' are called anhydrides, but the degrees of oxi- 
 dation are distinguished as before, thus : 
 
 so, 
 
 co z 
 
 SiO a 
 
 New Names. 
 
 Sulphurous Anhydride 
 Sulphuric Anhydride 
 Nitrous Anhydride 
 Nitric Anhydride 
 Phosphorous Anhydride 
 Phosphoric Anhydride 
 Carbonic Anhydride 
 Silicic Anhydride 
 
 Old Names. 
 
 or Sulphurous Acid 
 
 " Sulphuric Acid 
 
 " Nitrous Acid 
 
 " Nitric Acid 
 
 " Phosphorous Acid 
 
 " Phosphoric Acid 
 
 " Carbonic Acid 
 
 " Silicic Acid. 
 
 The names in common use, even among chemists, of the 
 earths, the alkaline earths, and the alkaline oxides, make 
 another important exception to the general rules given above, 
 thus : 
 
 Al. 2 s Aluminic Oxide is commonly called Alumina 
 
 BaO Baric Oxide " " " Baryta 
 
 SrO Strontic Oxide " " " Strontia 
 
 CaO Calcic Oxide " " " Lime 
 
 MgO Magnesic Oxide " " " Magnesia 
 
 K n O Potassic Oxide " " " Potassa 
 
 Na 2 Sodic Oxide " " " Soda. 
 
 As this last class of oxides stands in the same relation to the 
 bases in whicli the previous class stands to the acids, they have 
 also been called by some chemists anhydrides. 
 
 The names of the binary compounds of the other elemenis 
 are formed like those of the oxides. 
 
CHEMICAL NOMENCLATURE. 
 
 103 
 
 Compounds of Chlorine are called Chlorides 
 
 " Bromine " 
 
 u 
 
 Bromides 
 
 " Iodine " 
 
 It 
 
 Iodides 
 
 " Fluorine " 
 
 it 
 
 Fluorides 
 
 " Sulphur " 
 " Nitrogen " 
 " Phosphorus " 
 " Arsenic " 
 
 It 
 It 
 it 
 
 Sulphides 
 Nitrides 
 PhosphiWes 
 Arsenides 
 
 " Antimony " 
 " Carbon " 
 
 u 
 
 Antivaonides 
 Ca,rbonides. 
 
 Moreover, the specific names of the several compounds also 
 follow the analogy of the oxides, thus : 
 
 or 
 
 Old Names. 
 Protochloride of Tin 
 Perchloride of Tin 
 Subsulphide of Iron 
 Protosulphide of Iron 
 Sesquisulphide of Iron 
 Bisulphide of Iron 
 Fluoride of Calcium. 
 
 Here, again, must be noticed several exceptions to the gen- 
 eral rule. Several simple compounds of the elements with hy- 
 drogen, of which the hydrogen is easily replaced with a metal 
 or positive radical, are called acids, and retain the specific 
 names of the old nomenclature, thus : 
 
 SnCl 
 SnCl, 
 Fe S 
 FeS 
 
 FeS* 
 CoFL 
 
 is 
 
 u 
 tt 
 It 
 a 
 tt 
 
 New Names. 
 Stannous Chloride 
 Stannic Chloride 
 Diferrous Sulphide 
 Ferrous Sulphide 
 Ferric Sulphide 
 Ferric Bisulphide 
 Calcic Fluoride 
 
 HCl 
 
 HBr 
 
 HI 
 
 HFl 
 
 H 2 S 
 
 Hydric Chloride is called 
 
 Hydric Bromide " " 
 
 Hydric Iodide " " 
 
 Hydric Fluoride " " 
 
 Hydric Sulphide " " 
 
 Hydrochloric Acid 
 Hydrobromic Acid 
 Hydriodic Acid 
 Hydrofluoric Acid 
 Hydrosulphuric Acid. 
 
 The last compound is frequently called also sulphuretted 
 hydrogen, and several other hydrogen compounds are named 
 after the same analogy, while others again are always called by 
 their well-known trivial names, thus : 
 
 H 3 Sb 
 H 3 As 
 H 3 P 
 
 Antimoniuretted Hydrogen 
 
 Arseniuretted Hydrogen 
 
 Phosphuretted Hydrogen 
 
 Ammonia Gas 
 
 Marsh Gas or Light Carburetted Hydrogen 
 
 Olefiant Gas or, as a radical, Ethylene. 
 
104 CHEMICAL NOMENCLATURE. 
 
 48. Ternary Compounds. Of the old class of ternary 
 compounds, it is only those which are formed after the type of 
 water for which the rules of the nomenclature need at present 
 be explained. 
 
 49. Bases. These we call simply hydrates, and for the 
 specific name we take the name of the positive radical, chang- 
 ing the termination into ic or ous, and using such prefixes as 
 circumstances may require, thus : 
 
 New Names. Old Names. 
 
 K-O-H is Potassic Hydrate or Hydrate of Potassa 
 
 Ca=0 2 =H 2 " Calcic Hydrate " Hydrate of Lime 
 
 Fe*OfH. Ferrous Hydrate (Hydrate of Protox- 
 
 ( ide of Iron. 
 
 Fe^H 6 Ferric Hydrate j Hydrate of Sesquiox- 
 
 ( ide of Iron. 
 
 (0=Fe-Fe--0)=OfH 2 Diferric Hydrate, the mineral Gothite. 
 
 50. Acids. The inorganic acids all take their specific names 
 from the name of the most characteristic element of the nega- 
 tive radical, which is modified by terminations' and prefixes as 
 before, only the last are usually taken from the Greek rather 
 than the Latin. Here the old and the new names coincide. 
 
 H-O-NO* is called Nitric Acid 
 
 HfOfSOt " " Sulphuric Acid 
 
 " Sulphurous Acid 
 
 H 2 =0 Z =(S-0-S) " " Hyposulphurous Acid 
 
 The specific names of the organic acids are, as a rule, arbitrary, 
 like tartaric acid, citric acid, malic acid, gallic acid, uric acid, 
 and the like. 
 
 51. Salts. The name of a salt is formed from the name 
 of the acid from which the salt is derived, preceded by the 
 names of the basic radicals. When the name of the acid ends 
 in ic the termination is changed into ate, when in ous into ite. 
 Moreover, the terminations ous and ic are retained in connec- 
 tion with the name of the basic radical, and such prefixes are 
 used as may be necessary for distinction, thus : 
 
CHEMICAL NOMENCLATURE. 105 
 
 Ca=0 2 =CO is Cakic Carbonate or 
 
 New Names. Old Names. 
 
 Carbonate of 
 Lime 
 
 Ca*O f (S-0-S) Calcic Hyposulphite ( H yPsulphite 
 
 ( of Lime 
 
 Ba-O f SO " Baric Sulphite Sulphite of 
 
 ( Baryta 
 
 Fe-O f SO t Ferrous Sulphate ^sulphate 
 
 of Iron 
 
 " Ferric Sulphate ' Pehate f 
 
 Q, Mg^O/PO " Ammonio-magnesic Phosphate 
 H, (NHJ, Na=0 3 =PO " Hydro-ammonio-sodic Phosphate. 
 
 The terms "acid" and "basic" have been used as parts of the 
 name of a salt very confusedly. We would propose to limit 
 this special use of these words to such salts as still contain 
 atoms of hydrogen, replaceable by a radical, basic in the first 
 case and acid in the other. This use has been followed on 
 page 87, where the distinction has been pointed out between 
 salts of this class arid those basic and acid salts which may 
 be regarded as formed by the cementing together of several 
 radicals into a single complex group. Salts of this last kind 
 we would distinguish by appropriate prefixes, but as examples 
 of names of both forms have already been given on the page 
 cited, it will be unnecessary to multiply them here. 
 
 Questions and Problems. 
 
 1. Give the names of the compounds represented by the follow- 
 symbols : 
 
 a. KCt-, 
 
 b. FeO; Fe=0=If; Fe = 0=GO', Fe=0. 2 =C 2 2 ; 
 
 c. H-Cl; N-F-, H-0-N0 2 -, H-0-NO-, fffOfSO a ; 
 ff 2 =0 2 =SO-, HfOfPO. 
 
 d. Hg-Gl^ \Hg^Clt\ Cu=S-, [CW 2 ]=S; Pft/ a ;\ KBr; 
 
 3 ; ZnO 
 
106 
 
 CHEMICAL NOMENCLATURE. 
 
 e. H,K=OfSOii R 
 
 ff,K=0 2 =(C 2 2 ). 
 
 /. N-N; N 2 0; NO-, 
 
 mo 
 
 ; MnO; 
 
 2. Write the symbols of the following compounds : 
 
 a. Calcic Sulphide ; Calcic Sulphite ; Calcic Hyposulphite ; Cal- 
 cic Sulphate ; Calcic Hydrate ; Calcic Sulphohydrate ; Calcic Car- 
 bonate ; Calcic Sulphocarbonate ; Calcic Silicate. 
 
 b. Water ; Potassic Hydrate ; Nitric Acid ; Potassic Nitrate ; 
 Nitric Anhydride; Potassic Oxide. 
 
 c. Magnesia Oxide ; Magnesic Hydrate ; Magnesic Nitrate ; 
 Magnesic Carbonate ; Magnesic Phosphate ; Ammonio-magnesic 
 Phosphate. 
 
 d. Cuprous Chloride ; Cupric Chloride ; Ferr6us Chloride ; Fer- 
 ric Chloride ; Sulphurous Anhydride ; Sulphuric Anhydride ; 
 Phosphorous Anhydride ; Phosphoric Anhydride. 
 
 N. B. Examples like the above should be greatly multiplied by 
 the teacher, pains being taken to group together the names and 
 symbols in the way besj; calculated to exhibit their relations and to 
 assist the memory. 
 
CHAPTER XI. 
 
 SOLUTION AND DIFFUSION. 
 
 52. Solution. The solvent power of water is one of the 
 most familiar facts of common experience, and all liquids pos- 
 sess the same power to a greater or less degree, but they differ 
 very widely from each other in the manifestation of their 
 solvent power, which for each liquid is usually limited to a 
 certain class of solids. Thus mercury is the appropriate sol- 
 vent of metals, alcohol of resins, ether of fats, and water of salts 
 and of similar compounds of its own type. Water is by far the 
 most universal solvent known, and for this reason, as well as 
 on account of its very wide diffusion in nature, it becomes the 
 medium of most chenfical changes. The phenomena of aqueous 
 solution form therefore a very important subject of chemical 
 inquiry, and these alone will be considered in this connection. 
 
 The solvent power of water, even on bodies of its own type, 
 differs very greatly. Some solids, like potassic carbonate, or 
 calcic chloride, liquefy in the atmosphere by absorbing the 
 moisture it contains. Such salts are said to deliquesce, and are 
 rendered liquid by a very small proportion of water. Other 
 salts, like calcic sulphate, require for solution several hundred 
 times their weight of water, and others again, like baric sul- 
 phate, are practically insoluble. 
 
 As a general rule the solvent power of water increases with 
 the temperature ; but here, again, we observe the greatest dif- 
 ferences between different substances. While the solubility 
 of some salts increases very rapidly with the temperature, that 
 of others increases not at all, or only very slightly ; and there 
 are a few which are actually more soluble in cold water than 
 in hot. The solubility of each substance is absolutely definite 
 for a given temperature, ar >d we can determine by experiment 
 the exact amount which 100 parts of water will in any case 
 dissolve. The results of such experiments are best represented 
 to the eye by means of a curve drawn as in the accompanying 
 figure on the principles of analytical geometry. 
 
108 SOLUTION AND DIFFUSION. 
 
 Fig. 2. 
 
 The figures on the horizontal line indicate degrees of tempera- 
 ture, and those on the vertical line parts of salt soluble in 100 
 parts of water. To find the solubility of any salt, for a stated 
 temperature, the curve being given, we have only to follow up 
 the vertical line corresponding to the temperature until it 
 reaches the curve, and then, at the end of the horizontal line 
 which intersects the curve at the same point, we find the num- 
 ber of parts required. These curves also show in each case 
 the law which the change of solubility obeys. 
 
 When a liquid has dissolved all of a solid that it is capable of 
 holding at the temperature, it is said to be saturated ; but when 
 saturated with one solid the liquid will still exert a solvent 
 power over others ; indeed, in some cases the solvent power is 
 thereby increased. When several salts are dissolved together 
 in water, a definite amount of metathesis seems always to take 
 place, and the different positive radicals are divided between 
 the several acids in proportions which depend on the relative 
 strength of their affinities, and on the quantities of eacb pres- 
 ent. If in this way either an insoluble or a volatile product is 
 formed, the solid or the gas at once falls out of the solution, 
 and, the equilibrium being thus destroyed, a new metathesis 
 takes place, and this goes on so long as any of these products 
 can be formed. Here, then, we find a simple explanation of the 
 two important laws already stated on page 37. 
 
f: CTL^ 6^p H^TCO ^-0-r^r^v*; /^u * / /^x</ 
 
 ^ SOLUTION AND DIFFUSION. 109 
 
 53. Solution of Gases. Most liquids, but especially water 
 and. alcohol, exert on gases a greater or less solvent power, 
 which is marked by differences of manifestation similar to 
 those we have already studied in the case of solids, although 
 the peculiar physical conditions of the gas somewhat modify 
 the result. Under the same conditions, the volume of gas dis- - 
 solved is always the same ; but it varies with the pressure of [* 
 the gas on the surface of the liquid, with the temperature, and 
 
 with the peculiar nature of the gag an& t 
 - 
 
 rp, j r ,. , 
 
 I he quantity 1 of gas dissolved by ^liquid on which it exerts a 
 
 pressure of 76 c. m. is called the coefficient of absorption. 
 This coefficient, in almost every instance, diminishes with the 
 temperature ; but, as in the case of solids, each substance obeys 
 a law of its own, which must be determined by experiment. The 
 observed values at different temperatures for several of the best 
 known gases, when absorbed by water and alcohol, are given in 
 the Chemical Physics, Table VII. With these data we can 
 easily calculate the quantity of any of these gases which a 
 given volume of water or alcohol will absorb, assuming that 
 the gas exerts on the liquid a pressure of 76 c. m. Moreover, 
 since the quantity of a gas absorbed by a liquid varies directly 
 as the pressure which the gas exerts upon it, we can easily 
 calculate from the first result the quantity absorbed at any 
 given pressure. Again, it is a direct consequence of the last 
 principle that at a fixed temperature a given mass of liquid will 
 dissolve the same volume of gas, whatever may be the pressure. 
 Lastly, if a mass of liquid is exposed to an atmosphere of 
 mixed gases, it will absorb of each the same quantity as if this 
 gas was alone present and exerting on the liquid the same 
 partial pressure which falls to its share in the atmosphere. 
 The amount dissolved of each gas is easily calculated when the 
 partial pressure and the coefficient of absorption are known. 
 It is thus that water absorbs the oxygen and nitrogen gases of 
 our terrestrial atmosphere ; and the fact that these two gases 
 are found dissolved in the ocean in very different proportions 
 from those present in the atmosphere is a conclusive proof that 
 the air is a mixture, and not, as was formerly supposed, a chem- 
 ical compound. 
 
 1 By quantity of gas is 1 here meant the volume in cubic centimetres meas- 
 ured under the standard conditions of temperature and pressure. 
 
 " '' ' 
 
110 SOLUTION AND DIFFUSION. 
 
 54. Solution and Chemical Change. There seems at first 
 sight to be a wide difference between solution and chemical 
 change ; for, while in the first the solid body becomes diffused 
 through the liquid menstruum without losing its chemical 
 identity or destroying that of the liquid, there is in the second 
 a complete identification of the combining substances in the 
 resulting compound. 
 
 The same wide difference appears also between mechanical 
 and chemical solution, which are sometimes confounded by 
 students, because, unfortunately, the same term has been applied 
 to both. When salt or sugar is dissolved in water, the 
 differences between salt and solvent are preserved ; but when 
 chalk is dissolved in hydrochloric acid, or copper in nitric acid, 
 there is a complete identification of the differences in the 
 resulting compound; and the only ground for calling such 
 chemical changes solution is the fact that the solution of the 
 resulting salt in the water, used as the medium of the chemical 
 change, is frequently an essential condition of the process. 
 
 But if, instead of comparing extreme cases, we study the 
 whole range of chemical phenomena, we shall find that the 
 distinction is by no means so clearly marked. In many cases 
 what seems to be a simple solution can be shown to be a mixed 
 effect at least of solution and chemical combination ; and be- 
 tween this condition of things, where the evidence of chemical 
 combination is unmistakable, and a simple solution, like that of 
 sugar in water, we have every degree of gradation. To such 
 an extent is this true, that the facts seem to justify the opinion 
 that solution is in every case a chemical combination of the 
 substances dissolved with the solvent, and that it differs from 
 other examples of chemical change only in the weakness of the 
 combining force. 
 
 The metallic alloys afford another striking illustration of the 
 same principle. They are originally solutions of one metal in 
 another ; but in many cases the result is greatly modified by 
 the chemical affinities of the metals and their tendency to form 
 definite chemical compounds. 
 
 55. Liquid Diffusion. Closely connected with the phe- 
 nomena of solution are those of liquid diffusion. These phe- 
 nomena may be studied in their simplest form, by placing an 
 open vial filled with a solution of some salt in a much larger 
 
SOLUTION AND DIFFUSION. Ill 
 
 jar of pure water, as shown in Fig. 3, and so carefully arranging 
 the details of the experiment that the surfaces of the two 
 liquids may be brought in contact without mixing them me- 
 chanically. It will then be found that the salt molecules will 
 slowly escape from the vial and spread 
 throughout the whole volume of the 
 water. The rate of the diffusion in- 
 creases with the temperature equally 
 for all substances, and the whole phe- 
 nomenon is probably caused by that 
 same molecular motion to which we 
 refer the effects of heat. At best, how- 
 ever, the diffusion is very slow, as we 
 should expect, considering the limited 
 freedom of motion which the liquid 
 molecules possess. It is found, also, that 
 
 the rate of diffusion differs very greatly 
 
 for the different soluble salts ; but these may be divided into 
 groups of equidiffusive substances, and the rates of diffusion of 
 the several groups bear to each other simple numerical ratios. 
 If a mixture of salts be placed in the vial, it is found that the 
 presence of one salt affects to some degree the diffusion of the 
 other ; but if the difference of rate is considerable, a partial 
 separation may be effected, and even weak chemical compounds 
 may be thus decomposed. 
 
 56. Crystalloids and Colloids. There is a very great differ- 
 ence of diffusive power between the ordinary crystalline salts 
 (including most of the common acids and bases) and such sub- 
 stances as gum, caramel, gelatine, and albumen, which are 
 incapable of crystallizing, and which give insipid viscid solu- 
 tions, readily forming into jelly ; hence the name colloids, from 
 KoXX?;, glue. The last class is distinguished by a remarkable 
 sluggishness and indisposition to diffusion ; as is illustrated by 
 the fact that sugar, one of the least diffusible of the crystalloids, 
 diffuses seven times more rapidly than albumen, and fourteen 
 times more rapidly than caramel. Our theories would lead us 
 to believe that this great difference of diffusive power is caused 
 by the fact that the molecules of colloids are far more complex 
 atomic aggregates than those of crystalloids, and therefore are 
 heavier and move more slowly. Moreover, the diffusive power 
 
112 SOLUTION AND DIFFUSION. 
 
 is only one of many characters which point to a great molecu- 
 lar difference between these two classes of substances. 
 
 57. Dialysis. The. difference of diffusive power between 
 the two classes of compounds distinguished in tbe last section 
 is still further increased when the aqueous solution is separated 
 from the pure water by some colloidal membrane, and upon this 
 fact Professor Graham of London, to whom we owe our whole 
 knowledge of this subject, has based a simple method of sepa- 
 rating crystalloids from colloids, which he calls dialysis. 
 
 A shallow tray is prepared by stretching parchment paper 
 (which is itself an insoluble colloid) over one side of a gutta- 
 percha hoop, and holding it in place by a somewhat larger hoop 
 of the same material. The solution to be dialysed is poured into 
 this tray, which is then floated on pure water whose volume 
 should be eight or ten times greater than that of the solution. 
 Under these conditions the crystalloids will diffuse through the 
 porous septum into the water, leaving the colloids on the tray, 
 and in the course of two or three days a more or less complete 
 separation of these two classes of substances will have taken 
 place. 
 
 In this way arsenious acids and similar crystalloids may be 
 separated from the colloidal materials, with which, in cases of 
 poisoning, they are frequently found mixed in the stomach ; and 
 by an application of the same method alumina, ferric oxide, 
 chromic oxide, stannic, metastannic, titanic, molybdic, tungstic, 
 and silicic acids have all been obtained dissolved in water in a 
 colloidal condition. All these substances usually exist in a 
 crystalline condition. The colloidal condition appears to be an 
 abnormal state, and in almost all such substances there is a 
 tendency towards the crystalloid form. 9 
 
 58. Diffusion of Gases. Gases diffuse much more rapidly 
 than liquids, as we should naturally expect from the greater 
 freedom of motion which their molecules possess. Moreover, 
 if the theory of the molecular condition of gases is correct, we 
 ought to be able to calculate the relative rates of diffusion of 
 different gases from their respective molecular weights. If it 
 is true, as stated on page 11, that at any given temperature 
 
 then it follows that 
 
 = y/Sp. Gr'. : y/Sp. Gr. 
 
SOLUTION AND DIFFUSION. 113 
 
 Hence, if two masses of gas are in contact, the molecules of 
 either gas must move into the space filled by the other with 
 velocities which are inversely proportional to the square roots 
 of the respective specific gravities. If one gas is hydrogen ( Sp. 
 Gr. 1), and the other oxygen (Sp. Gr. = 16), the molecules 
 of hydrogen must move past the section separating the two 
 masses four times as rapidly as those of oxygen ; and, since all 
 gas molecules occupy the same volume, it follows further that 
 four volumes of hydrogen must enter the space filled by the 
 oxygen, while one volume of oxygen is passing in the opposite 
 direction Numerous experiments have fully confirmed this 
 theoretical deduction, and the close agreement between theory 
 and experiment furnishes important evidence in favor of the 
 theory itself. Such experiments can be made, moreover, with 
 great accuracy, since the molecular motion is not arrested 
 by various porous septa, which may be used to separate the 
 two masses of gas, and which entirely prevent the passage of 
 gas currents that might otherwise vitiate the results. 
 
CHAPTER XII. 
 
 COMBUSTION. 
 
 59. The Atmosphere. The earth is surrounded by an ocean 
 of aeriform matter called the atmosphere, and many of the most 
 important chemical changes which we witness in nature are 
 caused by the reaction of this atmosphere on the substances 
 which it surrounds and bathes. The great mass of the atmos- 
 phere consists of the two elementary gases, oxygen and nitro- 
 gen, mixed together in the proportions indicated in the follow- 
 ing table : 
 
 Air Composition Composition 
 
 contains. By Volume. By Weight. 
 
 Oxygen, 20.96 23.185 
 
 Nitrogen, 79.04 76.815 
 
 100. 100. 
 
 That the air is a mixture, and not a chemical compound, is 
 proved by the action of solvents upon it ( 50) ; but, neverthe- 
 less, the analyses of air collected in different countries, and at 
 different heights in the atmosphere, show a remarkable con- 
 stancy in its composition. Besides these two gases, which make 
 up over 93 per cent of its whole mass, the air always contains 
 variable quantities of aqueous vapor, carbonic anhydride, and 
 ammonia, and sometimes also traces of various other gases and 
 vapors. 
 
 60. Burning. Of the two chief constituents of the atmos- 
 phere, nitrogen gas is a very inert substance, and serves chiefly 
 to restrain its more energetic associate. Oxygen gas, on the 
 other hand, is endowed with highly active affinities, and tends 
 to enter into combination with other elementary substances, 
 and with many compounds which are not already saturated 
 with this all-pervading element. Many of these substances, 
 such as phosphorus, sulphur, petroleum, coal, and wood, have 
 such^a strong affinity for oxygen, that, under certain conditions, 
 they will absorb it from the atmosphere, and combine with it 
 
COMBUSTION. 115 
 
 under the evolution of heat and light. These substances are 
 said to be combustible, and the process of combination is called 
 combustion. Moreover, all burning with which we are familiar 
 in common life consists in the union of the burning body with 
 the oxygen of the air. The chemical process in these cases 
 may be expressed, like any other chemical reaction, in the form 
 of an equation. 
 
 Burning of Hydrogen Gas. 
 
 Hydrogen Gas. Aqueous Vapor. 
 
 2 Si-Si + = = 2SJ/. 
 Burning of Carbon (Charcoal). 
 
 Carbon. Carbonic Anhydride. 
 
 C + = = 
 
 Burning of Benzole. 
 
 f 6SI 2 . [55] 
 
 Burning of Alcohol. 
 
 Alcohol. 
 
 3= == 
 
 ^Sulphurous Anhydride. 
 
 Burning of Sulphur. 
 
 Sulphurous An 
 
 U-i3 \- 2 = 23.>. 
 i a 
 
 Burning of Phosphorus. 
 
 Phosphoric Anhydride. 
 
 Burning of Magnesium. 
 
 Magnesie Oxide. 
 
 2 MCg + = = 2 MgO. [59] 
 
 The four substances, hydrogen gas, charcoal, benzole, and 
 alcohol, may be regarded as types of our ordinary combustibles ; 
 and, as the first four reactions show, the products of their com- 
 bustion are aeriform. Moreover, these products are wholly 
 devoid of any sensible qualities, and hence the apparent annihi- 
 
116 COMBUSTION. 
 
 lation of the burning substance, and the reason that for so long 
 a period the nature of the process remained undiscovered. That 
 these qualities of the products of ordinary combustion are not ne- 
 cessary conditions of the process, but remarkable adaptations in 
 the properties of those combustibles which are our artificial 
 sources of light and heat, is shown by the fact, that, in the last 
 two reactions, the products of the combustion are solids, while 
 in [57] the product is a noxious suffocating gas. 
 
 A careful inspection of the reactions will also teach the 
 student several other important facts in regard to the processes 
 here represented. It will be seen that, in the burning of 
 hydrogen gas, two volumes of hydrogen gas and one volume 
 of oxygen gas combine to form two volumes of aqueous vapor. 
 It will further be noticed, that, in the burning of carbon and of 
 sulphur, a given volume of oxygen gas yields in each case its 
 own volume of the aeriform product. The carbon in the one 
 case, and the sulphur in the other, are absorbed, as it were, by 
 the gas, without any increase of volume. Further, if the ex- 
 periments are made, which these reactions represent, it will 
 appear that, in all those cases where the combustible is repre- 
 sented as a gas, the combustion is accompanied by flame, while 
 in the case of carbon, which is a fixed solid, there is no proper 
 flame. Hence we learn that flame is burning gas, and that 
 only those substances burn with flame which are either gases 
 themselves, or which, at a high temperature, become vola- 
 tilized, or generate combustible vapors. Still other important 
 facts connected with the process of combustion will be learned 
 by solving the following problems according to the rules al- 
 ready given ( 24 and 25). 
 
 Problem. How many cubic centimetres of hydrogen gas, 
 and how many of oxygen gas, are required to form one cubic 
 centimetre of liquid water? 1 Ans. 1,240 cm 8 of hydrogen 
 gas, and 620 c m B of oxygen gas. 
 
 Problem. How many cubic metres of air are required to 
 burn 448 kilogrammes of coal, assuming that the coal is pure 
 cafbon ? Ans. 833.333 m 3 of oxygen gas, or 3,975.83 m* of 
 atmospheric air. 
 
 ^ 1 Here, as in all other problems throughout the book, it is understood, unless 
 otherwise expressly stated, that the measurements and weights are all taken at 
 the standard temperature and pressure. (Compare 10 and 13.) _ 
 
 ss/ 
 
COMBUSTION. 117 
 
 Problem. How many cubic metres of carbonic anhydride 
 are formed by the burning of 1,000 kilogrammes of coal, as- 
 suming, as before, that the coal is pure carbon ? Ans. 1,860. 
 
 Problem. How many litres of carbonic anhydride, and 
 how many of aqueous vapor, would be formed by burning one 
 litre of benzole vapor ? Ans. Simple inspection of the equa- 
 tion shows that 6 litres of the first and 3 litres of the second 
 would be formed. 
 
 Problem. How many litres of carbonic anhydride, and how 
 many of aqueous vapor, would be formed by burning one litre 
 of liquid alcohol (C 2 H G 0) ? Sp. G-r. of liquid at = 0.815. 
 Ans. One litre of alcohol weighs 815 grammes or 9,097 criths, 
 and, since the Sp. Gr. of alcohol vapor is 23, this quantity of 
 liquid would yield 395.6 litres of vapor. Hence there would 
 be formed 2 X 395.6 = 791.2 litres of carbonic anhydride, and 
 3 X 395.6 = 1,186.8 litres of aqueous vapor. \/A 
 
 61. Heat of Combustion. The reactions of'tjae'- laist section 
 represent only the chemical changes in the processes of burning. 
 The physical effects which accompany the chemical changes 
 our equations do not indicate, but it is these remarkable mani- 
 festations of power which chiefly arrest the student's attention, 
 and on this power the importance of the processes of combus- 
 tion as sources of heat and light wholly depends. 
 
 The immediate cause of the power developed in the process 
 of combustion is to be found in the clashing of material atoms. 
 Urged by that immensely powerful attractive force we call 
 chemical affinity, the molecules of oxygen in the surrounding 
 atmosphere rush, from all directions, and with an incalculable 
 velocity, upon the burning body. The molecules of oxygen 
 thus acquire an enormous moving power ; and when, at the 
 moment of chemical union, the onward motion is arrested, 
 this moving power is distributed among the surrounding mole- 
 cules, and is manifested in the phenomena of heat and light. 1 
 (Compare 12.) 
 
 1 According to our best knowledge, the phenomena of light are merely 
 another manifestation of the same molecular motion which causes the phe- 
 nomena of heat. When we speak of the amount of heat produced, we refer 
 always to the total amount of molecular motion ; although, even in the most 
 brilliant illumination, the amount of mechanical power manifested as light 
 appears to be inconsiderable as compared with that which takes the form of 
 heat. 
 
118 COMBUSTION. 
 
 The quantity of heat evolved during combustion varies 
 very greatly with the nature of the combustible employed, but 
 it is always constant for the same combustible if burnt under 
 the same conditions, arid is exactly proportional to the weight 
 of combustible consumed. We give in the following table the 
 amount of heat evolved by one kilogramme of several of the 
 most common combustibles when they are burnt in oxygen 
 gas in their ordinary physical state. The numbers represent 
 what is called the calorific power of the combustible. With 
 the exception of the two last, which are only approximate 
 values, they are the results of very accurate experiments 
 made by Favre and Silbermann. 
 
 Calorific Power of Combustibles. 
 
 Units. Units. 
 
 Hydrogen, 34,462 Sulphur, 2,221 
 
 Marsh Gas, 13,063 Wood Charcoal, 8,080 
 
 Olefiant Gas, 11,858 Carbonic Oxide, 2,400 
 
 Ether, 9,027 Dry Wood (about), 3,654 
 
 Alcohol, 7,184 Bituminous Coal, " 7,500 
 
 The calorific power of our ordinary hydrocarbon fuels may 
 be calculated approximately when their composition is known. 
 Most of these combustibles contain more or less oxygen, and 
 it is found, as might be expected, that the amount of heat 
 developed by the perfect combustion of the fuel is equal 
 to that which would be produced by the perfect combus- 
 tion of all the carbon, and of so much of the hydrogen as 
 is in excess of that required to form water with the oxygen 
 present. The rest of the hydrogen may be regarded, so far 
 as relates to the present problem, as in combination with oxy- 
 gen in the state of water ; and in estimating the available heat 
 produced, we must deduct the amount of heat required to con- 
 vert, not only this water into steam, but also any hygroscopic 
 water which may be present. Moreover, if we use in our cal- 
 culation the value of the calorific power of hydrogen given in 
 the table above, we must also deduct the amount of heat re- 
 quired to convert into vapor all the water formed in the process 
 of burning, because, in the experiments by which this value 
 was obtained, the aqueous vapor formed was subsequently con- 
 densed to water and gave out its latent heat. 
 
 Problem. Given the average composition of air-dried wood 
 as in the table, to find the calorific po\vrr. 
 
Carbon, 400 
 
 Hydrogen, 48 
 
 Oxygen, 328 
 
 Nitrogen and Ash, 24 
 Hygroscopic Water, 200 
 1000 
 
 COMBUSTION. 119 
 
 From the results of analysis we easily 
 
 deduce 
 
 Quantity of H in combination with 41 
 
 " " available as fuel 7 
 
 Quantity of water formed by burn- ) . nn 
 
 ing 48 parts hydrogen 
 
 Hygroscopic Water 
 Total quantity of water evaporated 632 
 
 Units of Heat. 
 
 400 grammes of carbon yield 3,232 
 
 7 " " hydrogen " 241 
 
 3,473 
 
 Deduct amount of heat required to convert 632 grammes of 
 
 water into vapor. (See 14.) 339 
 
 Calorific power of air-dried wood 3,134 
 
 From the mechanical equivalent of heat given on page 11, 
 and from the data of the above table, we can easily calculate 
 the mechanical power developed in ordinary combustion, and 
 the student will be surprised to find how great this power is. 
 The burning of one kilogramme of charcoal produces an 
 amount of heat which is equivalent to 8,080 X 423 = 3,41 7,840 
 kilogramme metres ; that is, the moving power which is de- 
 veloped by the clashing of the atoms during the combustion 
 of this small amount of coal is equal to that which would be 
 produced by the fall of a mass of rock weighing 8,080 kilo- 
 grammes over a precipice 423 metres high, and, could this 
 power be all utilized, it would be adequate to raise the same 
 weight to the same height, or to do any other equivalent 
 amount of work. The steam-engine is a machine for apply- 
 ing this very power to produce mechanical results ; but, unfor- 
 tunately, in the best engines we do not utilize much more than 
 ^ ! of the power of the fuel ; and to find a more economical 
 means of converting heat into mechanical effect is one of the 
 great problems of the present age. 
 
 62. Calorific Intensity. The calorific intensity of fuel is to 
 be carefully distinguished from its calorific power. By calorific 
 power is meant, as we have seen, the total quantity of heat 
 developed by the combustion of a given amount of fuel. By 
 ,calorific intensity, we mean the maximum temperature de- 
 veloped in the process of combustion. Provided the products 
 are the same, the total amount of heat produced in any case is 
 
120 COMBUSTION. 
 
 % 
 
 not materially influenced by the rapidity of the process ; but 
 it is evident that the temperature of the burning fuel will de- 
 pend, other things being equal, on the rapidity with which the 
 heat is developed as compared with the rapidity with which it 
 is dissipated through surrounding objects ; and, when the com- 
 bination with oxygen is very slow, the heat may be dissipated 
 as fast as it is generated, and then the temperature of the 
 burning body will not rise above that of the surrounding at- 
 mosphere, as is the case in many of the processes of slow com- 
 bustion. 
 
 Assuming, however, that all the heat is retained by the 
 products of combustion, we can calculate the maximum tem- 
 perature which can in any case be produced, provided the 
 calorific power of the fuel and the specific heat of the products 
 of combustion are known. The calorific intensity is simply 
 the temperature to which the heat generated by the burning 
 of each portion of the fuel can raise the products of its own 
 combustion. Assume that the quantity burnt is one kilo- 
 gramme, that the calorific power or number of units of heat 
 produced is (7, that the weights of the various products of com- 
 bustion are W, W, W", &c., and that the specific heats of 
 these products are S, S', S", &c. Then WS -f W'S 1 + W"S" 
 -f- &c., represents the amount of heat required to raise the tem- 
 perature of the whole mass of the products one centigrade de- 
 gree ( 16), and the maximum temperature, to which these 
 products can be raised in the process of Combustion, must be 
 
 (7 
 ~ WS+W'S-+W"S" 
 
 Problem. Find the calorific intensity of charcoal burnt in pure 
 oxygen, and also in air under constant atmospheric pressure. 
 
 Solution. By [54] we easily find that each kilogramme of 
 carbon yields, by burning, 3.67 kilogrammes of carbonic anhy- 
 dride, which is the sole product of its combustion when burnt 
 in pure oxygen. The specific heat of carbonic anhydride 
 (Chem. Phys. 235) is 0.2164. The calorific power of charcoal 
 is 8,080. By substituting these values in [60] we get T = 
 10,174. 
 
 When the charcoal burns in air, the 3.67 kilogrammes of 
 carbonic anhydride formed by the combustion are mixed with a 
 
COMBUSTION. 121 
 
 large mass of inert nitrogen, which must be regarded as one of 
 the products of the combustion. The weight of this nitrogen is 
 easily calculated from the known composition of air by weight 
 ( 56) and from the amount of oxygen consumed in the process. 
 
 23.2 : 76.8 = 2.67 : x ; or x = 2.67 X 3.31 = 8.84. 
 
 We have now, besides the values given above, W = 8.84 
 and S, 1 the specific heat of nitrogen, equal to 0.244. Whence 
 T 2,738. 
 
 Problem. Find the calorific intensity of hydrogen gas burnt 
 in oxygen and burnt in air. 
 
 Solution. One kilogramme of hydrogen yields 9 kilogrammes 
 of aqueous vapor. The specific heat of aqueous vapor is 0.4805. 
 The calorific power of hydrogen is not so great when the gas 
 is burnt under ordinary conditions as that given in the table on 
 page 118 ; for in the experiments of Favre and Silbermann the 
 vapor formed by the combustion was subsequently condensed 
 to water, and gave out its latent heat, while in a burning flame 
 of hydrogen no such condensation takes place. Hence C = 
 34,462 (537 X 9) = 29,629. We also have W = 9 and 
 S= 0, 475. Whence T= 6,853. 
 
 When hydrogen is burnt in air, the nitrogen, mixed with the 
 aqueous vapor, weighs 26.49 kilogrammes and S 1 is the same 
 as in the previous problem. Whence T = 2,746. 
 
 It appears then from these problems, that, although the 
 calorific power of hydrogen is much greater than that of car- 
 bon, its calorific intensity is less. But it must be remembered 
 that the conditions assumed in these problems are never real- 
 ized in practice, for the heat generated by the combustion is 
 never wholly retained in the products. The process of com- 
 bustion requires a certain time, and during this time a portion 
 of the heat escapes. Moreover, more air passes through the 
 combustible than is required for perfect combustion, and many 
 of the data which enter into the calculation are uncertain. 
 The results, therefore, can only be regarded as approximate. 
 The theoretical conditions are most nearly realized in a gas 
 flame, and especially in that form of burner known as the 
 Bunsen lamp. The temperature of the flame of this lamp, 
 when carefully regulated, is very nearly that which the theory 
 would assign. 
 
122 COMBUSTION. 
 
 63. Point of Ignition. In order that a combustible body 
 should take fire, and continue burning in the atmosphere, it 
 must be heated to a certain temperature, and maintained at 
 this temperature. This temperature is called the point of igni- 
 tion ; and although it cannot always be accurately measured, 
 and is undoubtedly more or less variable under different con- 
 ditions, yet, nevertheless, it is tolerably constant for each sub- 
 stance. For different substances it differs very greatly. Thus 
 phosphorus takes fire below the boiling point of water, sulphur 
 at 260, wood at a low red heat, anthracite coal only at a full 
 red heat, while iron requires the highest temperature of a 
 forge. If a burning body is cooled below its point of ignition, 
 it goes out ; and our ordinary combustibles continue burning 
 in the air only because the heat evolved by the burning main- 
 tains the temperature above the required point. If the tem- 
 perature of the combustible is not maintained sufficiently high, 
 either because the chemical union is too slow, or because the 
 calorific power is too small, then the combustible will not con- 
 tinue to burn in the air of itself, although it may burn most 
 readily if its temperature is sustained by artificial means. 
 Hence many of the metals which will not burn in the air 
 burn readily in the flame of a blowpipe, and am iron watch- 
 spring burns like a match in an atmosphere of pure oxygen. 
 The calorific intensity of all combustibles, when burnt in the 
 atmosphere, is, as we have seen, greatly reduced by the pres- 
 ence of nitrogen ; and hence it is that, although the burning 
 watch-spring is maintained above the point of ignition in pure 
 oxygen, it soon falls below this temperature, and goes out 
 when ignited in the air. Thus it is that the nitrogen of our 
 atmosphere exerts a most important influence on the action of 
 the fire element ; and it can easily be seen that, were it not for 
 these provisions in the constitution of nature, by which the 
 active energies of oxygen are kept within certain limits, no 
 combustible material could exist on the surface of the earth. 
 
 64. Calorific Power derived from the Sun. The great mass 
 of the crust of our globe consists of saturated oxygen com- 
 pounds, or, in other words, of burnt material* ; and the total 
 amount of combustible materials which exists on its surface is, 
 comparatively, very small. That which exists naturally consists 
 almost entirely of carbon and its compounds, such as coal, 
 
COMBUSTION. 123 
 
 naphtha, and wood ; and all these substances are the results of 
 vegetable growth, either of the present age or of earlier geo- 
 logical epochs. Moreover, whatever subsequent changes the 
 material may have undergone, it was all originally prepared 
 by the plant from the carbonic acid and water of our atmos- 
 phere ; for, in the economy of nature, these products of com- 
 bustion have been made the food of the vegetable world. The 
 sun's rays, acting on the green leaves of the plant, exert a mys- 
 terious power, which decomposes carbonic anhydride, and per- 
 haps also water ; and, as the result of this process, oxygen is 
 returned to the atmosphere, while carbon and hydrogen are 
 stored up in the growing tissues of the plant. The sun thus 
 undoes the work of combustion, and parts the atoms which the 
 chemical affinities had drawn together. In doing this, the 
 sun exerts an enormous power ; and the work which it thus ac- 
 complishes is the precise measure of the calorific power of the 
 combustible material, which it then prepares. When we wind 
 up the weight of a clock, we exert a certain power which reap- 
 pears in its subsequent motions ; and so, when the sun's rays 
 part these atoms, the great power it exerts is again called into 
 action, when in the process of combustion the atoms reunite. 
 Moreover, what is true of calorific power is true of all mani- 
 festations of power on the surface of the earth. Every form 
 of motion is sustained by the running down of some weight 
 which the sun has wound up ; and, according to the best theory 
 we can form, the sun's power itself is sustained by the gradual 
 falling of the whole mass of the solar system towards its com- 
 mon centre. However varying in its manifestation, all power 
 in its essence is the same, and the total amount of power in the 
 universe is constant. 
 
 65. Heat of Chemical Combinations. The heat of combus- 
 tion is only a striking manifestation of a very general principle, 
 which holds true in all chemical changes. It would appear 
 that whenever, in a chemical reaction, atoms or molecules are 
 drawn together by their mutual affinities, a certain amount of 
 moving power is developed, which takes the form of heat ; and 
 whenever, on the other hand, these same atoms or molecules 
 are drawn apart by the action of some superior force, the same 
 amount of moving power is expended, and heat disappears. 
 Every chemical reaction is a mixed effect of such combina- 
 
124 COMBUSTION. 
 
 tions and decompositions, and it is simply a complex problem in 
 the mechanical theory of heat to determine what must be in 
 any case the thermal effect. The numerous facts with 
 which we are acquainted in regard to the heat of chemical 
 combination generally agree with the mechanical theory ; and, 
 where the facts do not appear to conform to it, the discrepancy 
 probably arises from our ignorance of the nature of the chem- 
 ical change in question. It would be incompatible with our 
 design to discuss these facts in this book. It must be sufficient 
 to state a few general results, which may be summed up in the 
 following propositions : 
 
 First. The heat absorbed in the decomposition of a com- 
 pound is equal to the heat evolved in its formation, provided 
 the initial and the final states are the same. 
 
 Second. The heat evolved in a series of successive chemical 
 changes is equal to the sum of the quantities which would be 
 evolved in each separately, provided the bodies are finally 
 brought into identical conditions. 
 
 Third. The difference between the quantities of heat evolved 
 in two series of changes starting from two different states, but 
 ending in the same final state, is equal to that which is evolved 
 or absorbed in passing from one initial condition to the other. 
 
 For example, if a body m evolves a certain amount of heat 
 in uniting with n to form m n, and if the body m n is decom- 
 posed by a third body p, so that m p is formed, the quantity 
 of heat evolved in this last reaction is less than that which 
 would be evolved in the direct union of m and p by the amount 
 evolved in the formation of m n. 
 
 All these propositions, however, are but special cases under 
 a more general principle which is at the basis of the whole 
 mechanical theory of heat, and which may be enunciated as 
 follows: Whenever a system of bodies undergoes chemical 
 or physical changes, and passes into another condition, what- 
 ever may have been the nature or succession of the changes, 
 the quantity of heat evolved or absorbed depends solely on the 
 initial and final conditions of the system, provided no mechan- 
 ical effect has been produced on bodies outside. 
 
COMBUSTION. 125 
 
 Questions and Problems. 
 
 1. Plow many times more space does the carbonic anhydride 
 formed by burning charcoal (Sp. Gr. = 2) occupy than the char- 
 coal burnt ? 
 
 Ans. One cubic centimetre or two grammes of charcoal yields 
 3.720 litres. Hence the gas occupies 3.720 times the volume 
 of the charcoal. 
 
 2. How many litres of oxygen gas are required to burn one litre 
 of alcohol vapor, and how many litres of aqueous vapor, and how 
 many of carbonic anhydride, will be formed in the process ? 
 
 Ans. 3 litres of oxygen, 3 litres of aqueous vapor, 2 litres of car- 
 bonic anhydride. 
 
 3. Given the symbol of alcohol C Z H 6 O to find its calorific power. 
 Ans. 6,572 units, or 7,200 units, assuming that the steam formed 
 
 was condensed. 
 
 4. The composition of dried peat is as follows : Carbon, 625.4 ; 
 Hydrogen, 68.1 ; Oxygen, 292.4 ; Nitrogen, 14.1. Find the calor- 
 ific power. Ans. 5,521 units. 
 
 5. Find the calorific intensity of marsh gas burnt in oxygen. 
 
 <7# 4 + 20=0 = G0 2 + 2H 2 
 
 Calorific power of marsh gas, 13,063. Specific heat of steam, 0.4805 ; 
 of C0 2 , 0.2164. Ans. 7,793. 
 
 6. Find the calorific intensity of olefiant gas burnt in oxygen. 
 
 C 2 ff 4 + 30-0 = 2<70 2 -f- 2E 2 
 
 Calorific power of C Z H 11,858. Specific heat of steam and. car- 
 bonic anhydride as in last problem. Ans. 9,136. 
 
 7. Find the calorific intensity of marsh gas and olefiant gas burnt 
 in air. Besides the data already given, we have also specific heat of 
 nitrogen 0.244. Ans. 2,662, and 2,916. 
 
CHAPTER XIII. 
 
 MOLECULAR WEIGHT AND CONSTITUTION. 
 
 66. Determination of Molecular Weights. It has already 
 been stated that the molecular weight of a substance is an 
 essential element in fixing its symbol and in judging of its 
 chemical relations, but until now the student has not possessed 
 the knowledge necessary in order to understand the methods 
 by which this important constant is determined. 
 
 Whenever the substance is a gas, or is capable of being vola- 
 tilized without decomposition at a manageable temperature, we 
 always ascertain the molecular weight from the specific gravity 
 on the principle already several times enforced (17). The 
 problem then resolves itself into finding the specific gravity of 
 the substance in the state of gas. The methods used in such 
 cases are described on page 21, and more in detail in the au- 
 thor's work on Chemical Physics (330 et seq.), and in the same 
 book tables are given which very greatly facilitate the calcula- 
 tion of the results. The specific gravity of the gas or vapor 
 having been found by either of these methods, and referred to 
 hydrogen gas as the unit, the molecular weight of the substance 
 is simply twice the number thus determined. But in applying 
 this important principle, on which our modern chemical philoso- 
 phy so greatly rests, two precautions are essential. 
 
 It is only true that equal volumes of all substances contain 
 the same number of molecules when they are in the condition 
 of true gases. Now, while some substances, like alcohol, assume 
 this condition at temperatures only a few degrees above their 
 boiling point, at least nearly enough for all practical pur- 
 poses, others, like acetic acid, only attain it at temperatures one 
 or two hundred degrees above their boiling point, and others 
 still, like sulphur, only at the very highest temperatures at 
 which we have been able to experiment. For this reason, the 
 specific gravity of sulphur vapor was for a long time an anomalous 
 fact in the science, and it was not until St. Clair Deville, by 
 
MOLECULAR WEIGHT AND CONSTITUTION. 127 
 
 using a porcelain globe, succeeded in determining its specific 
 gravity at a very high temperature, that its value was found to 
 correspond with the probable molecular weight, and it is pos- 
 sible that a similar anomaly which still exists in the case of 
 phosphorus and arsenic may be due to the same cause. 
 
 The chemist, however, can always have a sure criterion of 
 the condition of any vapor whose specific gravity he is deter- 
 mining by repeating his experiment at a somewhat higher tem- 
 perature. If the second result does not agree with the first, it 
 is a proof that the vapor is not yet in a proper condition, and 
 that the temperature employed in the experiment was too low. 
 A series of determinations of the specific gravity of the vapor 
 of acetic acid made by Cahours furnish an excellent illustra- 
 tion of the importance of the precaution we are discussing, and 
 will also point out another important relation of this whole sub- 
 ject. This acid when in the most concentrated state boils at 
 120, and the specific gravity of its vapor referred to hydrogen 
 at the same temperature and pressure was found to have the 
 following values at the temperatures annexed : 
 
 At 125 
 
 45.90 
 
 At 170 
 
 35.30 
 
 At 240 
 
 30.16 
 
 " 130 
 
 44.82 
 
 " 180 
 
 35.19 
 
 " 270 
 
 30.14 
 
 " 140 
 
 41.96 
 
 " 190 
 
 34.33 
 
 310 
 
 30.10 
 
 " 150 
 
 39.37 
 
 " 200 
 
 32.44 
 
 " 320 
 
 30.07 
 
 " 160 
 
 37.59 
 
 " 220 
 
 30.77 
 
 " 336 
 
 30.07 
 
 It will be noticed that, as the temperature increases, the 
 specific gravity diminishes, at first very rapidly, afterwards 
 more slowly, and does not become constant until the tempera- 
 ture has risen 200 above the boiling point, when we have the 
 true specific gravity of acetic acid in the state of gas. This 
 gives for the molecular weight of acetic acid 60 very nearly, 
 which corresponds to the received formula, C 2 ff 4 0. 2 . The slight 
 difference between the theoretical and the observed results 
 may be in part due to errors of observation, but is most prob- 
 ably to be referred to the same cause which determines even 
 in the permanent gases, when under the atmospheric pressure, 
 a variation from Mariotte's law. We do not expect, moreover, 
 to find from the specific gravity the exact molecular weight. 
 The precise value is determined by the results of analysis, which 
 are, as a rule, far more accurate, and the specific gravity is 
 
128 
 
 MOLECULAR WEIGHT AND CONSTITUTION. 
 
 only used to decide which of several possible multiples must be 
 the true value. (Compare carefully 23.) 
 
 67. Disassociation. -7- But, besides taking care that the tem- 
 perature is sufficiently high to bring the substance we are 
 studying into the condition of a true gas, we must look out that 
 the compound is not decomposed in the process. It is now well 
 known that at very high temperatures the disassociation of 
 the elements of a compound body is a constant result, and it is 
 probable that in some cases the same effect is produced at the 
 much lower temperatures which are employed in the determi- 
 nation of vapor densities. The specific gravity of the vapor 
 of ammonic chloride, instead of being 26.75, as we should ex- 
 pect from the undoubted weight of its molecule, NHCl, is 
 only about one half of this amount ; and the reason probably is, 
 that, when heated, the molecule breaks into two, and in conse- 
 quence the volume of the vapor doubles. 
 
 It is very difficult, however, to obtain any further evidence 
 that such a change has taken place ; for, as soon as the tempera- 
 ture falls, the molecules recombine in assuming the solid condi- 
 tion, and all the phenomena attending the change of state are 
 precisely the same as those observed in any other volatile 
 body. Indeed, although many very ingenious experiments 
 have been made with a view of settling the question, it is still 
 uncertain, not only in this, but also in several other cases, 
 whether disassociation has taken place or not. The question 
 is of great importance to the theory of chemistry. If disasso- 
 ciation does not take place, the cases referred to are exceptions 
 to the law of equal molecular volumes, and specific gravity can 
 no longer be regarded, as now, the sole measure of molecular 
 weight. If, however, it can be proved that such a change does 
 take place, then the unity of our present theory is preserved, 
 and the chemist has only to guard against this cause of error 
 ,in his experiments. 
 
 68. Indirect Determination of Molecular Weight. Al- 
 though our modern chemical theories rest in great measure on 
 the molecular weight of a few typical compounds determined, 
 
MOLECULAR WEIGHT AND CONSTITUTION. 129 
 
 at least approximately, by their specific gravities, yet it is only 
 in a comparatively few cases that we are able to refer the 
 molecular weight of a substance directly to this fundamental 
 measure. Most substances are so fixed, or so easily decom- 
 posed by heat, that it is impossible to determine the specific 
 gravity of their vapor, even when such a condition is possible. 
 In these cases, however, we endeavor to refer the molec- 
 ular weight indirectly to the fundamental measure, by estab- 
 lishing a relation of chemical equivalency between the sub- 
 stance whose molecular weight is sought and some closely 
 allied volatile substance whose molecular weight has been pre- 
 viously determined in the manner described above. A few ex- 
 amples will make the application of this principle intelligible. 
 
 It is required to determine the molecular weight of nitric 
 acid. A careful study of the numerous nitrates leads to the 
 conclusion that this acid, like hydrochloric acid, ffd, con- 
 tains but one atom of replaceable hydrogen. For example, we 
 find but one potassic nitrate and one sodic nitrate, whereas we 
 should expect to find several, if the acid were polybasic. 
 Hence we conclude that, one molecule of argentic nitrate, like 
 one molecule of argentic chloride, AgCl, contains but one 
 atom of silver. Next, we analyze argentic nitrate, and find 
 that 100 parts of the salt contain 63.53 parts of silver. We 
 know the atomic weight of silver, 108, and evidently this must 
 bear the same relation to the molecular weight of argentic 
 nitrate that 63.53 bears to 100. But 63.53:100 = 108: 
 x170, which is the molecular weight of argentic nitrate, 
 and, since the molecule of nitric acid differs from that of argen- 
 tic nitrate only in containing an atom of hydrogen in place of 
 the atom of silver, its own weight must be 170 108 -|- 1 
 
 = 63. 
 
 It is required to determine the molecular weight of sul- 
 phuric acid. A comparison of the different sulphates shows 
 that sulphuric acid is dibasic. We find two sulphates of potas- 
 sium and sodium, an acid sulphate and a neutral sulphate, and 
 hence we conclude that this acid contains two replaceable 
 atoms of hydrogen, and hence that one molecule of neutral 
 potassic sulphate contains two atoms of potassium. In ana- 
 lyzing potassic sulphate it appears that 100 parts of the salt 
 contain 44.83 parts of potassium, and evidently this weight 
 9 
 
130 MOLECULAR WEIGHT AND CONSTITUTION. 
 
 bears the same relation to 100 that the weight of two atoms of 
 potassium bears to the weight of the molecule of potassic sul- 
 phate. Thus we have, 
 
 44.83 : 100 = 78 : x = 174 ; the M. W. of Potassic Sulphate, 
 and 174 78 + 2 = 98 ; the M. W. of Sulphuric Acid. 
 
 By a similar course of reasoning we may deduce from the 
 results of analysis, and from the general chemical rela- 
 tions, the molecular weight of any other acid or base. If 
 there is any question in regard to the basicity of the acid or 
 the acidity of the base, there will be the same question as to 
 the molecular weight ; but we cannot be led far into error, for 
 the true weight will be some simple multiple or submultiple of 
 the one assumed, and the progress of science will sooner or 
 later correct our mistake. From the molecular weight of any 
 acid we easily deduce the molecular weights of all its salts. 
 
 When the substance is not distinctively an acid or a base, but 
 is capable of entering into combination with other bodies, we 
 can frequently discover its molecular weight by determining 
 experimentally how much of this substance is equivalent to a 
 known weight of some sillied but volatile substance whose 
 molecular weight is known. Thus ammonia gas, whose molec- 
 ular weight is one of the best-established data of chemistry, 
 enters into direct union with a compound of platinic chloride 
 and hydrochloric acid (PtCl G II. 2 ) to form a definite crystalline 
 salt whose composition is exactly known. 
 
 PtCl.H 2 + 2N a = PtCl 6 (Nff 4 ) f [61] 
 
 Now a very large number of substances allied to ammonia 
 form with this same platinum salt equally definite products, so 
 that by simply determining the weight of platinum in these 
 compounds, which is very easily done, their molecular weights 
 may at once be referred to the molecular weight of ammonia. 
 
 Lastly, if other means fail, we may sometimes discover the 
 molecular weight of a compound by carefully studying the reac- 
 tions by which it is formed or decomposed, and inferring the 
 weight of the compound from that of its factors or products. We 
 seek to express the reaction in the simplest possible way, and 
 give that value to the molecular weight which best satisfies the 
 
MOLECULAR WEIGHT AND CONSTITUTION. 131 
 
 chemical equation. Evidently, however, such results are less 
 trustworthy than those obtained by either of the other methods. 
 
 69. Constitution of Molecules. It is a favorite theory with 
 some chemists that no molecule can exist in a free condition 
 with any of its affinities unsatisfied, but those who hold this 
 view are compelled to admit that two points of attraction in 
 the same atom may, in certain cases, neutralize each other. 
 Hence, they would distinguish between a dyad atom like that 
 of oxygen ( }, with its affinities open, and a dyad atom like 
 that of mercury (p"^), with its affinities closed through their own 
 mutual attraction. The first could not exist in a free condition, 
 while the last could. In like manner any atom, having an even 
 number of points of attraction, can exist in a free state because 
 all its affinities may be satisfied within itself; but an atom hav- 
 ing an uneven number of points cannot, for at least one of its 
 
 affinities must be open as is shown by the symbol ( -). As 
 
 thus interpreted it must be admitted that the theory explains 
 many facts. 
 
 For example, among the univalent elements, chlorine, bro- 
 mine and iodine are all known to have molecules consisting of 
 two atoms. So, also, the molecule of cyanogen gas consists of 
 two atoms of the radical CN, and the same is true of ethyl, 
 propyl, &c., at least if the hydrocarbons so named .have really 
 the constitution first assigned to them. 
 
 Passing next to the dyads, we find that, while oxygen, sulphur, 
 selenium and tellurium have molecules consisting of two atoms, 
 the metals mercury and cadmium, and the radicals ethylene, 
 propylene, &c. (O 2 ff 4 and C Z H^, have molecules which coincide 
 with their atoms. 
 
 Of the well-defined triad elements none are volatile, but the 
 two triad radicals which have been obtained in a free state 
 allyl 1 (O 8 ff s ) and kakodyl ((Cff 3 ) 2 As) both have double 
 atomic molecules. 
 
 In like manner none of the tetrad elements are volatile, 
 and the only tetrad radicals known in a free state have single 
 atomic molecules. 
 
 Of the pentad elements nitrogen has a molecule of two 
 atoms, while phosphorus and arsenic have molecules of four 
 
 1 See page 78; Problem 7. 
 
132 MOLECULAR WEIGHT AND CONSTITUTION. 
 
 atoms. No compound radicals of this order are known in a 
 free state. 
 
 Lastly, the only hexad radical known in a free state, benzine, 
 C 6 ff G , has a molecule which coincides with its atom. 
 
 Thus it appears that in general the theory is sustained by the 
 
 facts. Nevertheless, there are several well-marked exceptions 
 
 in i 
 
 to it. Thus the well-known compounds NO and N0. 2 have 
 
 molecules which act as radicals of uneven atomicities and yet 
 contain but one complex atom. We must be careful, therefore, 
 not to give too much weight to this hypothesis, but still it may 
 be useful in co-ordinating facts. It leads at once to three gen- 
 eral principles which will be found to be almost universally 
 true. 
 
 The first is that the sum of the atomicities of the atoms of 
 every molecule is an even number. 
 
 The second is that the atomicity of any radical is an odd 
 or even number according as the sum of the atomicities of 
 its elementary atoms is odd or even. 
 
 The third is that the qu an ti valence of elementary atoms 
 must be, as stated on page 59, either even or odd. They are 
 artiads or perissads, and the two characters can never be mani- 
 fested by the same elements. 
 
 It has also been a question among chemists whether molec- 
 ular combination was possible ; in other words, whether it is 
 possible for molecules of different kinds to combine chemically, 
 each preserving its integrity in the compound. Some of the 
 advocates of the unitary theory, in the reaction against the 
 dualistic system, have been inclined to doubt the possibility of 
 such compounds, and have attempted to represent the symbols 
 of all compounds in a single molecular group ; but any ante- 
 cedent improbability, on theoretical grounds, is far more than 
 outweighed by the evidence of a large number of compounds 
 whose constitution is most simply explained on the hypothesis 
 of molecular combination. For example, in the crystalline salts 
 it is impossible to doubt that the water exists as such, not as a 
 part of the salt molecule, but combined with it as a whole. So, 
 also, there are a number of double salts whose constitution is 
 most simply explained on a similar hypothesis, and, in the pres- 
 ent state of the science, it seems unnecessary to complicate 
 their symbols by forcing them into the unitary mould. It is a 
 
MOLECULAR WEIGHT AND CONSTITUTION. 133 
 
 characteristic of such molecular compounds as are here assumed, 
 that the force which holds together the molecules is much feebler 
 than that which binds together the atoms in the molecule. When 
 the molecular attraction is very strong, it is probable that in 
 almost all cases the different molecules coalesce into one ; and 
 between the extreme limits we find compounds in which it is 
 difficult to determine whether true molecular combination ex- 
 ists or not. Such coalescing of distinct molecules seems always, 
 however, to be attended with a greater development of heat, and, 
 in general, with a more marked manifestation of physical ener- 
 gies, than usually attends either molecular aggregation or atomic 
 metathesis. 
 
 In the notation of this book molecular combination is indi- 
 cated by writing together the symbols of the different molecules 
 thus united, but separating these symbols by periods. Thus 
 the symbols ^KCLPtCl^ and 3NaF.SbF 3 represent compounds 
 of this class. 
 
 70. Isomerism, Allotropism, Polymorphism. We should 
 infer from the doctrine of chemical types that the same atoms 
 might be grouped together in different ways, so as to form 
 different molecules which in their aggregation would present 
 essentially distinct qualities. Hence, we should expect to find 
 distinct substances having the same composition ; and in fact 
 our science, organic chemistry especially, is rich in examples 
 of this kind. Such substances are said to be isomeric, and the 
 phenomenon is called isomerism. There are different phases 
 of isomerism, which it will be well to distinguish, not so much 
 on account of any essential differences in the phenomena as in 
 order to make ourselves better acquainted with its manifesta- 
 tions. 
 
 In the first place, we have examples of isomeric bodies 
 having the same centesimal composition, but showing no rela- 
 tion to each other in their properties or in their chemical 
 reactions. Sometimes we have assigned to them the same 
 formula, but in other cases the symbol of one is a simple 
 multiple of that of the other. Thus aldehyde and oxide of 
 ethylene have both the symbol C 2 ff 4 0', cane sugar and gum 
 arabic, the common formula C 12 H 2 . 2 U ; lactic acid, the formula 
 C^ff Pt O s ', and glucose, C ti ff l2 6 . These compounds bear no 
 resemblance to each other, and have no relations in common 
 
134 MOLECULAR WEIGHT AND CONSTITUTION. 
 
 save the single fact that their centesimal composition is the 
 same. 
 
 In the second place, we have numerous examples of isomeric 
 compounds which belong to the same chemical type, and there- 
 fore present the same chemical reactions, but in which the two 
 factors of the molecule are in a measure complementary to 
 each other. Thus ethylic formiate has exactly the same com- 
 position as methylic acetate, 
 
 (C 2 ff 5 )-0-(CHO), (Cff 3 )-0-(C. 2 H 3 0); 
 
 for while the basic radical of the first contains the quantity 
 Cff 2 more than the basic radical of the second, the acid radi- 
 cal of the first falls short of the acid radical of the second by 
 exactly the same amount. 
 
 In the third place, we have several groups of isomeric com- 
 pounds, especially among the hydrocarbons, which have the 
 same general properties and the same percentage composition, 
 but which differ from each other in their molecular weights ; so 
 that the symbol of one is a multiple of that of the rest. The 
 hydrocarbous ethylene C. 2 ff^ propylene C 3 ff 6 , butylene 4 ff s , 
 form a group of this kind. Compounds of this class are fre- 
 quently called polymeric, and sometimes the heavier com- 
 pounds may be regarded as condensed forms of the lighter. 
 
 Lastly, we may distinguish still a fourth class of isomeric 
 compounds which have the same general properties, the same 
 symbol, and the same general system of reactions, but which 
 differ in a few marked qualities, physical or chemical, and 
 which preserve these characteristics to a greater or less extent in 
 their compounds. The two forms of toluic acid, G^H^O^ be- 
 long to this class, and such compounds are isomeric in the 
 fullest sense of the word. 
 
 In all the above examples the differences between the iso- 
 meric compounds are sufficiently jrreat to lead chemists to 
 assign to each a distinct name. When, however, the differ- 
 ences are not sufficiently great to justify a distinct name, the 
 two bodies are said to be different allotropic states of the same 
 substance. Thus there are two varieties of tartaric acid ; the 
 first of which deviates the plane of polarization of a ray of light 
 to the left, while the second deviates it to the right ; but since 
 in almost every other respect these two bodies are identical, 
 
MOLECULAR WEIGHT AND CONSTITUTION. 135 
 
 we do not speak of them as different substances, but merely us 
 different allotropic states of tartaric acid. There are also three 
 other varieties of tartaric acid, but these differ so greatly from 
 the normal acid in crystalline form, in solubility, and also in 
 other relations, that they may fairly be regarded as distinct 
 substances. 
 
 Again, there are many substances where the difference of 
 state or allotropism is associated with difference of crystalline 
 form ; and when this difference of form is fundamental, the 
 substance is said to be dimorphous or trimorphous, as the case 
 may be, and the phenomenon is called polymorphism. Thus 
 common calcic carbonate crystallizes in two fundamentally dis- 
 tinct forms, corresponding to the two mineralogical species, 
 calcite and aragonite. Such difference of form, however, is 
 invariably accompanied by a marked difference of properties, 
 so that polymorphism is merely one of the indications of allo- 
 troi>i:-m. 
 
 Differences of condition similar to those we have described 
 manifest themselves even more markedly among elementary 
 substances ; and indeed the word allotropism was first applied 
 to phenomena of this last class. Thus there are two allotropic 
 states of phosphorus, which differ so much from each other that 
 no one would suspect from their external characters that there 
 was any identity between them, and to these two states corre- 
 spond two fundamentally different crystalline forms. In some 
 cases the differences between the allotropic states of the same 
 element are far greater than any which are seen between the 
 most unlike isomeric compounds. No substances could be 
 better defined by well-marked and utterly distinct qualities 
 than diamond, plumbago, and charcoal, and yet they are all 
 three allotropia modifications of the one elemental substance 
 we call carbon ; and suHi phenomena as these give us strong 
 grounds for believing that our present elements may have a 
 composite structure. 
 
136 MOLECULAR WEIGHTS AND CONSTITUTION. 
 
 Questions and Problems 
 
 1. What are the molecular weights of alcohol and camphor as de- 
 duced from the results of the jn (>r. determinations given on page 
 23? 
 
 Ans. 45.5 and 155, which, although not closely agreeing with the 
 theoretical numbers, enables us to decide that the symbols 
 of these compounds are C^H 6 and Ci H l6 as the simplest 
 interpretation of the analyses would indicate. 
 
 2. At the temperature of 470 the 0p. (>r. of the vapor of sul- 
 phuric acid is approximately 1.697. How does this result agree with 
 the generally received symbol of this compound, and how do you 
 explain the discrepancy ? 
 
 3. A study of the different tartrates has led to the conclusion 
 already expressed that tartaric acid, although tetratomic, is dibasic. 
 It also appears that one hundred parts of neutral argentic tartrate 
 yield when ignited 55.39 parts of metallic silver. Required the 
 molecular weight of tartaric acid. Ans. 176. 
 
 4. An hundred parts of baric oxide, BaO, (whose composition is 
 assumed to be known) yield when treated with sulphuric acid 152.3 
 parts of baric sulphate. Further it is assumed, as the result of care- 
 ful study, that sulphuric acid is bibasic, and the metal barium a biva- 
 lent radical. Required the molecular weight of sulphuric acid. 
 
 Ans. 98. 
 
 5. The well-known base aniline gives with platinic chloride a 
 definite crystalline product, one hundred parts of which yield on 
 ignition 32.99 parts of platinum. Required the molecular weight of 
 aniline. How does this result agree with the 0p. (J5r. of aniline 
 vapor, which has been found by observation to be 3.210. V 
 
 Ans. 93; which corresponds to 0p. (r. f 3.223. 
 
 6. The base triethylamine gives in like manner a platinum salt, 
 one hundred parts of which yield on ignition 33.67 parts of plati- 
 num. Required the molecular weight. Ans. 101. 
 
 7. Compare together the symbols of the compounds of the va- 
 rious alcohol radicals on pages 90 to 93 and point out the exam- 
 ples of isomerism. 
 
CHAPTER XIV. 
 
 CRYSTALLINE FORMS. 
 
 71. Relations to Chemistry. Almost every substance 
 affects a definite polyhedral form, although it may manifest 
 this tendency only under favorable conditions. Such forms are 
 called crystals, and the process of crystalline growth, or de- 
 velopment, is called crystallization. The one essential condi- 
 tion of crystallization is a certain freedom of motion, and crys- 
 tals, more or less perfect, are usually formed whenever a molten 
 liquid " sets," or a solid is deposited from a condition of solution 
 or of vapor ; and in each case the slower the process the larger 
 and the more perfect are the crystals. The crystalline condi- 
 tion is, in fact, the normal state of solid matter. It is true that 
 there are a few substances which, like glue, are only known in 
 the colloid state; but in most of the so-called colloid sub- 
 stances this state is abnormal, and there is a constant tendency 
 to crystallization. Moreover, its peculiar crystalline form is one 
 of the most characteristic, and apparently one of the most es- 
 sential, properties of a substance, and is therefore of great value 
 in determining its chemical affinities. The study of the geomet- 
 rical relations of these forms is, however, in itself a separate 
 science, and in this connection we can only dwell on the few 
 elementary principles of the subject on which our system of 
 chemical classification in part rests. 
 
 72. Definitions. In the forms of crystals the idea of sym- 
 metry is the great controlling principle. Each substance fol- 
 lows a certain law of symmetry, which seems to be inherent, 
 and a part of its very nature ; and when, from any cause, the 
 character of the symmetry changes, the substance loses its 
 identity, and, even if its chemical composition remains the 
 .ame, it becomes, to all intents and purposes, a different sub- 
 stance. In every crystal the symmetry points to a few direc- 
 tions, to which not only the position of the planes, but also the 
 physical properties of the body,, are closely related. Certain of 
 
138 
 
 CRYSTALLINE FORMS. 
 
 Fig. 4. 
 
 these directions, more or less arbitrarily chosen, are called the 
 axes of the crystals, and a crystalline form may be defined as 
 a group of similar planes symmetrically disposed around these 
 axes. As is evident from this definition a 
 crystalline form, like a geometrical form, is 
 a pure abstraction, and this conception is 
 carefully to be kept distinct from the idea 
 of a crystal, which implies not only a cer- 
 tain form, but also a certain structure. 
 Moreover, in by far the larger number of 
 cases the same crystal is bounded by several 
 forms. Thus, in Fig. 4, which represents a 
 crystal of common quartz, the planes of the 
 prism and the planes of the pyramid are 
 distinct crystalline forms. 
 
 73. Systems of Crystals. A careful study of the forms of 
 crystals has shown that these forms may be classified under six 
 crystalline systems, each of which is distinguished by a peculiar 
 plan of symmetry. These divisions, it is true, are in a meas- 
 ure arbitrary ; for here, as elsewhere in nature, no sharp dividing 
 lines are found ; but nevertheless the distinctions on which the 
 classification rests are clearly marked. We can only give in 
 this book a very imperfect idea of these several plans of sym- 
 metry by representing with figures a few of the more charac- 
 teristic forms of each. 
 
 74. First or Isometric System. 1 The three most frequently 
 occurring forms of this system are the regular octahedron, the 
 
 Fig. 5. 
 
 Fig. 6. 
 
 Fig. 7. 
 
 rhombic dodecahedron and the cube, Figs. 5, 6, and 7. These 
 and all the other forms of the system may be regarded as 
 
 1 Called also monometric. 
 
CRYSTALLINE FORMS. 
 
 139 
 
 grouped around three equal and similar axes at right angles to 
 each other, and hence the name isometric (equal dimensions). 
 They present the same symmetry on all sides, and the appear- 
 ance of the form is identical, whichever axis is placed in a ver- 
 tical position. In this system no variation in the relative posi- 
 tions or lengths of the axes is possible, for this would change 
 the plan of symmetry on which the system is based. 
 
 75. Second or Tetragonal System. 1 The plan of symmetry 
 in this system is best illustrated by the square octahedron, Fig. 
 8. Of this form the basal section, Fig. 9, is a square, and to 
 
 this fact the name of the system refers. The vertical section, 
 on the other hand, is a rhomb, Fig 10. Here, as in the first 
 system, the forms may all be referred to three rectangular axes, 
 but only two have the same length ; the third may be either 
 longer or shorter than the others. The last is the dominant 
 axis of the form, and hence we always place it in a vertical 
 position and call it the vertical axis. The length of the verti- 
 cal axis bears a constant ratio to that of the lateral axes in all 
 crystals of the same substance, but this ratio differs very greatly 
 for different substances, and is therefore an important crystal- 
 lographic character. The familiar square prism is another very 
 characteristic form of this system. 
 
 Fig. 11. Fig. 12. 
 
 Moreover, the plane* both of the prism and of the octahedron 
 may have different positions with reference to the lateral axes, 
 as is shown by the two basal sections, Fisrs. 11 and 12 ; 
 
 Called also dimetric. 
 
140 
 
 CRYSTALLINE FORMS. 
 
 and this leads us to distinguish two square prisms and two 
 square octahedrons, one of which is said to be the inverse of 
 the other. 
 
 76. Third or Hexagonal System. In the last system the 
 planes were arranged by fours around one dominant axis, while 
 in this system they are arranged by sixes. The most character- 
 istic forms of this system are the hexagonal pyramid, Fig. 13, 
 and the hexagonal prism, Fig. 14. The basal section through 
 either of these forms is a regular hexagon, Fig. 15, and, besides 
 
 Fig. 13. 
 
 Fig. 14. 
 
 Fig. 15. 
 
 the dominant or vertical axis, we also distinguish as lateral axes 
 the three diagonals of this hexagonal section. These lateral 
 axes stand at right angles to the vertical axis, but between 
 themselves they subtend angles of 60, Here, as before, the 
 ratio of the length of the vertical axis to the common length of 
 the lateral axes has a constant value on crystals of the same 
 substance, but differs very greatly with different substances, 
 the vertical axis being sometimes longer and sometimes shorter 
 
 Fig. 17. 
 Fig. 16. 
 
 than the other three. The rhombohedron, Fig. 16, and the 
 scalenohedron, Fig. 17, are also forms of this system, and occur 
 
CRYSTALLINE FORMS. 141 
 
 even more frequently than the more typical forms first men- 
 tioned. Lastly, a difference of position in the planes of the 
 prism or pyramid with reference to the lateral axes gives rise 
 in this system to the same distinction between the direct and 
 the inverse forms as in the last. 
 
 77. Fourth or Orthorhombic System. 1 The most character- 
 istic forms of this system are the rhombic octahedron, Fig. 18, 
 and the right rhombic prism, from which the system takes its 
 name. The three principal sections of the octahedron, repre- 
 sented by Figs. 19, 20, and 21, and also the basal section of the 
 
 Fig. 18. Fig. 19. 
 
 prism, are all rhomb?, whose relations to the form are indicated 
 by the lettering of the figures. We easily distinguish here three 
 axes at right angles to each other, but of unequal lengths, and 
 in regard to the ratios of these lengths the remarks of the last 
 two sections are strictly applicable. 
 
 78. Fifth or Monoclinic System. The forms classed together 
 under this system may be referred to three unequal axes, one of 
 which stands at right angles to the plane of the other two, while 
 they are inclined to each other at an angle, which, though con- 
 stant on crystals of the same substance, varies very greatly with 
 different substances, as vary also the relative dimensions of the 
 axes themselves. Fig. 22 represents an octahedron of this 
 system, and Figs. 23 and 24 represent two sections made 
 through the edges FF and DD of this form. A section 
 through the edges GO would be similar to Fig. 23, and these 
 three sections give a clear idea of the relative positions of the 
 axes. The section, Fig. 24, containing the two oblique axes, 
 
 1 Called also trimetric. 
 
142 CRYSTALLINE FORMS. 
 
 is called the plane of symmetry, and the faces on all monoclinic 
 crystals are disposed symmetrically solely with reference to this 
 plane. In a word, the symmetry is bilateral, and corresponds 
 
 Fig. 22. Fig. 23. Fig. 24. 
 
 to the type with which we are so familiar in the structure of 
 the human body. This plan of symmetry is well illustrated by 
 Figs. 25, 26, and 27, which represent the commonly occurring 
 forms of gypsum, augite, and felspar, three of the most com- 
 mon minerals. These figures, however, do not, like those of the 
 previous sections, represent simple crystalline forms. The crys- 
 tals here represented are in each case bounded by several forms, 
 and indeed in this system such compound forms are alone pos- 
 sible, for no simple monoclinic form can of itself enclose space. 
 
 Fig. 25. Fig. 26. Fig. 27. 
 
 79. Sixth or Triclinic System. This system is distinguished 
 by an almost complete want of symmetry. Only opposite planes 
 Fig. 28. are similar, and two such planes constitute a 
 
 complete crystalline form. Hence on every 
 crystal there must be at least three simple forms. 
 We may refer the planes of any crystal to 
 three unequal axes all oblique to each other, 
 but the position we assign to them is quite ar- 
 bitrary, and they have therefore little value as 
 crystallographic elements. Fig. 28 represents 
 a crystal of sulphate of copper, one of the very few subtances 
 which crystallize in this system.. 
 
CRYSTALLINE FORMS. 
 
 143 
 
 80. Modifications on Crystals. When several crystalline 
 forms appear on the same crystal, some one is usually more 
 prominent or dominant than the rest, and gives to the crystal 
 its general aspect, the planes of the secondary forms only ap- 
 pearing on its edges or solid angles, which are then said to be 
 modified or replaced. Thus, in Figs. 29, 30, and 31, the solid 
 angles of a qube are replaced (or truncated) by the faces of an 
 octahedron ; in Fig. 32 the edges of the cube are replaced by 
 the faces of the dodecahedron ; in Fig. 33 the edges of the 
 octahedron are modified in the same way ; arid in Fig. 34 the 
 solid angles of a dodecahedron are replaced by the faces of an 
 
 Fig. 29. 
 
 Fig. 31. 
 
 octahedron. These are all forms of the isometric system, and 
 the relations of the simple forms to each other, which deter- 
 mine in every case the position of the secondary planes, will 
 be readily seen on comparing together the figures already 
 given on page 138. These figures, like all crystallographic 
 drawings, are geometrical projections, and represent the planes 
 in the same relative position towards the crystalline axes which 
 they have on the crystal itself. Moreover, since in all figures 
 of crystals of this system the axes are drawn in absolutely 
 the same position on the plane of the paper, the same face has 
 also the same position throughout. 
 
 As a general rule, all the similar parts of a crystal are 
 simultaneously and similarly modified. This important law, 
 
144 
 
 CRYSTALLINE FORMS. 
 
 which is a simple inference from the principles already stated, 
 is illustrated by the figures just given, and also by Figs. 
 
 Fig. 35. Fig. 33. Fig. 37. Fig. 38. 
 
 35 to 50. By carefully studying these figures, as well as Figs. 
 25 to 28 on page 142, the student will be able to refer each of 
 
 rig. 39. 
 
 ^ 40 - Fi,, 41. 
 
 the compound crystals here represented to one or the other of 
 the systems of symmetry already described, and from this and 
 
 Fig. 42. 
 
 Fig. 43. 
 
 Fig. 41. 
 
 similar practice he will learn, better than from any descrip- 
 tions, how clearly the modifications on a crystal point out its 
 crystallographic relations. 
 
CRYSTALLINE FORMS. 
 
 145 
 
 81. Hemihedral Forms. To the law governing the modi- 
 fications of crystals just stated, there is one important excep- 
 
 Fig. 45. 
 
 Fig. 46. 
 
 Fig. 47. 
 
 Fig. 48. 
 
 tion. It not unfrequently happens that half the similar parts 
 of a crystal are modified independently of the other half. Thus 
 
 Fig. 49. 
 
 Fig. 50. 
 
 in Fig. 51 only one half of the solid angles of the cube are 
 truncated. The modifying form in this case is the tetrahedron, 
 
 Fig. 52. 
 
 Fig. 53, also a simple form of the isometric system. When 
 all the solid angles of the cube are truncated, the modifying 
 form, as has been shown, is the octahedron, and the relation 
 which the tetrahedron bears to the octahedron is shown by 
 Fig. 52. The rhombohedron, Fig. 54, stands in a similar re- 
 lation to the hexagonal pyramid, Fig. 55. From these figures 
 
116 CRYSTALLINE FORMS. 
 
 it is evident that while the octahedron and the hexagonal pyra- 
 mid have all the planes which perfect symmetry requires, the 
 
 Fig. 55. 
 
 tetrahedron and the rhombohedron have only half the number, 
 and in crystallography all forms which bear a similar relation 
 to the forms of perfect symmetry are said to be Amifeedral, 
 while the forms of perfect symmetry are distinguished as holo- 
 hedral. The hemihedral forms are quite numerous in all the 
 systems, but with the exception of the tetrahedron, rhombohe- 
 dron, and scalenohedron (Fig. 17), they seldom appear except 
 as modifying planes on the edges or solid angles of the more 
 perfect forms. As a general rule, they are easily recognized, 
 but not unfrequently they give to a crystal the aspect of a dif- 
 ferent system from that to which it really belongs, and may 
 lead to false inferences ; but these can, in most cases, be cor- 
 rected by a careful study of the interfacial angles. 
 
 82. Identity of Crystalline Form. As has already been 
 stated, every substance is marked by certain peculiarities of 
 outward form, which are among its most essential qualities, and 
 we must next learn in what these peculiarities consist. As a 
 general rule, the same substance crystallizes in the same form, 
 but under unusual circumstances it frequently appears in other 
 forms of the same system. Thus fluorspar is usually found 
 crystallized in cubes, but in large collections crystals of this 
 mineral may be seen in almost all the holohedral forms of the 
 isometric system, including their numerous combinations. In 
 like manner common salt usually crystallizes in cubes, but out 
 of a solution containing urea it frequently crystallizes in octa- 
 hedrons. Moreover, the sams principle holds true in regard 
 to substances crystallizing in other systems, most of whose 
 forms never appear except in combination. Thus the mineral 
 
CRYSTALLINE FORMS. 147 
 
 quartz generally shows the simple combination represented in 
 Fig. 4 ; but more than one hundred other forms, all, however, 
 belonging to the same system, have been observed on crystals 
 of this well-known substance. So also the crystals of gypsum, 
 augite, and felspar, in most cases present the forms already 
 figured on page 142, although other forms are common, which, 
 however, in each case all belong to the same crystalline system. 
 We never find the same substance in the forms of different sys- 
 tems except in those cases of polymorphism already described, 
 page 135, where the differences in other properties are so great 
 that the bodies can no longer be regarded as the same substance. 
 
 Among substances crystallizing in the isometric system the 
 crystalline form is not so distinctive a character as it is in other 
 cases. In this system the relative dimensions are invariable, 
 and the octahedron, the dodecahedron, and the cube, more or 
 less modified by different replacements, are the constantly re- 
 curring forms. Even here, however, specific differences may 
 at times be found in the fact that some substances affect hemi- 
 hedral forms on modification, while others do not. In all the 
 other systems the dimensions of the crystal (the relative lengths 
 of its axes and the values of the interaxial angles) distinguish 
 each substance from every other. But here, also, the general 
 statement must be somewhat modified. 
 
 We frequently find on the crystals of the same substance 
 several forms having different axial dimensions. Thus, on the 
 crystal represented by Fig. 56, belonging to the tetragonal 
 system, there are three different octahedrons, and three cor- 
 responding values of the vertical axis. But if, beginning with 
 the planes of the octahedron 0, we determine 
 the ratio which its vertical axis bears to the Flg " 56 ' 
 
 common length of the two lateral axes, and 
 call this value a, we shall find that the cor- 
 responding values for the two other octahe- 
 drons are 2a and a respectively. More- 
 over, if we extend our study we shall also 
 find that this example illustrates a general 
 principle, and that the crystalline forms of 
 a given substance include not only those of 
 identical axial dimensions, but also those whose dimensions bear 
 to each other some simple ratio* 
 
148 CRYSTALLINE FORMS. 
 
 This most important law gives to the science of crystallog- 
 raphy a mathematical basis, and enables us to apply the exhaus- 
 tive methods of analytical geometry in discussing the various re- 
 lations of the subject. Among the actual forms of a given sub- 
 stance we fix on some one as the fundamental form, and, taking 
 the values of its axial dimensions as our standards, we are able 
 to express the position of the planes of all the possible forms by 
 means of very simple symbols, and also to express by mathe- 
 matical formulae the relations of the interfacial angles to the 
 same fundamental elements of the crystal; so that the one 
 may readily be calculated from the other. 
 
 It may seem at first sight that the crystallographic distinction 
 between different substances, insisted on above, is greatly ob- 
 scured by the important limitations just made. But it is not 
 so, at least to any great extent. The selection of the funda- 
 mental form of a given substance is not arbitrary, although it is 
 based on considerations which it lies beyond the scope of this 
 book to discuss. Moreover, an error in this choice is not fun- 
 damental, since the true conception of the form of a substance 
 includes not only the fundamental form, but all those which are 
 related to it. This conception, though not readily embodied in 
 ordinary language, is easily expressed by a general mathemat- 
 ical formula, and is as tangible to one familiar with the subject 
 as the general statement first made. 
 
 But however obscure, to those who are not familiar with 
 mathematical conceptions, may be the distinction between the 
 forms of different substances in the same system, the difference 
 between the different systems is clear and definite, and it is 
 with this broad distinction that we have chiefly to deal in our 
 chemical classification. 
 
 83. Irregularities of Crystals. It must not be supposed 
 that natural crystals have the same perfection of form and 
 regularity of outline which our figures might seem to indicate. 
 In addition to being more or less bruised or broken from acci- 
 dental causes, crystals are rarely terminated on all sides, one 
 or more of the faces being obliterated where the crystal is im- 
 planted on the rock, or where it is merged in other crystals. 
 But by far the most remarkable phase which the irregularities 
 of crystals present is that shown by Figs. 57 to 67. By com- 
 paring together the figures which have been here grouped to- 
 
CRYSTALLINE FORMS. 149 
 
 gether on the page, and which represent in each case different 
 phases of the same crystalline form, it will be seen that the 
 variations from the normal type are caused by the undue de- 
 Fig. 58 
 Fig. 57. HHHB Fig> 59 ' 
 
 velopment of certain planes at the expense of their neighbors, 
 or by an abnormal growth of the crystal in some one direction. 
 
 Fig. 61. 
 Fig. 60. 
 
 Such forms as these, however, although great departures 
 from the ideal geometrical types, are in perfect harmony with 
 
 Fig. 62. 
 
 mm 
 
 Fig. 63. 
 
 the principles of crystallography. The axis of a crystal is not 
 a definite line, but a definite direction ; and the face of a crystal 
 
150 
 
 CRYSTALLINE FORMS. 
 
 is not a plane of definite size, but simply an extension in two 
 definite directions. These directions are the only fundamental 
 elements of a crystalline form, and they are preserved under 
 
 Fig. 66. 
 
 Fig. 64. 
 
 all conditions, as is proved by the constancy of the interfacial 
 angles, and of the modifications, on crystals of the same sub- 
 stance, however irregular may have been the development. 
 
 84. Twin Crystals. Every crystal appears to grow by the 
 slow accretion of material around some nucleus, which is usually 
 a molecule or a group of molecules of the same substance, and 
 which we may call the crystalline molecule or germ. Now we 
 must suppose that these molecules have the same differences on 
 different sides which we see in the fully developed crystal, and 
 which, for the want of a better term, we may call polarity. As 
 a general rule, in the aggregation of the molecules a perfect 
 parallelism of all the similar parts is preserved. But, if molec- 
 ular polarity at all resembles magnetic polarity, it may well be 
 that two crystalline molecules might become attached to each 
 other in a reversed position, or in some other definite position 
 determined by the action of the polar forces. Assume now that 
 each of these crystalline molecules " germinates," and the result 
 would be such twin crystals as we actually find in nature. The 
 result is usually the same as if a crystal of the normal form 
 were cut in two by a plane having a definite position towards 
 the crystalline axes, and one part turned half round on the 
 other ; and twins of this kind are therefore called hemitropes. 
 Figs. 68 to 71. At other times the germinal molecules seem 
 to have become attached with their dominant axes at right 
 angles to each other, and then there result twins such as are 
 represented in Figs. 72 and 73 ; and many other modes of twin- 
 
CRYSTALLINE FORMS. 
 
 151 
 
 ning are possible. Some substances are much more prone to 
 the formation of twin crystals than others, and the same sub- 
 stance generally affects the same mode of twinning, which may 
 
 Fig. 71. 
 Fig. 68. Fig. 70. 
 
 Fig. 
 
 thus become an important specific character. The plane which 
 separates the two members of a twin crystal, called the plane 
 
 Fig. 73. 
 
 of twinning, has always a definite position, and is in every case 
 parallel either to an actual or to a possible face on both of the 
 two forms. 
 
 Twin crystals always preserve the same symmetry of group- 
 ing, and the values of the interfacial angles between the two 
 forms are constant on crystals of the same substance, so that 
 they might sometimes be mistaken for simple crystals by un- 
 practised observers. There is, however, a simple criterion by 
 which they can be generally distinguished. Simple crystals 
 never have re-entering angles, and, whenever these occur, the 
 faces which subtend them must belong to two individuals. 
 
 The same principle which leads to the formation of twin 
 crystals may determine the grouping of several germinal 
 molecules, and lead to the formation of far more complex com- 
 
152 CRYSTALLINE FORMS. 
 
 binations. Frequently, as it would seem, a large number of 
 molecules arrange themselves in a line with their principal 
 axes parallel and their dissimilar ends together, and hence re- 
 sult linear groups of crystals alternating in position, but so fused 
 into each other as to leave no evidence of the composite char- 
 acter except the re-entering angles, and frequently these are 
 marked only by the striations on the surface of the resulting 
 faces. Such a structure is peculiar to certain minerals, and 
 the resulting striation frequently serves as an important means 
 of distinction. The orthoclase and the klinoclase felspars are 
 distinguished in this way. 
 
 85. Crystalline Structure. The crystalline form of a body 
 is only one of the manifestations of its crystalline structure. 
 This also appears in various physical properties, which are fre- 
 quently of great value in fixing the crystallographic relations 
 of a substance, and such is especially the case when, on ac- 
 count of the imperfection of the crystals, the crystalline form is 
 obscure. Of these physical qualities one of the most impor- 
 tant is cleavage. 
 
 As a general rule, crystallized bodies may be split more or 
 less readily in certain definite directions, called planes of cleav- 
 age, which are always parallel either to an actual or to a pos- 
 sible face on the crystals of the substance, and are thus inti- 
 mately associated with its crystalline structure. At times the 
 cleavage is very easily obtained, when it is said to be eminent, 
 as in the case of mica or gypsum, which can readily be split 
 into exceedingly thin leaves, while in other cases it can only 
 be effected by using some sharp tool and applying considerable 
 mechanical force. With a few unimportant exceptions the 
 cleavage planes have the same position on all specimens of the 
 same substance. Thus specimens of fluor-spar may be readily 
 cleaved parallel to the faces of an octahedron, Fig. 5, those of 
 galena parallel to the faces of a cube, Fiji. 7, those of blende 
 parallel to the faces of a dodecahedron, Fig. 6, and those of 
 calc-spar parallel to the faces of a rhombohedron, Fig. 1 6. In 
 these cases, and in many others, the cleavage is a more distinc- 
 tive character than the external form, and can be more fre- 
 quently observed, and we generally regard the form produced 
 by the union of the several planes of cleavage as the funda- 
 mental form of the substance. 
 
 Again, we always find that cleavage is obtained with equal 
 
CRYSTALLINE FORMS. 153 
 
 ease or difficulty parallel to similar faces, and with unequal 
 ease or difficulty parallel to dissimilar faces. Moreover, the 
 dissimilar cleavage faces thus obtained may generally be dis- 
 tinguished from each other by differences of lustre, striation, 
 and other physical character ; and such distinctions are fre- 
 quently a great help in studying the crystallographic relations 
 of a substance. Similar differences on the natural faces of 
 crystals are also equally valuable guides. 
 
 But, of all the modes of investigating the crystalline structure 
 of a body, none can compare in efficiency with the use of polar- 
 ized light. It is impossible to explain the theory of this beau- 
 tiful application of the principles of optics without extending 
 this chapter to a length wholly incompatible with the design of 
 this book. It must suffice to say, that if we examine with a 
 polarizing microscope a thin slice of any transparent crystal of 
 either the second or third system, cut parallel to the dominant 
 axis, we see a series of colored rings, intersected by a black 
 cross, and it is evident that the circular form of the rings 
 answers to the perfect symmetry which exists in these systems 
 around the vertical axis. If, however, we examine in a similar 
 way a slice from a crystal of one of the last three systems, cut 
 in a definite direction, which depends on the molecular structure, 
 and must be found by trial, we see a series of oval rings with 
 two distinct centres, indicating that the symmetry is of a dif- 
 ferent type. Moreover, the distribution of the colors around 
 the two centres corresponds in each case to the peculiarities of 
 the molecular structure, and enables us to decide to which of 
 the three systems the crystal belongs. ' 
 
 The use of polarized light has revealed remarkable differ- 
 ences of structure in different crystals of the same substance, 
 connected with the hemihedral modifications described above. 
 The Figures 74 and 76 represent crystals of two varieties of 
 tartaric acid, which only differ from each other in the position 
 of two hemihedral planes, and are so related that when placed 
 before a mirror the image of one will be the exact representa- 
 tion of the other. The intermediate Figure, 75, represents the 
 same crystal without these modifications. Since the solid 
 angles are all similar, we should expect to find them all modi- 
 fied simultaneously ; but, while on crystals of common tartaric 
 acid only the two front angles (as the figure is drawn) are re- 
 placed, a variety of this acid has been discovered having simi- 
 
154 CRYSTALLINE FORMS. 
 
 lar crystals, whose back angles only are modified. Now, it is 
 found that a solution of the common acid rotates the plane of 
 polarization of a beam of light to the right, while a similar so- 
 
 Fig. 74. Fig. 75. 
 
 lution of this remarkable variety rotates the plane of polariza- 
 tion to the left. This difference of crystalline structure, more- 
 over, is associated with certain small differences in the chemi- 
 cal qualities of the two bodies ; but the difference is so slight 
 that we cannot but regard them as essentially the same sub- 
 stance, and the polarized light thus reveals to us the beginnings 
 of a difference of structure, which, when more developed, mani- 
 fests itself in the phenomena of isomerism. It is a remarkable 
 fact, worthy of notice in this connection, that these two varieties 
 of tartaric acid chemically combine with each other, forming a 
 new substance called racemic acid. 
 
 Questions. 
 
 1. By what peculiar mode of symmetry may each of the six crys- 
 talline systems be distinguished ? How may crystals belonging to 
 the 1st system be recognized ? How may crystals of the 2d, 3d, 
 and 4th systems be distinguished by studying the distribution of 
 the similar planes around their terminations or dominant axes ? 
 By what peculiar distribution of similar planes may the crystals of 
 the 5th and 6th systems be distinguished from all others ? State 
 the system to which each of the crystals, represented by the various 
 figures of this chapter, belongs, and give the reason of your answer 
 in every case. 
 
 2. We find in the mineral kingdom two different octahedral forms 
 of titanic acid belonging to the tetragonal system. In one of these 
 forms the ratio of the unequal axes is 1 : 0.6442, in the other it is 
 1 : 1.7723. Can these forms belong to the same mineral substance ? 
 
CHAPTER XV. 
 
 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 86. General Principles. If in a vessel of dilute sulphuric 
 acid (one part of acid to twenty of water) we suspend a 
 plate of zinc and a plate of platinum, opposite to each other, 
 and not in contact, we find that no chemical 
 action whatever takes place, provided the Fi S> 
 
 zinc and the acid are perfectly pure. As 
 soon, however, as the two plates are united by 
 a copper wire, as represented in Fig. 77, chem- 
 ical action immediately ensues, and the follow- 
 ing phenomena may be observed. First : 
 Bubbles of hydrogen gas are evolved from the 
 surface of the platinum plate. Secondly: 
 The zinc plate slowly dissolves, the zinc combining with the 
 radical of the acid to form zincic sulphate, which is soluble in 
 water. Lastly : A peculiar mode of atomic motion called 
 electricity is transmitted through the copper wire, as may be 
 made evident by appropriate means. If the connection be- 
 tween the plates is broken by dividing the conducting wire, 
 the chemical action instantly stops, and the current of elec- 
 tricity ceases to flow ; but, as soon as the connection is renewed, 
 these phenomena again appear. 
 
 Similar effects may be produced by other combinations than 
 the one just mentioned, provided only certain conditions are 
 realized. In the first place, the two plates must consist of 
 materials which are unequally affected by the liquid contained 
 in the vessel, or cell ; and the greater the difference in this 
 respect, within manageable limits, the better. In the second 
 place, the materials, both of plates and connector, must be con- 
 ductors of electricity ; and, lastly, the liquid must contain some 
 substance for one of whose radicals the material of one of the 
 plates has sufficient affinity to determine the decomposition of 
 the compound in solution. 
 
156 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 Practically, the combination first mentioned, with a few 
 
 slight modifications, is found to be the best adapted for general 
 
 use ; but, in order to bring the phenomena before our minds in 
 
 their simplest form, we will assume other things being the 
 
 same as before that the compound in solu- 
 
 Fig. 78. + - 
 
 tion is hydrochloric acid, HCl, since this con- 
 sists of a simple negative radical united to 
 a simple positive radical. In this case the 
 space between the plates is filled with mole- 
 cules consisting of hydrogen and chlorine 
 atoms, as is indicated in Fig. 78, where we 
 have attempted to represent by symbols a single one of the 
 innumerable lines of molecules of which we may conceive as 
 uniting the two plates. The zinc plate, in virtue of the power- 
 ful affinity of zinc for chlorine, attracts the chlorine atoms, 
 which rush towards it with immense velocity ; and the sudden 
 arrest of motion which attends the union of the chlorine with 
 the zinc has the effect of an incessant volley of atomic shot 
 against the face of the plate. Each of the atomic blows must 
 give an impulse to the molecules of the metal itself, which will 
 be transmitted from molecule to molecule, through the material 
 of the plate and the connecting wire, in the same way that a 
 shock is transmitted along a line of ivory balls ; and an elec- 
 tric current, as we conceive of it, is merely a wire, or other con- 
 ductor, filled with innumerable lines of oscillating molecules. 
 
 But these very impulses, which impart motion to the metal- 
 lic molecules, react on the liquid, forcing back the hydrogen 
 atoms towards the platinum, and the result is a constant me- 
 tathesis along the whole line of molecules between the two 
 plates ; so that, for every atom of chlorine which enters into 
 union with the zinc, an atom of hydrogen is set free at the face 
 of the platinum plate. Thus we have the singular phenome- 
 non produced of two coexisting atomic currents throughout 
 the mass of the liquids, a stream of chlorine atoms constantly 
 setting towards the zinc plate, and a stream of hydrogen atoms 
 flowing- in the opposite direction, in the same space, towards 
 the platinum plate. Corresponding to this motion in the ma.-s 
 of the liquid is the peculiar atomic motion in the metallic con- 
 ductors. The two, for some unknown reason, are mutunily 
 dependent ; and the moment the connection is broken, so that 
 
ELECTRICAL RELATIONS OF THE ATOMS. 157 
 
 the motion can no longer be transmitted through the con- 
 ductor, the motion in the liquid itself ceases. As regards 
 the mode of atomic motion in the solid metallic conductors, we 
 have been unable to form any clear conceptions. Although 
 apparently allied to heat, this peculiar mode of atomic motion, 
 called electricity, is capable of producing very different classes 
 of effects, and has the remarkable power of imparting to the 
 unlike atoms of almost all compound bodies the same opposite 
 motions which attend its first production. In our ignorance of 
 its nature, the direction we assign to the electric current is in 
 great measure arbitrary ; and it is more probable that a two- 
 fold current coexists in the conducting wire, corresponding to 
 that which we have recognized as actually flowing through the 
 liquid between the plates of the cell. These two currents have 
 in fact been distinguished by different names ; that flowing into 
 the conducting wire from the platinum, or inactive plate, being 
 called the positive current, and that from the zinc, or active 
 plate j the negative current. These names, however, are intended 
 to indicate merely some unknown opposition of relations be- 
 tween the two lines of moving atoms, and not an essential dif- 
 ference in the mode of the motion. Reasoning from certain 
 mechanical phenomena, the physicists originally assumed that 
 the electrical current flowed in but one direction, that is, through 
 the conducting wire from the platinum plate to the zinc, and 
 from the zinc plate through the liquid back again to the plat- 
 inum ; and now, when the direction of the current is spoken of, 
 it is this direction, that of the positive current, which is always 
 meant. 
 
 87. Electrical Conducting Power or Resistance. Different 
 materials transmit the electric current with very different de- 
 grees of facility ; for while in some this peculiar form of molec- 
 ular motion is easily maintained, in others the molecules yield 
 to it only with difficulty, and many substances seem not to be 
 susceptible of it. The conducting powers of different metallic 
 wires have been very carefully studied, and some of the most 
 trustworthy results are collected in the following table. Silver 
 is the best conductor known, and, assuming that a silver wire of 
 definite size and 100 centimetres long is taken as the standard, 
 the number opposite the name of each metal is the length in 
 centimetres of a wire made of .this metal, and of the same size 
 
158 
 
 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 as the first, which will oppose the same resistance to the trans- 
 mission of the current. The second column gives the relative 
 resistances of wires of the same materials when of equal size 
 and of equal lengths. The relative or specific resistances of two 
 such wires must evidently be inversely proportional to their 
 conducting powers, and thus the numbers of the second column 
 are easily calculated from those of the first. For the results 
 collated in this table we are indebted to the careful investiga- 
 tions of Professor Matthiessen. 
 
 Pure Metals. 
 
 Conducting Power. 
 
 Specific Resistance. 
 
 Silver 
 
 (hard drawn) 
 
 At 0. At 100. 
 
 100.00 71.56 
 
 At 0. At 100. 
 
 1.000 1.397 
 
 Copped 
 
 (hard drawn ) 
 
 99.95 70.27 
 
 1. 
 
 0005 1 .423 
 
 - Gold- 
 
 (hard drawn) 
 
 77.96 55.90 
 
 1. 
 
 283 1.788 
 
 v Zinc 
 
 
 
 29.02 20.67 
 
 3.445 4.838 
 
 Cadmium 
 
 23.72 16.77 
 
 4.216 5.964 
 
 - Cobalt 
 
 
 
 17.22 
 
 5. 
 
 808 
 
 Iron 
 
 (hard drawn) 
 
 16.81 
 
 5.948 
 
 Nickel 
 
 
 
 13.11 
 
 7.628 
 
 Tin 
 
 
 
 12.36 8.67 
 
 8.091 11.53 
 
 Thallium 
 
 9.16 
 
 10.92 
 
 ; Lead 
 
 
 
 8.32 5.86 
 
 12.02 17.06 
 
 Arsenic 
 
 
 
 4.76 3.33 
 
 21. 
 
 01 30.03 
 
 Antimony 
 
 4.62 3.26 
 
 21.65 30.68 
 
 Bismuth 
 
 
 
 
 1.245 0.878 
 
 80.34 1 13.9 
 
 Commercial 
 Metals. 
 
 C. P. 
 
 Sp. R. <P. 
 
 Commercial 
 Metals. 
 
 C. P. 
 
 Sp. R. 
 
 C=>. 
 
 Copper 
 
 77.43 
 
 1.291 18.8 
 
 Iron^ 
 
 14.44 
 
 6.924 
 
 20.4 
 
 Sodium 
 
 37.43 
 
 2.672 2L.7 
 
 Palladium ^ 
 
 12.64 
 
 7.911 
 
 17.21 
 
 Aluminum 
 
 33.76 
 
 2.962 195 
 
 Platinum 
 
 10.53 
 
 9.497 
 
 20.7 
 
 Magnesium 
 
 25.47 
 
 3.926 17,0 
 
 Strontium 
 
 6.71 
 
 14.90 
 
 20.5 
 
 Calcium 
 
 22.14 
 
 4.516 16 
 
 Mercurv 
 
 1.63 
 
 61.35 
 
 22.8 
 
 Potassium 
 
 20.85 
 
 4.795 20.4 
 
 Tellurium 
 
 0.00077 
 
 129,800 1 '.).<) 
 
 Lithium ... 
 
 19.00 
 
 5.262 20.0 
 
 Red Phosphorus 
 
 0.00000123 
 
 81,300,00024.0 
 
 If, next, we compare wires of the same material, but of dif- 
 ferent sizes, we find that the resistance increases as the length, 
 and diminishes as the area, of the section. Moreover, if we 
 adopt some absolute standard of resistance, like that selected by 
 the English physicists, we can easily express the resistance of 
 any given conductor in terms of this unit. It must be remem- 
 bered, however, in making such comparisons, that the resist- 
 ance varies with the temperature, and also that the conducting 
 power of the same metal is materially influenced both by its 
 and by the presence of impurities. 
 
 physical conditl 
 
ELECTRICAL RELATIONS OF THE ATOMS. 159 
 
 88. Ohm's Law. The first effect of the chemical forces in 
 the cell of an electrical combination is to marshal the dissimilar 
 atoms of the active liquid between the plates into lines, which 
 at once begin to move in parallel columns, but in opposite di- 
 rections (Fig. 78). Moreover, each one of these lines of moving 
 atoms is continued by a corresponding line of oscillating atoms 
 in the conducting wire, and thus is formed a continuous circuit 
 returning upon itself. The union of all the lines of force in 
 the two opposite coexisting streams constitutes in any case the 
 electrical current, and the different parts of this continuous chain 
 are so related that the total amount of motion is always the same 
 at every point on the circuit, and no more lines of moving atoms 
 form in the liquid between the plates than can be continued 
 through the oscillating atoms of the solid conductors. 
 
 If we adopt this theory, it is obvious that the strength of any 
 electrical current must depend, first, on the number of con- 
 tinuous lines of force, and secondly, on the strength of the 
 atomic blows transmitted through each of these channels. Of 
 these two elements, the first is determined solely by the total 
 resistance which the various parts of the circuit oppose to the 
 electrical motion, and the greater this resistance the less will 
 be the number of the lines of force. The second element is de- 
 termined by the value of the resultants of all the chemical forces 
 acting in any combination, which impel the dissimilar atoms 
 towards the opposite plates, a value which depends solely on 
 the chemical relations of the materials of the plates to that of the 
 active liquid, and is what is called the electromotive force of the 
 combination, a quantity we will represent by E. 
 
 It appears, then, from the above analysis, that an electrical 
 current is a continuous chain, which is sustained in a regulated 
 and equable motion in all its parts by the chemical activity in 
 the cell, and that the strength of this current at any point of the 
 chain must be directly proportional to the electromotive force, 
 and inversely proportional to the sum of the resistances through- 
 out the circuit. If, then, we represent the resistance in the con- 
 ducting wire by r, the resistance of the liquid between the plates 
 of the cell by R, 1 and also the strength of the current by (7, we 
 shall have, in every case, 
 
 1 The resistance of any circuit may be conveniently divided into two parts, 
 
160 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 The quantities (7, 7?, r, and E may all be accurately measured, 
 and stand in each case for a certain number of arbitrary units, 
 whose relations will hereafter be stated. 
 
 89. Electromotive Force and Strength of Current. It would 
 seem at first sight as if the strength of an electric current might 
 be increased by simply enlarging the size of the plates in the 
 combination employed, and obviously the number of possible 
 lines of moving atoms which could be marshalled in the liquid 
 between the plates would thus be increased ; but, as has been 
 stated, the parts of the circuit are so intimately connected that 
 no greater number of lines of atoms can form between the plates 
 than can be continued through the whole circuit, and practically 
 there may be formed between the smallest plates a vastly greater 
 number of atomic lines than can be continued through any con- 
 ductor, however good its quality or however ample its size. 
 Hence it is, that by increasing the size of the plates we mul- 
 tiply the lines of force only in so far as we thereby lessen the 
 resistance in the liquid part of the circuit. We thus simply 
 lessen the value of R in Ohm's formula [62] ; but if this value 
 is already small as compared with r, that is, if the resistance in 
 the cell is small compared with that in the conductor, no mate- 
 rial gain in the power of the current, or in the value of (7, will 
 result. On the other hand, if the exterior resistance, r, is small, 
 or nearly nothing, as when the plates are connected by a thick 
 metallic conductor, then the value of O will increase in very 
 nearly the same proportion as the size of the plates is enlarged, 
 and the value of J?, in consequence, diminished. Under these 
 conditions, the number of lines of moving atoms is greatly mul- 
 tiplied, and we obtain a current of very great volume, but only 
 flowing with the limited force which the single cell is capable 
 of maintaining. Such a current has but little power of over- 
 coming obstacles ; and if we attempt to condense it by using a 
 smaller conductor, we reduce, as has been said, the chemical 
 action which keeps the whole in motion, and thus lessen the 
 volume of the flow. This is generally expressed by saying 
 
 first, the resistance of the conducting wire, and secondly, the resistance of the 
 liquid portion of the circuit between the two plates of the cell. The resistance 
 of the solid conductor may be readily estimated on the principles stated in the 
 last section, and the resistance of liquid may be measured in a similar way. 
 The last depends, 1. On the conducting power of the liquid; 2. On the length 
 of the liquid circuit, which is determined by the distance apart of the plates; 
 3. On the area of the section of the liquid conductor, which is determined by 
 the size of the plates ; and, 4. On the temperature. 
 
ELECTRICAL RELATIONS OF THE ATOMS. 161 
 
 that the current has large quantity, but small intensity, or more 
 properly, electromotive power. 
 
 It must now be obvious from the theory, that we cannot in- 
 crease effectively the intensity of a current (its power of over- 
 coming obstacles) without in some way increasing the chemical 
 activity, or, in other words, the electro-motive force of the com- 
 bination employed, and Ohm's formula leads to the same result. 
 If the value of r in our formula is very large as compared 
 with R, we cannot increase it still farther without lessening the 
 total value, (7, unless at the same time we increase the value 
 of E. Now, this electro-motive force may be, to a certain ex- 
 tent, increased by using a more active combination ; but the 
 limit in this direction is soon reached, and the construction of 
 the cell which has been found practically to be the most effi- 
 cient will be described below. 
 
 We can, however, increase the effective electro-motive force 
 to almost any extent by using a number of cells, and coupling 
 them together in the manner represented by Fig. 79, the plati- 
 num plate of the first cell being united by a large metallic con- 
 nector to the zinc plate of the second, and so on through the 
 line, until finally the external conductor establishes a connec- 
 tion between the platinum plate of the last cell and the zinc 
 plate of the first. Such a combination as this is called a Gal- 
 vanic or Voltaic * battery, and the current which flows through 
 such a combination has a vastly greater power of overcoming 
 resistance than that of any single cell, however large. 
 
 The increased effect obtained with such a combination will 
 be easily understood, when it is remembered that each of the 
 innumerable closed chains of 
 
 v , Fig., 79. 
 
 moving molecules, now ex- 
 tends through the whole 
 combination, and that all its 
 parts move in the same close 
 mutual dependence as be- 
 fore. But whereas with a single cell the motion throughout 
 any single chain of molecules is sustained by the chemical 
 energy at only one point, it is here reinforced at several points ; 
 
 1 From the names of Galvani and Volta, two Italian physicists, who first 
 investigated this class of phenomena. 
 11 
 
162 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 and where before we had a single atomic blow, we have now 
 a number, which simultaneously send their united energy along 
 one and the same line. The effective electro-motive power is 
 then increased in proportion to the number of cells ; and the 
 effect on the current would be increased in the same proportion, 
 were it not for the fact that the current must keep in motion a 
 greater mass of liquid, and hence the resistance is increased at 
 the same time. The value of this resistance, however, is easily 
 estimated, since it is directly proportional to the distance through 
 which the current has to flow in the liquid ; and hence, if the 
 liquid is the same in all the cells, and the plates are at the 
 same distance apart in each, the liquid- resistance will be n 
 times as great in a combination of n cells as it is in one. 
 Moreover, since the effective electro-motive force is n times as 
 great also, while the external resistance remains unchanged, 
 the strength of the current from such a combination will still 
 be expressed by formula [62] slightly modified. 
 
 This formula shows at once, that, when the exterior resist- 
 ance is very small, or nothing, very little or no gain will result 
 from increasing the number of cells, for the ratio of nE to nR 
 is the same as that of E to R ; and, under such conditions, in 
 order to increase the strength of the current, we must increase 
 the surface of the plates. If, on the contrary, the exterior re- 
 sistance is very large, the formula shows that great gain will 
 result from increasing the number of the cells, and that little 
 or no advantage will accrue from enlarging the surface of the 
 plates. Moreover, the formula enables us in any case to de- 
 termine what proportion the number of cells should bear to the 
 size of the plates in order to obtain the full effect of any battery 
 in doing a given work; and in the numerous applications of 
 electricity in the arts we find abundant illustrations of the 
 principles it involves. The methods used in finding the val, 
 of the quantities represented in the formula lie beyond 
 scope of this work, and for such information the student 
 ferred to works on Physics. 
 
 90. Constructions of Cells. It is found practicall/^hat^fie 
 
ELECTEICAL RELATIONS OF THE ATOMS. 163 
 
 simple combination of plates and acid first described must be 
 slightly modified in order to obtain the best results. 
 
 In the first place, both the zinc and* sulphuric acid of com- 
 merce contain impurities, which give rise to what is called 
 local action, and cause the zinc to dissolve in the acid when 
 the battery is not in action. Fortunately, however, it has been 
 found that such local action can be wholly prevented by care- 
 fully amalgamating the surface of the zinc and filtering the 
 acidulated water. 
 
 The mercury on the surface of the zinc plates acts as a sol- 
 vent, and gives a certain freedom of motion to the particles of 
 the metal. These, by the action of the chemical forces, are 
 brought to the surface of the plate, while the impurities are 
 forced back towards the interior, so that the plate constantly 
 exposes a surface of pure zinc to the action of the acid. 
 
 By filtering we remove the particles of plumbic sulphate 
 which remain floating in the sulphuric acid for a long time 
 after it has been diluted with water, and which, when deposited 
 on the surface of the zinc, become points of local action, even 
 when the plates have been carefully amalgamated. 
 
 In the second place, the continued action of the simple com- 
 bination first described develops conditions which soon greatly 
 impair, and at last wholly destroy, its efficiency. 
 
 The hydrogen gas, which by the action of the current is 
 evolved at the platinum plate, adheres strongly to its surface, 
 and with its powerful affinities draws back the lines of atoms 
 moving towards the zinc plate, and thus diminishes the effec- 
 tive electro-motive force. Moreover, after the battery has been 
 working for some time, the water becomes charged with zincic 
 sulphate ; and then the zinc, following the course of the hydro- 
 gen, is also deposited on the surface of the platinum, which 
 after a while becomes, to all intents and purposes, a second 
 zinc plate, and then, of course, the electric current ceases. 
 
 Both of these difficulties, however, have also been sur- 
 mounted by a very simple means discovered by Mr. Grove, of 
 London. The Grove cell, Fig. 80, consists of a circular plate of 
 zinc well amalgamated on its surface, and immersed in a glass 
 jar containing dilute sulphuric acid. Within the zinc cylinder is 
 placed a cylindrical vessel of much smaller diameter, made of 
 porous earthenware, and filled with the strongest nitric acid, 
 
164 
 
 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 and in this hangs the plate of platinum, Fig. 81. The walls of 
 
 Fig. 81. 
 
 the porous cell allow both the hydrogen and the zinc atoms to 
 pass freely on their way to the platinum plate ; but the moment 
 they reach the nitric acid they are at once oxidized, and thus 
 the surface of the platinum is kept clean, and the cell in condi- 
 tion to exert its maximum electro-motive power. In this com- 
 bination we may substitute for the plate of platinum a plate 
 of dense coke, such as forms in the interior of the gas retorts, 
 which is very much cheaper, and enables us to construct large 
 cells at a moderate cost. The use of gas coke was first sug- 
 gested by Professor Bunsen of Heidelberg, and the cell so 
 constructed generally bears his name. The Bunsen cell, such 
 as is represented in Fig. 82, is exceedingly well adapted for use 
 
 Fig. 82. 
 
 in the laboratory. These cells are usually made of nearly a 
 
ELECTRICAL RELATIONS OF THE ATOMS. 165 
 
 uniform size, the zinc cylinders being about 8 c. m. in diameter 
 by 22 c. m. high, and they are frequently referred to as a rough 
 standard of electrical power. They may be united so as to 
 produce effects either of intensity or of quantity. The inten- 
 sity effects are obtained in the manner already described (see 
 Fig. 79), and the quantity effects are obtained with equal readi- 
 ness ; since by attaching the zinc of several cells to the same 
 metallic conductor, and the corresponding coke plates to a 
 similar conductor, we have the equivalent of one cell with large 
 plates. Many other forms of battery, differing in more or less 
 important details from those here described, and adapted to 
 special applications of electricity, are used in the arts, and are 
 fully described in the larger works on physics. 
 
 91. Electrolysis. As has been already stated, the electrical 
 current has the remarkable power of imparting to the unlike 
 atoms of almost all compound bodies motion in opposite direc- 
 tions, like that in the battery cell itself, and this, too, at what- 
 ever point in the circuit they may be introduced. The galvanic 
 battery thus becomes a most potent agent in producing chemi- 
 cal decompositions, and it is in consequence of this fact that the 
 theory of the instrument fills such an important place in the phi- 
 losophy of chemistry. 
 
 If we break the metallic conductor at any point of a closed 
 circuit, the two ends, which in chemical experiments we usually 
 arm wifh platinum plates, 1 are called poles. The end con- 
 nected with the platinum or coke plate, from which the positive 
 current is assumed to flow, is called the positive pole, and the 
 end connected with the zinc plate, from which the negative 
 current flows, is called the negative pole. Let us assume 
 that Fig. 83 represents the two platinum poles dipping in a 
 solution of hydrochloric acid in water, which 
 thus becomes a part of the circuit. The 
 moment the circuit is thus closed, the ZTand 
 Cl atoms begin to travel in opposite direc- 
 tions, just as in the battery cell below. The 
 hydrogen atoms move with the positive cur* 
 rent towards the negative pole, and hydro- 
 gen gas is disengaged from the surface of 
 
 1 We use platinum plates because this metal does not readily enter into 
 combination with the ordinary chemical agents. 
 
166 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 the negative plate, while the chlorine atoms move with the 
 negative current towards the positive pole, and chlorine gas 
 is evolved from the surface of the positive plate. More- 
 over, it will be noticed that each kind of atoms moves in the 
 same direction on the closed circuit, that is, follows the course 
 of the same current, both in the battery cell below and in the 
 decomposing cell above ; and wherever we break the circuit, 
 and at as many places as we may break it, the same phenomena 
 may be produced, provided only that our battery has sufficient 
 power to overcome the resistance thus introduced. 
 
 If next we dip the poles in water, the atoms of the water 
 will be set moving, as shown in Fig. 84; hy- 
 c drogen gas escaping as before from the neg- 
 L ative pole, and oxygen gas from the positive. 
 o o o o o o We find, however, that pure water opposes 
 
 2H2H 2 H2H2H 2 J a very great resistance to the motion of the 
 current ; and, unless the current has great 
 intensity, the effects obtained are inconsider- 
 able. But if we mix with the water a little sulphuric acid, the 
 decomposition at once becomes very rapid ; but then it is the 
 atoms of the sulphuric acid, and not those of the water, which 
 are set in motion. The molecule H 2 S0 4 divides into H. 2 and 
 S0-, the hydrogen atoms moving in the usual direction, and 
 the atoms of SO^ in the opposite direction. As soon, however, 
 as the last are set free at the positive pole, they <;ome in 
 contact with water, which they immediately decompose, 
 2ff 2 0-\-2S0 4 =2ff.>S0 4 -\- 0--0, and the oxygen gas thus 
 generated escapes from the face of the platinum plate. Thus 
 the result is the same as if water were directly decomposed, 
 but the actual process is quite different. 
 
 So also in many other cases of electrolysis, as these decom- 
 positions by the electrical current are called, the process is 
 complicated by the reaction of the water, which is the usual 
 medium employed in the experiments. Thus, if we interpose 
 between the poles a solution of common salt, Na (?/, the chlorine 
 atoms move towards the positive pole, and chlorine gas is there 
 evolved as in the first example. The sodium atoms move also, 
 but in the opposite direction. As soon, however, as they are 
 set free at the negative pole, they decompose the water present ; 
 hydrogen gas is formed, which escapes in bubbles from the 
 
ELECTRICAL RELATIONS OF THE ATOMS. 167 
 
 platinum plate, while sodic hydrate (caustic soda) remains in 
 solution, 
 
 = 2H, Na-0 + H-H. 
 
 We add but one other example, which illustrates a very 
 important application of these principles in the arts. We as- 
 sume, in Fig. 85, that the positive 
 pole is armed with a plate of copper, ^ 
 and that to the negative pole has been 
 fastened a mould of some medallion c J so * ** s * 
 we wish to copy, the surface of which, 
 at least, is a good conductor. We 
 assume further that both copper plate and mould are sus- 
 pended in a solution of sulphate of copper, Cu=S0 4 . In this 
 case the atoms of the compound are set in motion as before. 
 Those of copper accumulate on the surface of the mould ; and 
 at last the coating will attain such thickness that it can be re- 
 moved, furnishing an exact copy of the original medallion. 
 Meanwhile the atoms of S0 4 have found at the positive 
 pole a mass of copper, with whose atoms they have combined ; 
 and thus fresh sulphate of copper has been formed, and the 
 solution replenished. The process has in effect consisted in 
 a transfer of metal from the copper plate to the medallion ; 
 and, by using appropriate solvents, silver and gold- can be 
 transferred and deposited in the same way. 
 
 In all these processes of electrolysis, one remarkable fact has 
 been observed, which has a very important bearing on the 
 theory of the battery. If in any given circuit we introduce a 
 number of decomposing cells, containing acidulated water, we 
 find that in a given time exactly the same amount of gas is 
 evolved in each ; thus proving, what we have thus far assumed, 
 that the moving power is absolutely the same at all points on 
 the circuit. Moreover, the amount of gas which is evolved 
 from such a decomposing cell in the unit of time is an ac- 
 curate measure of the strength of the current actually flowing 
 in any circuit, and this mode of measuring the quantity of an 
 electrical current is constantly used. 
 
 We should infer from the facts already stated, and the prin- 
 ciple has been confirmed by the most careful experiments, that 
 the chemical changes which may take place at different points 
 
" 
 
 1G 
 
 < 
 
 S ELECTEICAL KELATIONS OF THE ATOMS. 
 
 L 
 
 of the same closed circuit are always the exact equivalents of 
 each other. If, for example, we have a series of Grove's cells, 
 arranged as in Fig. 79, and interpose in the external circuit 
 \}~ g two decomposing cells, as in Figs. 84 and 85, we shall find 
 (provided there is no local action) that the weight of zinc dis- 
 solved in each of the five Grove's cells is the exact chemical 
 equivalent, (26) not only of the weight of hydrogen gas evolved 
 from the first decomposing cell, but also of the weight of me- 
 llic copper deposited on the mould in the secHtd. For every 
 63.4 grammes of copper deposited, 2 grammes of hydrogen are 
 evolved, and 65.2 grammes of zinc are dissolved in each cell 
 of the battery. If there is also local action in the cells, the 
 chemical change thus induced is added to the normal effect of 
 the battery-current. 
 
 i <-, The examples which have been given are sufficient to illus- 
 trate the remarkable power which the electric current possesses 
 of setting in motion the atoms of compound bodies. Innuiner- 
 *W*&able experiments have shown that, in reference to their rela- 
 ' " tions to the current, 'the atoms, both simple and compound, may 
 i be divided into two great classes : first, those which travel on 
 "'the line of the circuit in the direction of the positive current 
 and follow in the lead of the hydrogen atoms ; and, secondly, 
 ^ I* those which follow the lead of the chlorine atoms, and move in 
 (J^the opposite direction with the negative current. The first 
 class of atoms, or radicals, we call positive ; and the second class, 
 negative. 
 
 if ^ The opposition in qualities of the chemical atoms, which the 
 \ study of these electrical phenomena has revealed, is, in jiiany 
 cases at least, relative, and not absolute. For, while there are 
 some atoms which always manifest the same character, there 
 are others which appear in some associations positive, and in 
 u, Bother associations negative. To. such an extent is this true, 
 ;. - that the electrical relations of tfte atoms are best shown by 
 ^Y grouping the elements in series, which may be so arranged that 
 each member of the series shall be electro-positive when in 
 \ ^ombWation with those elements which follow it, and electro- 
 negative when combined with those which precede it. 
 
 The simple mechanical theory of electrical currents which 
 has been presented in this chapter, is adequate to explain the 
 order of the chemical phenomena with which we are 
 
c 
 
 \\ * (**> V - -&$ W ^ *~*^ A 
 
 v ~ R 
 
 ELECTRICAL RELATIONS OF THE ATOMS. 169 
 
 more immediately concerned in this work. But there are other ^ 
 classes of electrical phenomena, of which this theory, at least C 
 in its present form, can give no account, and which have always'V 8 
 been referred to the presence of an assumed electrical fluid, " 
 pervading all nature, and consisting of two oppositely polar- 
 ized conditions of the same substance, the vitreous and 
 nous, or positive and negative electricities, which, when 
 arated by chemical action, by friction, or in other ways, constancy 
 tend to flow together through all those channels which we ckll 
 electrical conductors. It is, however, the tendency of mod 
 science to refer all physical changes to a simple mechanical 
 cause, and although the phenomena of statical electricity are 
 still best explained on the fluid hypothesis, we may hope that 
 further study will show that they also may be reconciled with 
 some dynamical theory. It is possible that the electrical fluid, 
 which would seem to appear in these phenomena, is an 
 "ethereal" atmosphere, surrounding the atoms, and that 
 through this medium the electrical impulses are transmitted. 
 (Compare 892.) ^ jr - 
 
 Questions and Problems. 
 
 4* 
 
 In the following problems the values C*, R or r and E of Ohm's / * 
 
 formula are assumed to be measured in terms of the following units. ~ 
 First. The unit of current is that which would produce, by the elec- 
 trolysis of water, 1 cTm. 3 of hydrogen and oxygen gas (measured un- 
 der standard conditions) in one minute. Secondly. The unit of re- 
 sistance is that offered by a pure silver or copper wire 1 m. lon 
 and 1 m. m. diameter at O . 1 Lastly, the unit of electromotive force 
 is that which transmits a unit current against a unit resistance in a 
 unit of time. "y ,.. 
 
 1. What resistance does the current suffer in an iron wire 50 me- 
 tres long and 5 m. m. diameter ? Sp. R. of iron 7. 
 
 Ans. 14 units. 
 
 2. Assuming that the Sp. R. of copper is 1.3 and that of iron 7, 
 what must be the diameter of an iron wire which will oppose no 
 greater resistance to the current than a copper wire of 2 m. m. dia- 
 meter ? Ans. 4.64 m. m. 
 
 i This unit is 0.02057 of the absolute unit recently adopted by the British 
 Association. 
 
5 
 
 70 ^-ELECTKICAL RELATIONS OF THE ATOMS. 
 
 K) ^ t ^ 
 
 3. It is found by experiment that a wire of German silver, 7.201 1 
 j^ ^HCiia nd 1.5 m. m. diameter, opposes the same resistance to the 
 
 currentas a wire of pure silver 10 m. long and ^ m. m. diameter. 
 cj Whatjs the Sp. R. of German silver. Ans. 12.5. 
 
 4. It is required to make with 132.8 grammes of pure silver, a 
 .wire which will offer a resistance of 81 units. What must be its 
 length and diameter ? Sp. Grr. of silver = 10.57. 
 
 m <Vv Solution. Representing by x the length in metres, and by y the 
 
 C diameter in millimetres, we deduce by [1] y* x 10.57 = 132.8 and 
 by the laws of conduction = 81. Whence x = 36 m. and y 
 
 -^ Y | m. m. 
 
 f 5. What is the length and diameter of an iron wire weighing 
 
 ^^ 97.38 grammes, which offers a resistance of 9,072 units ? It is known 
 that the Sp. Gr. of the iron = 7.75 and its Sp. R. = 7. 
 
 \ Ouu^ $*****' Ans - Length, 144 m. Diameter, \ m. m. 
 
 o. From a given wire there are four branches, of which the re- 
 sistance is respectively 10, 20, 30, and 40. Required the total 
 resistance when the current passes simultaneously through the four 
 branches. 
 
 . The resistance in the first branch may be represented 
 y a normal silver wire 10 m. long and 1 m. m. diameter. If we 
 call the area of a transverse section of this wire s, then the resist- 
 ance in the other three branches will be represented by normal wires 
 of the same length, but having on the cross sections the areas ^ s, 
 ^ s and ^ s respectively. If next we conceive of these wires as 
 *"* merged in one, having the common length 10m. and an area on the 
 
 section equal to (1 -|- % -|- | -}- ) s, it is evident that such a wire 
 will represent the resistance required. Hence we easily deduce, 
 
 Ans ' 4 ' 8 ' 
 
 7. flclosed circuit has two branches through which the current 
 
 multaneously. In one branch r = 100. What length of 
 e 5 m> m ' d' ameter must be used for the other that the 
 50 ? Ans. 2,500 metres. 
 
 8. A conductor has two branches, one having R = 756, the other 
 so adjusted that when the current passes at the same time through 
 both, the total resistance equals 540. Required the length of a Ger- 
 man silver wire \ m. m. diameter and Sp. R. = 12.5, which, when 
 inserted in the adjusted branch, will increase the total resistance to 630. 
 
 Solution. By principle of last problem we easily find that the 
 resistance in the adjusted branch before insertion equals 1,890, and 
 after insertion, 3,780. The difference between these values, 1,890, 
 is the resistance due to the inserted wire. Hence its length must be 
 37.8 metres. 
 
ELECTRICAL RELATIONS OF THE ATOMS. 171 
 
 9. We have a battery of six Daniells cells, in each of which 
 .E=475, 72 = 15, and the external resistance against which the 
 battery is to work, r = 10. The cells may be arranged, 1st, as six 
 single elements ; 2d, as three double elements ; l 3d, as two three-fold 
 elements ; 4th, as one six-fold element. Required the current strength 
 in each case. Ans. 28.5, 43.8, 47.5 and 38.0 respectively. 
 
 10. We have a battery of twelve Grove cells, in each of which 
 E = 830, and R =18, to work against an external resistance of 
 r = 24. Required the strength of current when the cells are ar- 
 ranged, 1st, as twelve single ; 2d, as six two-fold ; 3d, as four three- 
 fold; 4th, as three four-fold; 5th, as two six-fold, and 6th, as one 
 twelve-fold element. 
 
 Ans. 41.5, 63.8, 69.2, 66.4, 55.3, and 32.5 respectively. 
 
 11. With a single cell, where E and R have a constant value, 
 what is the maximum strength of current, and under what condi- 
 tions would it be obtained ? 
 
 ir? 
 
 Ans. -73 , when the external resistance is nothing. 
 
 12. With n cells in each of which E and R have the same value, 
 what is the maximum strength of current, and under what condi- 
 tions would it be obtained ? 
 
 -pi 
 
 Ans. n , when the cells are arranged as one n-fold element, 
 and work against no external resistance. 
 
 13. With n cells as above, working against a given external resist- 
 ance r, how should they be arranged so as to obtain the maximum 
 value of Cf 
 
 Ans. So as to make the internal resistance equal to that of the 
 external circuit. 
 
 Solution. If x represents the number of compound elements formed 
 with the n cells when C in Ohm's formula is a maximum, we should 
 evidently have under this condition x compound elements, each 
 
 formed of - cells. The electromotive force of such an arrangement 
 
 would be x E. The internal resistance would be -a; # - = R 
 
 x n 
 
 (compare problems 8 and 9), and the strength of the maximum 
 current required, 
 
 n xE 
 
 *2~~ 
 
 * + ' 
 
 1 By double elements is meant a group of two cells coupled for quantity 
 [89] and equivalent to a large cell having plates of twice the size. Six 
 double elements are six such groups arranged for intensity, and the other 
 terms have a similar meaning. 
 
172 ELECTRICAL RELATIONS OF THE ATOMS. 
 
 The first differential coefficient of this function of x when C is a 
 maximum must be equal to zero. Hence, 
 
 2 - R E 
 
 " = 
 
 or r=-* It. 
 
 n 
 
 That is, the strength of the current is at its maximum when the in- 
 ternal equals the external resistance, as stated above. Those who 
 are not familiar with the elementary principles of the differential 
 calculus may satisfy themselves of the truth of this result by com- 
 paring the answers obtained to problems 8 and 9. 
 
 14. We have, in the first place, for a single cell of a given combi- 
 
 TTT 
 
 nation working against a feeble resistance, the value C = ^ - ; 
 in the second place, for n cells of the same combination working 
 
 against n times the resistance, the identical value C == ^ . In 
 
 nR -+- nr 
 
 " strength " the two currents are equal, but are they identical V 
 
 15. In a given cell E = 475 ; *R = 15. The current passes 
 through 30 metres pure copper wire 2 m. m. diameter. It is re- 
 quired to arrange 8 cells so that C may be the greatest possible. 
 
 Ans. They should be arranged as two four-fold elements. 
 
 16. We have a battery of four Bunsen cells (E = 800, R = 4 
 each), coupled as four single elements. The circuit is closed through 
 500 grammes of pure copper wire. Required the greatest strength 
 of current, and the dimensions of the wire that this maximum may 
 be obtained. 
 
 17. A simple Voltaic cell, whose electromotive force E is known, 
 working against an unknown total resistance R' (both external and 
 internal), produces a given effect upon a galvanometer. Another 
 cell differently constructed, working against a total resistance R", 
 also unknown, produces the same effect upon the galvanometer. It 
 is also observed that a measured length I of normal copper wire, in- 
 serted in the first circuit, produces on the galvanometer the same 
 difference of effect as a length /' inserted in the second circuit. 
 Required the electromotive force E' of the seco/id cell. 
 
 Solution. We easily deduce from Ohm's formula the two equations 
 
 % = 7 an <* jgqr? = VT> whence we obtain - 
 
 Ans. E' = E - 
 
ELECTKICAL RELATIONS OF THE ATOMS. 173 
 
 18. In order to determine the electromotive force of a Bunsen's 
 cell, it was compared, as in last problem, with a Daniell's cell whose 
 electromotive force was known to be 470. After adjusting the ex- 
 ternal resistances so that both produced the same effect upon the 
 galvanometer, it was found that the insertion of 5.6 m. of copper 
 wire into the first circuit cause'd the same change in the instrument 
 as the insertion of 3.29 metres of the same wire in the circuit of the 
 Daniells cell. What was the electromotive force sought ? 
 
 Ans. 800. 
 
 19. A battery of 40 Bunsen's cells remains closed for an hour, and 
 during that time furnishes a current whose strength C == 30. How 
 much zinc will be consumed in this time, assuming that there is 
 no local action ? 
 
 Solution. Such a current would produce, by the electrolysis of 
 water, 30 cTm. 3 of gas in one minute, or 1.8 litres in one hour. Of 
 this gas 1.2 litres or 1.2 criths would be hydrogen. The chemical 
 equivalent of zinc being 32.6, the amount of zinc dissolved in each 
 cell must be 1.2 X 32.6 =^39.12 criths, and in the forty cells 
 1564.8 criths, equal to 140 grammes, the answer required. 
 
 20. In an electrotype apparatus, Fig. 85, 16.36 grammes of cop- 
 per were deposited on the negative mould in 24 hours. What was 
 the strength of current ? Ans. 6 units. 
 
 21. In an electrotype apparatus the electromotive force of the 
 single cell employed is 420, and the internal resistance 5. The ex- 
 ternal resistance, including decomposing cell, is 0.25. How much 
 copper will be deposited on the negative mould in one hour, and 
 how much zinc will be dissolved in the battery during the same 
 time ? Ans. 9.088 grammes copper and 9. 346 grammes of zinc. 
 
 22. Thirty-two Grove cells (E = 830, R = 20 each) are con- 
 nected as 4 eight-fold compound elements and the current employed 
 to work an electro-silvering apparatus, in which the total resistance 
 external to the battery was equivalent to 10. Required the number 
 of grammes of silver deposited each hour, and the number of grammes 
 of zinc dissolved during the same time in the battery. 
 
 Ans. 64.24 grammes of silver and 77.56 grammes of zinc. 
 
 23. Assuming that the external resistance cannot be changed, 
 would the same number of cells of the battery described in last 
 problem be so arranged as to deposit more silver in the same time ? 
 
 Ans. They could not. 
 
 Could they be so arranged as to deposit the same amount of silver 
 with less expense of zinc ? What would be the most economical ar- 
 rangement, and under these conditions how much silver would be 
 deposited in one hour and how much zinc dissolved ? 
 
 Answer to last question, 30.25 grammes silver, and 9.13 grammes 
 of zinc. 
 
CHAPTER XVI. 
 
 RELATIONS OF THE ATOMS TO LIGHT. 
 
 92. Light a Mode of Atomic Motion. It lias already been 
 intimated ( 53, note), that the phenomena of vision are the 
 effects of an atomic motion transmitted from some luminous 
 body to the eye through continuous lines of material particles, 
 and such lines we call rays of light. This motion may origi- 
 nate with the atoms of various substances ; but in order to 
 explain its transmission, we are obliged to assume the existence 
 of a medium filling all space, of extreme tenuity, and yet 
 having an elasticity sufficiently great to transmit the luminous 
 pulsations with the incredible velocity of 186,000 miles in a 
 second of time. This medium we call the ether, but of its 
 existence we have no definite knowledge except that obtained 
 through the phenomena of light themselves, and these require 
 assumptions in regard to the constitution of the ethereal medium 
 which are not realized even approximately in the ordinary 
 forms of matter ; for while the assumed medium must be 
 vastly less dense than hydrogen, its elasticity must surpass that 
 of steel. 
 
 According to the undulatory theory, motion is transmitted 
 from particle to particle along the line of each luminous wave 
 very much in the same way that it passes along the line of 
 ivory balls in the well-known experiment of mechanics. The 
 ethereal atoms are thus thrown into waves, and the order of 
 the phenomena is similar to that with which all are familiar 
 in the grosser forms of wave motion. But in this connection 
 we have no occasion to dwell on the mechanical conditions 
 attending the transmission of the motion. The motion itself 
 may be best conceived as an oscillation of each ether particle 
 in a plane perpendicular to the direction of the ray, not 
 
RELATIONS OF THE ATOMS TO LIGHT. 175 
 
 necessarily, however, in a straight line ; for the orbit of the 
 oscillating molecule may be either a straight line, an ellipse, or a 
 circle, as the case may be. Such oscillations may evidently 
 differ both as regards their amplitude and their duration, and 
 on these fundamental elements depend two important differences 
 in the effect of the motion on the organs of vision, viz. intensity 
 and quality, or brilliancy and color. 
 
 If our theory is correct, it is obvious that the intensity of 
 the luminous impression must depend upon the force of the 
 atomic blows which are transmitted to the optic nerves, and it 
 is also evident that this force must be proportional to the 
 square of the velocity of the oscillating atoms, or what amounts 
 to the same thing, to the square of the amplitude of the 
 oscillation ; assuming, of course, that the oscillations are 
 isochronous. 
 
 The connection of color with the time of oscillation is not so 
 obvious, and why it is that the waves of ether beating with 
 greater or less rapidity on the retina should produce such 
 sensations as those of violet,.blue, yellow, or red, the physiologist 
 is wholly unable to explain. We have, however, an analogous 
 phenomenon in sound, for musical notes are simply the effects of 
 waves of air beating in a similar way on the auditory nerves ; 
 and, as is well known, the greater the frequency of the beats, 
 or, in other words, the more rapid the oscillations of the 
 aerial molecules, the higher is the pitch of the note. Red 
 color corresponds to low, and violet to high notes of music, 
 and, the gradations of color between these extremes, passing 
 through various shades of orange, yellow, green, blue, and 
 indigo, correspond to the well-known gradations of musical 
 pitch. 
 
 From well-established data we are able to calculate the 
 rapidity of the oscillations which produce the different sensa- 
 tions of color, and also to estimate the corresponding lengths 
 of the ether waves, and the following table contains the 
 results. It must be understood, however, that these numbers 
 merely correspond to a few shades of color definitely marked 
 on the solar spectrum by certain dark lines hereafter to be men- 
 tioned ; and that equally definite values may be assigned to 
 the infinite number of intermediate shades which intervene 
 between these arbitrary subdivisions of the chromatic scale. 
 
176 RELATIONS OF THE ATOMS TO LIGHT. 
 
 Number of waves or oscilla- Length of waves in frac- 
 
 Color. tions in one second. tions of a millimetre. 
 
 Red 477 million million. 650 millionths. 
 
 Orange 506 " 609 " 
 Yellow 535 
 
 Green 577 
 
 Blue 622 
 
 Indigo 658 
 
 Violet 699 
 
 576 " 
 
 " 536 " 
 
 " 498 " 
 
 470 
 
 442 
 
 " 
 
 93. Natural Colors. It follows, as a necessary consequence 
 of the fundamental laws of mechanics, that an oscillating mole- 
 cule can only transmit to its neighbor motion which is isochronous 
 with its own. Hence a single ray of light can only produce a def- 
 inite effect of color, and this quality of the ray will be preserved 
 however far the motion may travel. A beam of light is simply 
 a bundle of rays, and if the motion is isochronous in all its 
 parts, that is, if the beam consists only of rays of one shade of 
 color, such a beam will produce the simplest chromatic sensa- 
 tion possible, that of a pure color. If, however, the beam 
 contains rays of different colors, we .shall have a more complex 
 effect, and the infinite varie'ty of natural tints are thus produced. 
 When, lastly, the beam contains rays of all the colors mingled 
 in due proportion, we receive an impression in which no single 
 color predominates, and this we call white light. 
 
 The colors of natural objects, whether inherent or imparted 
 by various dyes, are simply effects upon the retina produced by 
 the beam after it has been reflected from the surface or trans- 
 mitted through the mass of the body, and the peculiar chromatic 
 effects are due to the unequal proportions in which the dif- 
 ferent colored rays are thus absorbed. The color reflected, and 
 that absorbed or transmitted, are always complementary to 
 each other, and if mingled they would reproduce white. It is 
 obvious, moreover, that no beam of light, however modified by 
 reflection or transmission, could produce the sensation of a 
 given color, if it did not contain from the first the correspond- 
 ing colored rays. Hence it is that the colors of objects only 
 appear naturally by daylight, and when illuminated by a 
 monochromatic light, all colors blend in that of this one pure 
 tint. 
 
 94. Chromatic Spectra and Spectroscopes. When a beam 
 of light is passed through a glass prism placed as shown in Fig. 
 
RELATIONS OF THE ATOMS TO LIGHT. 
 
 177 
 
 Fig. 86. 
 
 86, it is not only refracted,th&t is, bent from its original rectilinear 
 course, but the colored rays of which the beam consists, being 
 bent unequally, are separated to a greater or less extent, and fall- 
 ing on a screen produce an elongated image colored with a suc- 
 cession of blending tints> which we call the spectrum. The red 
 rays, which are bent the least, are said to be the least refran- 
 gible, while the violet rays are the most refrangible, and inter- 
 mediate between these we have, in the order of refrangibility, 
 the various tints of orange, yellow, green, blue, and indigo. 
 Thus a prism gives an easy means of analyzing a beam of 
 light, and of discovering the character of the rays by which a 
 given chromatic effect is produced. Such observations are 
 very greatly facilitated by a class of instruments called spectro- 
 scopes, and Figs. 87 and 90 will illustrate the principles of 
 their construction. 
 
 In the very powerful instrument first represented, the beam 
 of light is passed in succession through nine prisms (each 
 having an angle of 45), and the extreme rays are thus widely 
 separated, while the beam itself is bent around nearly a whole 
 circumference. The only other essential parts of the instru- 
 ment are the collimator A and the telescope B. The light first 
 enters the collimator through a narrow slit, and having passed 
 through the prisms is received by the telescope. The tele- 
 scope is adjusted as it would be for viewing distant objects, 
 
178 
 
 RELATIONS OF THE ATOMS TO LIGHT. 
 
 and a lens at the end of the collimator serves to render the 
 rays diverging from the slit parallel, so that when the two 
 
 Fig. 87. 
 
 tubes are in line, one sees through the telescope a mag- 
 nified image of the slit, just as if the slit were at a great 
 
 Fig. 88. 
 
 distance. In like manner when the telescopes are placed as 
 in Fig. 88, and when the light before reaching the telescope 
 
RELATIONS OF THE ATOMS TO LIGHT. 179 
 
 Fig. 89. 
 
 AaBC .D Eb F 
 
 |Ora-|Yel-| Green. I Blue. I Indigo. 
 
 Inge. I low. | 
 
 passes through the whole series of prisms, we still see a single 
 definite image whenever the slit is illuminated by a pure 
 monochromatic light. Moreover, this image has a definite 
 position in the field of view, which, when the instrument is 
 similarly adjusted, depends solely on the refrangibility of the 
 light. 
 
 Thus, if we place in front of the slit a sodium flame, which 
 emits a pure yellow light, we see a single yellow image of this 
 longitudinal opening, as in Fig. 89, Na. If we use a lithium 
 flame, we see a similar image, 1 but colored red, and at some 
 distance from the first, to the left, if the parts of our in- 
 strument are disposed as in Fig. 88. If we use a thalium 
 flame, we in like manner see a single image, but colored 
 green, and falling considerably to the right of both of the 
 other two. If now we illuminate the slit by the three 
 flames simultaneously, we see all three images at once in the 
 same relative position as before. So also if we examine the 
 
 i The second image shown in Fig. 89, Li is not ordinarily seen. 
 
180 RELATIONS OF THE ATOMS TO LIGHT. 
 
 flame of a metal, which emits rays of several definite degrees 
 of refrangibility, we see an equal number of 'definite images 
 of the slit. If, next, we illuminate the slit with sunlight, 
 which contains rays of all degrees of refrangibility, we see an 
 infinite number of images of the slit spread out along the field 
 of view, and these, overlapping each other, form that continuous 
 band of blending colors which we call the solar spectrum. If, 
 lastly, we examine with our instrument the light reflected from 
 a colored surface, or transmitted through a colored medium, 
 we also see a band of blending colors, but at the same time we 
 observe that certain portions of the normal solar spectrum are 
 either wholly wanting or greatly obscured. 
 
 With a spectroscope of many prisms like the one represented 
 by Fig. 87, we can only see a small portion of the spectrum at 
 once. By moving the telescope, which, fastened to a metallic 
 arm, revolves around the axis of the instrument, different 
 portions of the spectrum may be brought into the field of view ; 
 while a vernier, attached to the same arm and moving over a 
 graduated arc, enables us to fix the position of the spectrum 
 fines, as the images of the slit are usually called. The other 
 mechanical details shown in the figure are required in order 
 to adjust the various parts of the instrument, and especially in 
 order to bring the prisms to what is termed the angle of 
 minimum deviation. But an instrument of this magnitude and 
 power is not required for the ordinary applications of the 
 spectroscope in chemistry. For this purpose a small instru- 
 ment consisting of a collimator, a single prism, and a telescope, 
 all in a fixed position, are amply sufficient. In the field of such 
 a spectroscope the whole spectrum may be seen at once ; and 
 the position of the spectrum lines is very easily determined by 
 means of a photographic scale placed at one side, and seen by 
 light reflected into the telescope from the face of the prism. 
 
 The various parts of the instrument, as arranged for ob- 
 servation, are shown in Fig. 90. A is the collimator, P the 
 prism, and B the telescope. The tube C carries the photo- 
 graphic scale, and has at the end nearest to the prism a 
 lens of such focal length that the image both of the slit and 
 the scale may be seen through the telescope at the same time, 
 the one appearing projected upon the other. The screw e 
 serves to adjust the width of the slit. Moreover, one half of the 
 
RELATIONS OF THE ATOMS TO LIGHT. 
 Fig. 90. 
 
 181 
 
 length of the slit is covered by a small glass prism so arranged 
 that it reflects into the collimator tube the rays from a lamp 
 placed on one side. Thus the two halves of the slit may be 
 illuminated independently by light from different sources, and 
 the two spectra, which are then seen superimposed upon each 
 other (see Fig. 91), exactly compared. The various screws, 
 which appear in Fig. 90, are used for adjusting the different 
 parts of the instrument. 
 
 95. Spectrum Analysis. The atoms of the different chem- 
 ical elements, when rendered luminous under certain definite 
 conditions, always emit light whose color is more or less 
 characteristic, and which, when analyzed with the spectroscope, 
 exhibit spectra similar to those which are represented in Fig. 
 89, so far as is possible without the aid of color. Sometimes 
 we see only a single line in a definite position, as in the case 
 of Na, Li, and Th, already referred to. At other times 
 there are several such lines ; and, still more frequently, to 
 these lines (or definite images of the slit) there are super- 
 added more or less extended portions of a continuous spectrum. 
 Moreover, not only is the general aspect of each spectrum 
 exceedingly characteristic, but also the occurrence of its 
 peculiar lines is, so far as we know, an absolute proof of the 
 
182 RELATIONS OF THE ATOMS TO LIGHT. 
 
 presence of a given element, and these lines may be readily 
 recognized by their position, even when the character of the 
 spectrum is otherwise obscure. It is evident then that we 
 have here a principle which admits of most important ap- 
 plications in chemical analysis, and it only remains to con- 
 sider under what conditions the elementary atoms emit their 
 characteristic light. 
 
 First. All bodies when intensely heated are rendered lumi- 
 nous, and, other things being equal, the higher the temperature 
 the more intense is the light. The brilliancy of the light 
 emitted at the same temperature by different bodies varies 
 very greatly, the densest bodies being, as a general rule, the 
 most intensely luminous. 
 
 Secondly. Solid and liquid bodies, if opaque, emit when 
 ignited white light, or at least light which shows with the spec- 
 troscope a continuous spectrum more or less extended. At a 
 red heat the light from such bodies consists chiefly of red rays, 
 but as the temperature rises first- to a white and then to a blue 
 heat, the more refrangible rays become more abundant and 
 finally predominate. 
 
 Thirdly. The elementary substances give out their pecu- 
 liar and characteristic light only in the state of gas or vapor. 
 Hence, when we examine with a spectroscope a source of light, 
 we may infer that a continuous spectrum indicates the presence 
 of solid or liquid bodies, while a discontinuous spectrum, with 
 definite lines or images of the slit, indicates the presence of 
 gases and vapors ; and in the last case we can, as has been seen, 
 infer from the position of the lines the nature of the luminous 
 atoms. It would seem, however, from recent investigations, 
 that under certain conditions even a gas may show a continu- 
 ous spectrum, and there are other seeming exceptions which 
 admonish us that the general principles just stated should be 
 applied with caution. 
 
 Fourthly. At the very high temperatures at which alone 
 gases or vapors become luminous, compound bodies, as a rule, 
 appear to be decomposed, and the elementary atoms disasso- 
 ciated. Hence the observations with the spectroscope have 
 been almost entirely confined to the spectra of the elementary 
 substances, and our knowledge of the spectra of compound sub- 
 stances is exceedingly limited. In some few cases where the 
 
RELATIONS OF THE ATOMS TO LIGHT. 183 
 
 spectrum of a compound has been obtained, it has been noticed 
 that, as the temperature rises, this spectrum is suddenly re- 
 solved into the separate spectra of the elements of which the 
 compound consists. 
 
 Fifthly. At a high temperature the metallic atoms of a 
 compound body are far more luminous than those of the other 
 elementary atoms with which they are associated. Hence, 
 when the vapor of a metallic compound is rendered luminous, 
 the light emitted is so exclusively that of the metallic atoms, 
 disassociated by the heat, that when examined with the spec- 
 troscope the spectrum of the metal is alone seen ; and this is 
 the probable explanation of the fact that the salts of the same 
 metal, when treated as will be described in the next para- 
 graph, all show, as a general rule, the same spectrum as the 
 metal itself. 
 
 Lastly. The substance, on which we wish to experiment, 
 may be rendered luminous in several ways. If the substance 
 is a volatile metallic salt, the simplest method is to expose a 
 bead of the substance (supported on a loop of platinum wire) 
 to the flame of a Bunsen's burner (Fig. 90), which by itself 
 burns with a nearly non-luminous flame. The flame soon be- 
 comes filled with the disassociated atoms of the metal and 
 shines with their peculiar light. 
 
 In order to study the spectra of the less volatile metals like 
 aluminum, iron, or nickel, we use two needles of the metal, and 
 pass between the points, when about one fourth of an inch 
 apart, the electric discharges of a powerful Ruhmkorff coil, 
 condensed by a large Leyden jar. The metal is volatilized 
 by the heat of the electric current, and the space between the 
 points becomes filled with the intensely ignited vapor, which 
 then shines with its characteristic light." 1 
 
 In a similar way we can experiment on the permanent gases 
 and lighter vapors, enclosing them in a glass tube with plati- 
 num electrodes, and before sealing the tube reducing the ten- 
 sion with an air pump, when the discharge will pass through 
 a length of several inches of the attenuated gas. The light 
 then emitted comes from the atoms or molecules of the gas, and 
 where the electric current is condensed as in the capillary por- 
 
 1 An electric spark is in every case merely a line of material particles ren- 
 dered luminous by the current. 
 
184 RELATIONS OF THE ATOMS TO LIGHT. 
 
 tion of the tubes constructed for this purpose, the light is suf- 
 ficiently intense to be analyzed with the spectroscope. 
 
 The three different modes of experimenting just described do 
 oot by any means always give the same spectrum when ap- 
 plied to the same chemical element. It constantly happens 
 that as the temperature rises new lines appear, which are usu- 
 ally those corresponding to the more refrangible rays, and at 
 the very high temperatures generated by the electric discharge 
 many of the spectra change their whole aspect. The ill-defined 
 broad bands or luminous spaces which are so conspicuous at a 
 low temperature (see Fig. 89), disappear, and are replaced by 
 a greater or less number of definite spectrum lines. Gen- 
 erally, however, the characteristic lines which mark the ele- 
 ment at the lower temperature are seen also at the higher ; but 
 sometimes there is a sudden and complete change of the whole 
 spectrum. The cause of these differences is not understood, 
 but it has been thought by some investigators that the normal 
 spectra of the elementary atoms consist of bright bands alone, 
 and that the more or less continuous spectra, which are also 
 seen at the lower temperatures, are to be referred to the im- 
 perfect disassociation of the atoms, whose mutual attractions 
 or partial combinations produceNif state of aggregation ap- 
 proaching the condition which\Metmines the corftinuous spec- 
 
 tra of liquid or solid bodies.^/ \/ \ 
 
 96. Delicacy of the Methofi\- Having now stated the 
 general principles of spectrum analysis, and the conditions 
 under which these principles may be applied, it need only be 
 added that the method is one of extreme delicacy. It enables 
 us to detect wonderfully minute quantities of many of the 
 metallic elements, and has already led to the discovery of four 
 elements of this class which had eluded all methods of investi- 
 gation previously employed. The names of these elements, 
 Rubidium, Caesium, Thallium and Indium, all refer to the 
 color of their most characteristic spectrum bands. 1 
 
 97. Solar and Stellar Chemistry. When a beam of sun- 
 light is examined with a powerful spectroscope, the solar 
 spectrum is seen to be crossed by an almost countless number 
 of dark lines distributed with no apparent regularity, and dif- 
 
 1 The different bands of the same element are usually distinguished by 
 Greek letters, following the order of relative brilliancy. 
 
RELATIONS OF THE ATOMS TO LIGHT. 
 
 185 
 
 fering very greatly in relative strength or intensity. These 
 lines were first accurately described by the German optician 
 Fraunhofer, and have since been known as the Fraunhofer 
 lines. A few of the most prominent of these lines are shown 
 in Fig. 89, with the letters of the alphabet by which they are 
 designated. These lines, like the bright lines of the elements, 
 correspond in every case to a^ definite degree of refrangibility, 
 and therefore have a fixed position on the scale of the spectro- 
 scope. Moreover, what is very remarkable, the bright and 
 the dark lines have in several cases absolutely the same 
 position. 
 
 It is easy to construct the spectroscope so that the two halves 
 of the slit may be illuminated from different sources. If then 
 we admit a beam of sunlight through one half, and the light 
 of a sodium flame through the other half, we shall have the 
 two spectra super-imposed in the same field, as in Fig. 91, 
 
 Fig. 91. 
 
 and it will be seen that the two parts of the sodium band, 
 which appears as a double line under a high power, coincide 
 absolutely in position with the double dark line D in the 
 solar spectrum. But a still more striking coincidence has 
 been observed in the case of iron, for the eighty well-marked 
 bright lines in the spectrum of this metal correspond absolutely 
 both in position and in strength with eighty of the dark lines 
 of the solar spectrum. Now, the chances that such coinci- 
 dences are the result of accident, are not one in one billion 
 billion ; and we are therefore compelled to believe that the 
 two phenomena must be connected. A simple experiment 
 shows what the relation probably is. 
 
 If we place before the spectroscope a sodium flame, we see, 
 of course, the familiar double line. If now we place behind 
 
186 RELATIONS OF THE ATOMS TO LIGHT. 
 
 the sodium flame a candle flame, so that the candle also shines 
 into the slit, but only through the sodium flame, we shall see 
 the same bright lines projected upon the continuous spectrum 
 of the candle. If, however, we put in place of the candle an 
 electric light, we shall find that while the continuous spectrum 
 is now far more brilliant than before, the sodium lines appear 
 black. The explanation of this singular phenomenon is to be 
 found in a principle, now well established both theoretically 
 and experimentally, that a mass of luminous vapor, while other- 
 wise transparent, powerfully absorbs rays of the same refrangi- 
 bility which it emits itself. Hence, in our experiment, the 
 very small portion of the spectrum covered by the sodium line 
 is illuminated by the sodium flame alone, while all the rest of 
 the spectrum is illuminated from the source behind, and the 
 effect is merely one of contrast, the sodium lines appearing 
 light or dark according as they are brighter or darker than the 
 contiguous portions of the spectrum. 
 
 In a similar way the bright lines of a few other elements 
 have been inverted, and these experiments would lead us to 
 infer that the Fraunhofer lines themselves are formed by a 
 brilliant photosphere shining through a mass of less luminous 
 gas. In other words, it would appear that the sun's luminous 
 orb is surrounded by an immense atmosphere which intercepts 
 a portion of his rays, and that we see as dark lines what would 
 probably appear as bright bands, could we examine the light 
 from the atmosphere alone. 
 
 If then our generalization is safe, the dark and the bright 
 lines are the same phenomena seen under a different aspect, 
 and the one as well as the other may be used to identify the 
 different chemical elements. Hence, then, there must be both 
 iron and sodium in the sun's atmosphere, and for the same 
 reason we conclude that our luminary must contain Calcium, 
 Magnesium, Nickel, Chromium, Barium, Copper, and Zinc, while 
 there is equally good evidence that Gold, Silver, Mercury, Alumi- 
 num, Cadmium, Tin, Lead, Antimony, Arsenic, Strontium, and 
 Lithium are not present, at least in large quantities. It is true, 
 however, that the elements thus recognized in the sun only 
 account for a very insignificant portion of the dark lines, and 
 it is difficult to reconcile this fact with our actual knowledge 
 and present theories. Since the meteorites have brought to 
 
RELATIONS OF THE ATOMS TO LIGHT. 187 
 
 us no new elements, their evidence, as far as it goes, would 
 not lead us to expect to find in the sun's atmosphere such a 
 vast number of unknown elements as the dark lines would in- 
 dicate ; and this obvious explanation of their countless num- 
 ber cannot therefore be regarded as probable. It has been 
 observed, however, in the few cases which have been investi- 
 gated, that the spectrum of a compound body is far more 
 complex than the different spectra of its elements combined ; 
 and it is possible that the complexity we see in the solar 
 spectrum may arise from the partial combination or mutual 
 interference of elements now known, in the outer and colder 
 portions of that immense atmosphere which is supposed to 
 extend many thousand miles beyond the luminous surface of 
 the sun. 
 
 If next we turn the spectroscope on some of the brighter 
 fixed stars, we shall see continuous spectra like the solar 
 spectrum, of greater or less extent, and covered by dark lines. 
 A careful comparison of these lines would seem to indicate 
 that the stars differ very greatly from each other, although in 
 general they are bodies similar to our sun ; and if our theory 
 is correct, we have been able to detect the presence of sodium, 
 magnesium, hydrogen, calcium, iron, bismuth, tellurium, 
 antimony, and mercury in Aldebaran, and other elements in 
 other stars. 
 
 The most remarkable result of stellar chemistry remains yet 
 to be noticed. On examining the nebulae with the spectro- 
 scope, it has been found that while some of them show. a con- 
 tinuous spectrum, there are a number of these remarkable 
 bodies which exhibit the phenomena of bright lines. This 
 would lead us to the conclusion that the last are really, as the 
 nebular theory assumes, masses of incandescent gas, while the 
 first are not true nebulae, but simply clusters of very distant 
 stars. An examination of the comets has confirmed the pre- 
 vious conclusion that they also are mere masses of gas, but, 
 singularly enough, the light from the coma of one of those 
 bodies gave a continuous spectrum, due probably to reflected 
 sunlight. 
 
 98. Absorption Spectra. When a luminous flame is viewed 
 with a spectroscope through a solution of any salt of the 
 metal Erbium, the otherwise continuous spectrum of the flame 
 
188 RELATIONS OF THE ATOMS TO LIGHT. 
 
 is seen to be interrupted by several broad bands, which have a 
 definite position, and are a valuable means of recognizing the 
 presence of this very rare element. This absorption spectrum, 
 as it is called, is simply the reverse, the " negative " of the 
 luminous spectrum of the same element. 
 
 In like manner the salts of Didymium give an equally 
 characteristic, although very different, absorption spectrum, 
 which is in fact the only sure test we possess for this remark- 
 able elementary substance ; and as the bands may under some 
 conditions be seen with reflected, as well as with transmitted 
 light, we may apply the test even to opaque solids. Also, the 
 same absorption bands are obtained either when the light is 
 transmitted through a liquid solution, or through a solid crystal 
 of any salt of the metal ; and, moreover, the incandescent vapor 
 of the metal shows bright bands corresponding to the dark 
 bands in position. These facts would seem to show that the 
 characteristic spectrum bands of an element may be, at least 
 to some extent, independent both of the state of aggregation, 
 and of the condition of combination of the elementary atoms. 
 
 Many substances besides the compounds of the elements 
 just noticed, give characteristic absorption spectra which have 
 been found to be useful chemical tests, especially in the case 
 of blood, and certain other bodies of organic origin. The 
 most remarkable phenomena of this class are the absorption 
 spectra which are seen when a luminous flame is viewed with 
 a spectroscope through various colored vapors, such as those 
 of nitric per-oxide, bromine, and iodine. The dark bands are 
 then very numerous, and in some cases may be resolved into 
 well-defined lines. Indeed, the absorption bands are a class of 
 phenomena closely allied to the Fraunhofer lines, many of 
 which are known to result from the absorption by the earth's 
 atmosphere of solar rays of certain degrees of refrangibility ; 
 and all these facts, with many others, prove that gases and 
 vapors may exert their peculiar power of elective absorption 
 at the ordinary temperature, as well as when incandescent. 
 As a general rule, however, the absorption bands are not, like 
 the bright lines of the metallic spectra or their representatives 
 among the dark lines of the solar spectrum, definite images of 
 the slit, but they are darker portions of the spectrum more or 
 less regularly shaded, and correspond to the broad bands or 
 
RELATIONS OF THE ATOMS TO LIGHT. 189 
 
 luminous spaces in the spectra of the metallic vapors when 
 not intensely heated. In each case the effect results from the 
 blending of a greater or less number of images of the slit, 
 differing in relative position and intensity. 
 
 99. Theory of Exchanges. The facts of the two last 
 sections are all illustrations of a general principle already 
 referred to in connection with the reversal of the sodium 
 spectrum. This principle is known as the " Theory of Ex- 
 changes," and has been stated as follows : " The relation 
 between the power of emission, and power of absorption 
 for each kind of rays (light or heat) is the same for all 
 bodies at the same temperature." . . . . " Let R denote the 
 intensity of radiation of a particle for a given description of 
 light at a given temperature, and let A denote the proportion 
 of rays of this description incident on the particle which it 
 absorbs ; then R-i-A has the same value for all bodies at the 
 same temperature, that is to say, this quotient is a function 
 of the temperature only." 
 
 The law of exchanges finds its widest application in the 
 phenomena of radiant heat, and so far as experiments have 
 been made, it appears to be true in its greatest generality. In 
 applying it to explain the reversal of the spectra of colored 
 flames, we have only to deal with a single body in its relations 
 to rays of different qualities. If the principle is true, the 
 absorbing power of such a body at a given temperature must 
 bear a fixed ratio to its power of emission for each kind of 
 ray. If, for example, it has a great power of emitting certain 
 rays of red light, it has a proportionally great power of 
 absorbing the same rays. If, again, it has a feeble power of 
 emitting violet rays of definite quality, its power of absorbing 
 such rays is proportionally feeble, and bears the same ratio to 
 the power of emission as before ; and, lastly, it has no power 
 of absorption over such rays as it does not itself emit. More- 
 over, it would follow that, although the relation of the absorb- 
 ing to the radiating power might vary very greatly, so that, 
 as the temperature falls, the last may become inconsiderable 
 as compared with the first, or even vanish, no essential change 
 in the character of the elective absorption would be thus in- 
 duced. Hence, we should expect that bodies would absorb 
 when cold rays of the same quality which they emit when hot, 
 
190 RELATIONS OF THE ATOMS TO LIGHT. 
 
 and also that opaque solids when heated would emit white 
 light. We have seen that the general order of the phenomena 
 is that which the law of exchanges would predict, and here, for 
 the present, our knowledge stops. We have as yet been able 
 to form no satisfactory theory in regard to the relations of the 
 molecular structure of bodies to the medium through which the 
 waves of light or heat are transmitted. It is, however, 
 worthy of notice that Euler, one of the earliest and ablest 
 investigators of undulatory motion, predicted the discovery of 
 the law of exchanges, in assuming as a fundamental principle of 
 the undulatory theory that a body can only absorb oscillations 
 isochronous with these of which it is itself susceptible. 
 
 100. General Conclusions. The facts that have been 
 stated in this chapter are sufficient to show, that, although yet 
 in its infancy, spectrum analysis promises to be one of the 
 most powerful instruments of investigation ever applied in 
 physical science. It seems to be the key which will in time 
 open to our view the molecular structure of matter ; and even 
 now the results actually obtained suggest speculations in 
 regard to the ultimate constitution of matter, of the most 
 interesting character. The several monochromatic rays which 
 the atoms of the elements emit, must receive their peculiar 
 character from some motion in the atoms themselves which is 
 isochronous with the motion they impart. Is it not then in 
 this motion that the individuality of the element resides, and 
 may not all matter be alike in its ultimate essence? Such 
 speculations, however wild, are not wholly unprofitable, if only 
 they stimulate investigation and thus lead to further dis- 
 coveries. 
 
CHAPTER XVII. 
 
 CHEMICAL CLASSIFICATION. 
 
 101. General Principles. The glimpses that we have been 
 able to gain of the order in the constitution of matter give us 
 grounds for believing that there is a unity of plan pervading 
 the whole scheme, and encourage a confident expectation that 
 hereafter, when our knowledge becomes more complete, chem- 
 ists may attain to at least such a partial conception of this 
 plan as will enable them to classify their compounds under 
 some natural system ; and in imagination we may even look 
 forward to the time when science will be able to express all 
 the possibilities of this scheme with a few general formulae, 
 which will enable the chemist to predict with absolute cer- 
 tainty the qualities and relations of any given combination of 
 materials or conditions. But although to a very slight extent 
 the idea has been realized for a small class of the compounds 
 of carbon, yet as a whole this grand conception is as yet but a 
 dream. The more advanced student will find that in limited 
 portions of some few fields of investigation a fragmentary clas- 
 sification is possible, as in mineralogy ; but, when he attempts 
 to comprehend the whole domain, he becomes painfully aware 
 of the immense deficiencies of his knowledge ; he is confused 
 by the numerous chains of relationship, which he follows, with 
 no result, to sudden breaks, and soon becomes convinced that 
 all such efforts must be fruitless until more of the missing links 
 are supplied. 
 
 The best that can now be done in an elementary treatise on 
 chemistry is to group together the elements, or, rather, the 
 elementary atoms, in such families as will best show their 
 natural affinities ; and then to study, under the head of each 
 element, the more important and characteristic of its com- 
 pounds. However little value such a classification may have 
 in its scientific aspect, it will bring together, to a greater or less 
 extent, the allied facts of the science, and thus will help the 
 mind to retain them in the memory. 
 
192 CHEMICAL CLASSIFICATION. 
 
 In classifying the elementary atoms, the three most impor- 
 tant characters to be observed are the Prevailing Quantivalence, 
 the Electrical Affinities, and the Crystalline Relations. The 
 first of these characters serves more particularly to classify the 
 elements in groups, the second to determine their position in 
 the groups, and the last to control the indications of the other 
 two. 
 
 The crystalline relations of the atoms can only be deter- 
 mined by comparing the crystalline forms of allied compounds, 
 and involve the principles of isomorphism already discussed. 
 Moreover, in order to reach the most satisfactory scheme of 
 classification, we must take into consideration other properties 
 of these compounds besides the crystalline form; which, al- 
 though they may not be so precisely formulated, are frequently 
 important aids in forming correct opinions as to the relations of 
 the atoms. It will also be evident, from what has previously 
 been stated, that more trustworthy inferences as to these rela- 
 tions may frequently be drawn from the crystalline form and 
 properties of allied compounds than from those of the element- 
 ary substances themselves ; for, in addition to the fact that so 
 many of these substances crystallize in the isometric system, 
 whose dimensions admit of no variation, it is also true that, in 
 our ignorance of the molecular constitution of most of them, we 
 often have more certainty, in the case of compounds, that our 
 comparisons are made under identical molecular conditions. 
 i, 102. Metallic and Non-Metallic Elements. In all works on 
 chemistry since the time of Lavoisier, the elementary sub- 
 stances have been divided into two great classes, the metals 
 and the non-metals ; and the distinction is undoubtedly funda- 
 mental, although too much importance has been frequently 
 attached to the accident of a brilliant lustre. The character- 
 istic qualities of a metal, with which every one is more or less 
 familiar, are the so-called metallic lustre, that peculiar adapt- 
 ability of molecular structure known as malleability or ductility, 
 and the power of conducting electricity or heat. These qualities 
 are found united and in their perfection only in the true metals, 
 although one or even two of them are well developed in several 
 elementary substances which, on account of their chemical 
 qualities, are now almost invariably classed with the non- 
 metals, as, for example, in selenium, tellurium, arsenic, 
 
CHEMICAL CLASSIFICATION. 193 
 
 antimony, boron, and silicon. Besides the properties above 
 named, many persons also associate with the idea of a metal a 
 high specific gravity ; but this property, though common to most 
 of the useful metals, is by no means universal ; and, among the 
 metals with which the chemist is familiar, we find the lightest, 
 as well as the heaviest, of solids. The non-metallic elements, 
 as the name denotes, are distinguished by the absence of metal- 
 lic qualities ; but the one class merges into the other. 
 
 The presence or absence of metallic qualities in the ele- 
 mentary substances is for some unknown reason intimately 
 associated with the electrical relations of their atoms, those of 
 the metals being electro-positive, while those of the non- 
 metals are electro-negative, with reference, in each case, to the 
 atoms of the opposite class. In the classification given in 
 Table II. we have associated together in the same family both 
 the metals and the non-metals having the same quantivalence, 
 believing that such an arrangement not only best exhibits the 
 relations of the atoms, but also that in a course of elementary 
 instruction it presents the facts of chemistry in the most logical 
 order. 
 
 103. Scheme of Classification. The classification of the 
 elementary atoms which has been adopted in this book is shown 
 in Table II. 
 
 In the first place the atoms are divided into two large 
 families, the Perissads and the Artiads (27). 
 
 Secondly, these families are subdivided into groups (separated 
 by bars in the table) of closely allied elements. The atoms of any 
 one of these groups are isomorphous ; and they are arranged 
 in the order of their weights, which is found to correspond also, 
 in almost every case, to their electrical relations. Each group 
 forms a very limited chemical series ; and not only the weights 
 and the electrical relations of the atoms, but also many of the 
 physical qualities of the elementary substances, vary regularly 
 as we pass from one end of the series to the other. The order 
 of the variation, however, is not always the same ; for while in 
 some cases he lightest atoms of a series are the most electro- 
 negative, in other cases they are the most electro-positive. 
 
 Thirdly, in arranging the groups of allied atoms we have 
 followed the prevailing quantivalence of the group, and those 
 groups whose elementary atoms exhibit in general the lowest 
 
194 CHEMICAL CLASSIFICATION. 
 
 quantivalence are, as a rule, placed first in order; but with 
 our present limited knowledge there must be some uncertainty 
 in regard to the details of such an arrangement, and the prin- 
 ciple has sometimes been violated so as to bring together those 
 groups of atoms which are most allied in their chemical rela- 
 tions. 
 
 The remarks already made in regard to the general scheme 
 of chemical classification apply with almost equal force to the 
 partial system here attempted. The very attempt makes evi- 
 dent the fragmentary character of our knowledge, even in re- 
 gard to the exceedingly limited portion of the subject with 
 which we are dealing. The idea of classification by series was 
 first developed in the study of organic chemistry, where the 
 principle is much more conspicuous than among inorganic com- 
 pounds. Thus, as has been shown (40), we are acquainted 
 with twenty acids resembling acetic acid, which form a series 
 beginning with formic acid and ending with melissic acid. Each 
 member of this series differs in composition from the preceding 
 member by CH^ or by some multiple of this symbol ; and the 
 properties of the compounds vary regularly between the extreme 
 limits, according to well-established laws. Moreover, many 
 other similar, although more limited, series of compounds are 
 known, and the principle realized in these organic series seems 
 to be the true idea of all chemical classification. But, in attempt- 
 ing to apply it to the chemical elements, we find only two or three 
 groups of atoms where the series is of sufficient extent to make 
 the relations of the members evident. In most cases it would 
 seem as if we only knew one or two members of a series, and 
 this apparent ignorance not only throws doubt on the general 
 application of our principle, but also renders uncertain the details 
 of our scheme, even assuming that the principle of the classi- 
 fication is correct. Hence, also, great differences of opinion 
 may be reasonably entertained in regard to the position which 
 the different atoms ought to occupy in such a scheme. 
 
 Another very important cause of uncertainty in any scheme 
 of classifying the elements arises from the double relationships 
 which many of them manifest. Thus iron, which we have 
 associated with manganese and aluminum, is in some of its 
 relations closely allied to magnesium and zinc. Many other 
 elements resemble iron in having a similar two-fold character, 
 
CHEMICAL CLASSIFICATION. 195 
 
 and different authors may reasonably assign to such elements 
 different places in their systems of classification, according as 
 they chiefly view them from one or the other aspect. Hence 
 arises a degree of uncertainty which affects our whole system, 
 and cannot be avoided in the present state of the science. 
 
 Indeed, no classification in independent groups can satisfy 
 the complex relations of the elements. These relations cannot 
 be represented by a simple system of parallel series, but only 
 by a web of crossing lines, in which the same element may 
 be represented as a member of two or more series at once, 
 and as affiliating in different directions with very different 
 classes of elements. In the present fragmentary state of our 
 knowledge, such a classification as we have just indicated is 
 not attainable. The scheme adopted in this book only indi- 
 cates in each case a single line of relationship ; but we have 
 always endeavored to place each element in that relation 
 which is the most characteristic ; and, however imperfect such 
 a scheme may be, it will nevertheless assist study by bringing 
 before the student's mind the facts of the science in a syste- 
 matic and natural order. 
 
 104. Relations of the Atomic Weights. If the principle of 
 classification which we have adopted is correct, and the ele- 
 ments actually belong to series like those of the compounds of 
 organic chemistry, we should naturally expect that the atomic 
 weights would conform to the same serial law ; and it is a re- 
 markable fact that the differences between the atomic weights 
 of the elements of the same group are in most cases very nearly 
 multiples of 16. The value of this common difference varies 
 between 15 and 17, and we must admit in some cases the 
 simplest fractional multiples ; but the mean value is very 
 nearly 16, and the frequent occurrence of this difference is 
 very striking. This numerical relation is not absolutely exact, 
 but here, as in the periods of the planets, in the distribution of 
 leaves on the stem of a plant, and in other similar natural 
 phenomena, there is a marked tendency towards a certain nu- 
 merical result, which is fully realized, however, only in com- 
 paratively few cases. 
 
 Other numerical relations which have been noticed between 
 the atomic weights are probably only phases of the same law 
 of distribution in series. Thus the atomic weight of sodium is 
 
196 CHEMICAL CLASSIFICATION. 
 
 very nearly the mean between that of lithium and potassium ; 
 and the atomic weights of chlorine, bromine, and iodine, of glu- 
 cinum, yttrium and erbium, of calcium, strontium, and barium, 
 of oxygen, sulphur, and selenium, are similarly related. Again, 
 there are several pairs of allied elements, between whose 
 atomic weights there is very nearly the same difference. Thus 
 the difference between the atomic weights of indium and cad- 
 mium is very nearly the same as that between the atomic 
 weights of magnesium and zinc, and the difference between the 
 atomic weights of niobium and tantalum the same as that be- 
 tween the atomic weights of molybdenum and tungsten. A 
 careful study of the atomic weights will also reveal many other 
 approximate relations of the same sort; but although the 
 study of these relations is highly interesting, and may lead here- 
 after to valuable results, yet no great importance can be at- 
 tached to them in the present state of the science. 
 
TABLE I. 
 
 FRENCH MEASURES 
 
 Measures of Length. 
 
 1 Kilometre 
 
 = 
 
 1000 
 
 Metres. 
 
 1 Metre 
 
 = 
 
 1.000 
 
 Metre. 
 
 1 Hectometre 
 
 = 
 
 100 
 
 " 
 
 1 Decimetre 
 
 = 
 
 0.100 
 
 
 
 1 Decametre 
 
 
 
 10 
 
 tt 
 
 1 Centimetre 
 
 = 
 
 0.010 
 
 ii 
 
 1 Metre 
 
 
 
 1 
 
 tt 
 
 1 Millimetre 
 
 = 
 
 0.001 
 
 tt 
 
 Ar. Co. Log. 
 0.2066 188 
 
 Logarithms. 
 
 1 Kilometre = 0.6214 Mile. 9.7933 712 
 
 1 Metre = 3.2809 Feet. 0.5159 930 9.4840 070 
 
 1 Centimetre = 0.3937 Inch. 9.595-1 742 0.4048 258 
 
 The metre is one ten-millionth of a quadrant of the globe*. 
 
 Measures of Volume. 
 
 1 Cubic Metre m? = 1000.000 Litres. 
 
 1 Cubic Decimetre dHn. 3 = 1.000 " 
 1 Cubic Centimetre cTnf. 3 = 0.00 1 " 
 
 Cubic Metre =35.31660 Cubic Feet. 
 
 Cubic Decimetre =61.02709 Cubic Inches. 
 Cubic Centimetre = 0.06103 " " 
 Litre = 0.22017 Gallon. 
 
 Litre = 0.88066 Quart. 
 
 Litre = 1.76133 Pints. 
 
 Logarithms. 
 1.5479 790 
 1.7855 226 
 8.7855 226 
 9.3427 581 
 9.9448 083 
 0.2458 407 
 
 Ar. Co. Log. 
 8.4520 210 
 8.2144 774 
 1.2144 774 
 0.6572 419 
 0.0551 917 
 9.7541 593 
 
 FRENCH 
 
 1 Kilogramme = 1000 Grammes. 
 1 Hectogramme =100 " 
 1 .Decagramme =10 " 
 1 Gramme =1 " 
 
 WEIGHTS. 
 
 1 Gramme = 1.000 Gramme. 
 
 1 Decigramme =0.100 " 
 1 Centigramme = 0.010 " 
 1 Milligramme = 0.001 " 
 
 1 Kilogramme = 2.20462 Pounds Avoirdupois. 
 1 " = 2.67922 " Troy. 
 
 1 Gramme = 15.43235 Grains. 
 
 Logarithms. 
 0.3433 337 
 0.4280 083 
 1.1884 321 
 
 Ar. Co. Log. 
 9.6566 663 
 9.5719 917 
 8.8115 679 
 
 1 Crith 
 
 = 0.089578 Grammes. 
 
 8.9522 014 1.0477 986 
 
TABLE II. 
 
 ELEMENTARY ATOMS. 
 
 Perissad 
 
 Elements. 
 
 Atomic 
 Weights. 
 
 U 
 
 | 
 
 Quantiva- 
 lence. 
 
 Artiad 
 Elements. 
 
 Atomic 
 
 Weights. 
 
 Symbols 
 of 
 
 Molecules. 
 
 < 
 
 Hydrcrgen 
 
 1.0 
 19.0 
 35.5 
 80.0 
 127.0 
 .7.0 
 23.0 
 39.1 
 85.4 
 133.0 
 108.0 
 204.0 
 197.0 
 11.0 
 14.0 
 31.0 
 75.0 
 22.0 
 210.0 
 1.37 
 20.0 
 94.0 
 82.0 
 
 .H-H 
 F-F 
 
 Cl-Cl 
 Br-Br 
 I-I 
 Li-Li 
 
 Na-Na 
 K-K 
 Rb-Rb 
 Cs-Cs 
 Ag-Ag ? 
 77-77? 
 Au=Au? 
 
 I 
 
 (i 
 
 it 
 
 if 
 
 I or III 
 III 
 
 III or V 
 
 u 
 
 V 
 
 
 
 ; Copper 
 Mercury 
 
 63.4 
 200.0 
 40.0 
 87.6 
 137.0 
 207.0 
 24.0 
 65.2 
 72.0 
 112.0 
 9.3 
 61.7 
 112.6 
 92.0 
 93.6 
 95.0 
 58.8 
 58.8 
 55.0 
 56.0 
 27.4 
 52.2 
 04.4 
 99.2 
 04.4 
 96.0 
 06.6 
 97.4 
 50.0 
 18.0 
 89.6 
 31.4 
 28.0 
 12.0 
 
 Cu? 
 Hg 
 Ca? 
 Sr? 
 Ba? 
 Pb? 
 Mg? 
 Zn? 
 In? 
 Cd? 
 G? 
 Y? 
 E? 
 Ce? 
 La? 
 D? 
 Ni? 
 Co? 
 Mn? 
 Fe? 
 Al? 
 Cr? 
 Ru? 
 Os? 
 R? 
 Ir? 
 Pd? 
 Pt? 
 Ti? 
 Sn? 
 Zr? 
 Th? 
 Si? 
 C? 
 
 II 
 
 (4 
 
 a 
 
 II or IV 
 
 
 M 
 
 IV 
 
 H 
 
 I Fluorine 
 Chlorine 
 Bromine 
 Iodine 
 
 Calcium 
 Strontium 
 Barium 
 Lead 
 
 Lithium 
 Sodium 
 Potassium 
 Rubidium 
 Ccesium 
 
 Magnesium 
 Zinc 
 
 Indium 
 Cadmium 
 
 Silver 
 
 Glucinum 
 Yttrium 
 Erbium 
 
 Thallium 
 
 Gold 
 
 Boron 
 
 Cerium 
 Lanthanum 
 Didymium 
 
 Nitrogen 
 Phosphorus 
 Arsenic 
 Antimony 
 Bismuth* 
 
 As^As z 
 
 Nickel 
 Cobalt 
 
 Manganese 
 Iron 
 
 Vanadium 
 
 Uranium 
 
 Aluminum 
 Chromium 
 
 f jolumbium 
 Tantalum 
 
 TalTa? 
 
 Ruthenium 
 Osmium 
 
 Artiad 
 Elements. 
 
 16.0 
 32.0 
 79.4 
 128.0 
 960 
 184.0 
 
 0=0 
 
 Te=Te 
 Mo? 
 W? 
 
 II 
 
 Hor VI 
 
 
 
 T, 1 
 
 Rhodium 
 Indium 
 
 Palladium 
 Platinum 
 Titanium 
 Tin 
 
 Oxygen 
 
 Sulphur 
 Selenium 
 Tellurium 
 
 Zirconium 
 
 Thorium 
 
 Molybdenum 
 Tungsten 
 
 Silicon 
 
 Carbon 
 
TABLE III. 
 
 Specific Gravity of Gases and Vapors. 
 
 Names. 
 
 ' Symbols. 
 
 Air = 1. 
 
 sp.ffic. 
 
 H-H=1. 
 
 Half 
 Molecular 
 Weight. 
 
 Loga- 
 rithms. 
 
 Air 
 
 
 1.000 
 
 14.43 
 
 
 1.1593 
 
 Hydrogen 
 
 H-H 
 
 0.0693 
 
 1.00 
 
 1.00 
 
 0.0000 
 
 Acetylic Hydride (Aldehyde) 
 
 C 2 H 3 0-H 
 
 1.532 
 
 22.10 
 
 22.00 
 
 1.3424 
 
 Acetylic Chloride 
 
 C 2 H 3 O-Cl 
 
 2.87 
 
 41.42 
 
 39.25 
 
 1.5938 
 
 Acetic Anhydride 
 
 ( C 2 H 3 0),= O 
 
 3.47 
 
 50.07 
 
 51.00 
 
 1.7076 
 
 Acetic Acid 
 
 H-0-C 2 H 3 
 
 2.083 
 
 30.07 
 
 30.00 
 
 1.4771 
 
 Aluminic Chloride 
 
 [Al 2 ]iCl a 
 
 9.34 
 
 134.80 
 
 133.90 
 
 2.1268 
 
 Aluminic Bromide 
 
 [A1 2 ] ^Br 6 
 
 18.62 
 
 268.70 
 
 267.40 
 
 2.4272 
 
 Aluminic Iodide 
 
 [A1 2 ] 14 
 
 27. 
 
 389.60 
 
 408.40 
 
 2.6111 
 
 Antimonious Chloride 
 
 Sb = Cl 3 
 
 7.8 
 
 112.70 
 
 114.20 
 
 2.0577 
 
 Triethyistibine 
 
 ( C 2 H 5 ) 3 =Sb 
 
 7.23 
 
 104.40 
 
 104.50 
 
 2.0191 
 
 Arsenic 
 
 AsMs 2 
 
 10.6 
 
 153.00 
 
 150.00 
 
 2.1761 
 
 Arseniuretted Hydrogen 
 
 H 3 =As 
 
 2.695 
 
 38.90 
 
 39.00 
 
 1.5911 
 
 Triethylarsine 
 
 (C 2 H,) 3 =As 
 
 5.29 
 
 76.35 
 
 81.00 
 
 1.9085 
 
 Kakodyl 
 
 (CH 3 ) 2 As-(CH 3 ) 2 As 
 
 7.10 
 
 102.50 
 
 105.00 
 
 2.0212 
 
 Arsenious Chloride 
 
 
 6.3 
 
 90.90 
 
 90.75 
 
 1.9578 
 
 Arsenious Iodide 
 
 As=I 3 
 
 16.1 
 
 232.40 
 
 228.00 
 
 2.3579 
 
 Bismuthous Chloride 
 
 Bi = Cl s 
 
 11.35 
 
 163.90 
 
 158.25 
 
 2.1994 
 
 Boric Methide 
 
 (CH 3 ) 3 =B 
 
 1.931 
 
 27.90 
 
 28.00 
 
 1.4472 
 
 Boric Ethide 
 
 (C 2 H S ) 3 ~=B 
 
 3.401 
 
 49.10 
 
 49.00 
 
 1.6902 
 
 Boric Fluoride 
 
 B=F 3 
 
 2.37 
 
 34.20 
 
 34.00 
 
 1.5315 
 
 Boric Chloride 
 
 
 3.942 
 
 56.85 
 
 58.75 
 
 1.7690 
 
 Boric Bromide 
 
 B=Br 3 
 
 8.78 
 
 126.80 
 
 125.50 
 
 2.0986 
 
 Methylic Borate 
 
 ( CH ) = O^=B 
 
 3.59 
 
 51.80 
 
 52.00 
 
 1.7160 
 
 Ethylic Borate 
 
 (C 2 H 5 ) 3 =6 3 =B 
 
 5.14 
 
 74.20 
 
 73.00 
 
 1.8633 
 
 Bromine 
 
 Bi-Br 
 
 5.54 
 
 79.50 
 
 80.00 
 
 1.9031 
 
 Hydrobromic Acid 
 
 H-Br 
 
 2.71 
 
 39.10 
 
 40.50 
 
 1.6075 
 
 Carbonic Tetrachloride 
 
 C=Cli 
 
 5.415 
 
 78.14 
 
 77.00 
 
 1.8865 
 
 Carbonic Oxydichloride 
 
 
 
 
 
 
 (Phosgene Gas) 
 
 C= O, C1 2 
 
 3.399 
 
 49.06 
 
 49.50 
 
 1.6946 
 
 Dicarbonic Hexachloride 
 
 
 8.157 
 
 117.70 
 
 118.50 
 
 2.0737 
 
 Dicarbonic Tetrachloride 
 
 [C=C] = Cl t 
 
 5.82 
 
 84.00 
 
 83.00 
 
 1.9191 
 
 Dicarbonic Dichloride 
 
 [C=C] = C1 2 
 
 
 
 47.50 
 
 1.6767' 
 
 Carbonic Oxide 
 
 c=o 
 
 0.967 
 
 13.95 
 
 14.00 
 
 1.1461 
 
 Carbonic Anhydride 
 
 C=O 2 
 
 1.529 
 
 22.06 
 
 22.00 
 
 13424 
 
 Carbonic Sulphide 
 
 C=S 2 
 
 2.645 
 
 38.17 
 
 38.00 
 
 1.5798 
 
 Chlorine 
 
 Cl-Cl 
 
 2.44 
 
 35.22 
 
 35.50 
 
 1.5502 
 
 Hydrochloric Acid 
 
 H-CI 
 
 1.27 
 
 18.32 
 
 18.25 
 
 1.2613 
 
 Chromic Oxychloride 
 
 [O,] = O 9 , C1 2 
 
 5.5 
 
 79.40 
 
 78.25 
 
 1.8935 
 
 Columbic Chloride 
 
 Cb | Cl r> 
 
 9.6 
 
 138.60 
 
 135.70 
 
 2.1326 
 
 Columbia Oxychloride 
 
 C%|O, C1 3 
 
 7.9 
 
 114.00 
 
 108.20 
 
 2.0342 
 
 Cyanogen 
 
 CN-CN 
 
 1.806 
 
 26.06 
 
 26.00 
 
 1.4150 
 
 Hydrocyanic Acid' 
 
 H-CN 
 
 0.947 
 
 13.67 
 
 13.50 
 
 1.1303 
 
 Ethyl 
 
 C<,H r -C*H 5 
 
 2.0 
 
 28.86 
 
 29.00 
 
 1.4624 
 
 Ethylic Chloride 
 
 (CvHrJ-Cl 
 
 2.219 
 
 32.02 
 
 32.25 
 
 1.5085 
 
 Ethylic Oxide (Ether) 
 
 (C 2 H 5 }^O 
 
 2.586 
 
 37.32 
 
 37.00 
 
 1.5G82 
 
 Ethylic Hydrate (Alcohol) 
 
 C 2 H r -O-H 
 
 1.613 
 
 23.28 
 
 23.00 
 
 13317 
 
TABLE III. (Continued.} 
 
 Names. 
 
 Symbols. 
 
 Air =1. 
 
 H-H=l. 
 
 Half 
 Molecular 
 Weight. 
 
 Loga- 
 rithms. 
 
 Ethylene (Olefiant Gas) 
 
 C 2 H 4 
 
 0.978 
 
 14.11 
 
 14.00 
 
 1.1461 
 
 " Chloride (Dutch Liq.) 
 
 (C 2 H 4 ) = C1 2 
 
 3.443 
 
 49.69 
 
 49.50 
 
 1.6946 
 
 Ethylene Oxide 
 
 (C z H i )=O 
 
 1.422 
 
 20.52 
 
 22.00 
 
 1.3424 
 
 Ethylene Hydrate (Glycol) 
 
 (C 2 H^O Z =H Z 
 
 
 
 31.00 
 
 1.4914 
 
 Ferric Chloride 
 
 [Fe 2 ]lC7 6 
 
 11.39 
 
 164.40 
 
 162.50 
 
 2.2108 
 
 Iodine 
 
 /-/ 
 
 8.716 
 
 125.90 
 
 127.00 
 
 2.1038 
 
 Hydriodic Acid 
 
 H-I 
 
 4.443 
 
 64.12 
 
 64.00 
 
 1.8062 
 
 Mercury 
 
 Hg 
 
 6.976 
 
 100.70 
 
 100.00 
 
 2.0000 
 
 Mercuric Ethide 
 
 ( C z Hfi) 2 =Hg 
 
 9.97 
 
 143.90 
 
 129.00 
 
 2.1106 
 
 Mercuric Methide 
 
 (CH^Hg 
 
 8.29 
 
 119.60 
 
 115.00 
 
 2.0607 
 
 Mercuric Chloride 
 
 Hg = Cl 2 
 
 9.8 
 
 141.50 
 
 135.50 
 
 2.1319 
 
 Mercuric Bromide 
 
 Hg-Br z 
 
 12.16 
 
 175.60 
 
 180.00 
 
 2.2553 
 
 Mercuric Iodide 
 
 Hg~-I 2 
 
 15.9 
 
 229.60 
 
 227.00 
 
 2.3560 
 
 Mercurous Chloride 
 
 [Hg 2 } = Cl z 
 
 8.21 
 
 118.50 
 
 235.50 
 
 2.3720 
 
 Nitrogen 
 
 N=N 
 
 0.971 
 
 14.00 
 
 14.00 
 
 1.1461 
 
 Ammonia 
 
 H^N 
 
 0.591 
 
 8.535 
 
 8.51 
 
 0.9294 
 
 Methylamine 
 
 JT 2 , ( CH 3 ) =N 
 
 1.08 
 
 15.59 
 
 15.50 
 
 1.1903 
 
 Aniline 
 
 H 2 ,(C 6 H 5 )=N 
 
 3.21 
 
 46.33 
 
 46.50 
 
 1.6675 
 
 Nitrous Oxide 
 
 N 2 O 
 
 1.527 
 
 22.04 
 
 22.00 
 
 1.3424 
 
 Nitric Oxide 
 
 NO 
 
 1.038 
 
 14.97 
 
 15.00 
 
 1.1761 
 
 Nitric Peroxide 
 
 NO 2 
 
 1.72 
 
 24.82 
 
 23.00 
 
 1.3617 
 
 Osmic Tetroxide 
 
 Os O t 
 
 8.89 
 
 128.30 
 
 131.60 
 
 2.1193 
 
 Oxygen 
 
 O = O 
 
 1.1056 
 
 15.95 
 
 16.00 
 
 1.2041 
 
 Aqueous Vapor 
 
 H 2 = 
 
 0.6235 
 
 8.998 
 
 9.00 
 
 0.9542 
 
 Phosphorus 
 
 P 2 fP 2 
 
 4.42 
 
 63.78 
 
 62.00 
 
 1.7924 
 
 Phosphuretted Hydrogen 
 
 H 3 =P 
 
 1.184 
 
 17.09 
 
 17.00 
 
 1.2304 
 
 Phosphorous Chloride 
 
 P=C1 3 
 
 4.742 
 
 68.44 
 
 68.75 
 
 1.8373 
 
 Phosphoric Oxychloride 
 
 PIO, C1 3 
 
 5.3 
 
 76.49 
 
 76.75 
 
 1.8851 
 
 Oxide of Triethylphosphine 
 
 ((C 2 H 5 ) 3 =P)=O 
 
 4.6 
 
 66.39 
 
 67.00 
 
 1.8261 
 
 Selenium, at 771 
 
 Se=Se 
 
 5.68 
 
 81.96 
 
 79.40 
 
 1.8998 
 
 Seleniuretted Hydrogen 
 
 H 2 =Se 
 
 2.795 
 
 40.33 
 
 40.70 
 
 1.6096 
 
 Silicic Methide 
 
 (CH 3 ) t =Si 
 
 3.083 
 
 44.49 
 
 44.00 
 
 1.6435 
 
 Silicic Ethide 
 
 ( C 2 H 3 )i=Si 
 
 5.13 
 
 74.03 
 
 72.00 
 
 1.8573 
 
 Silicic Fluoride 
 
 Si =F t 
 
 3.600 
 
 51.95 
 
 5200 
 
 1.7160 
 
 Silicic Chloride 
 
 Si = CZ 4 
 
 5.939 
 
 85.72 
 
 85.00 
 
 1.9294 
 
 Ethylic Silicate 
 
 (C 2 H 5 ) t = Ot=Si 
 
 7.32 
 
 105.60 
 
 104.00 
 
 1.0170 
 
 Stannic Ethide 
 
 (C 2 H 5 ) t =Sn 
 
 8.021 
 
 115.80 
 
 117.00 
 
 2.0682 
 
 Stannic Dimethylo-diethide 
 
 (CH 3 ) 2 ,(C,H,,)i=Sn 
 
 6.838 
 
 98.68 
 
 103.00 
 
 2.0128 
 
 Stannic Chloro-triethide 
 
 Cl, ( C 2 H^=Sn 
 
 8.430 
 
 121.70 
 
 120.20 
 
 2.0799 
 
 Stannic Dichloro-diethide 
 
 Ctfg, ( CvH^Sn 
 
 8.710 
 
 125.70 
 
 123.50 
 
 2.0917 
 
 Stannic Chloride 
 
 Sn = a t 
 
 9.199 
 
 132.70 
 
 130.00 
 
 2.1139 
 
 Sulphur above 860 
 
 s=s 
 
 2.23 
 
 32.18 
 
 32.00 
 
 15051 
 
 Sulphur at 450 
 
 SQ 
 
 6.617 
 
 95.50 
 
 96.00 
 
 1.9823 
 
 Sulphuretted Hydrogen 
 
 Hf8 
 
 1.191 
 
 17.19 
 
 17.00 
 
 1.2304 
 
 Sulphurous Anhydride 
 
 S=Oy 
 
 2.234 
 
 32.24 
 
 32.00 
 
 1.5051 
 
 Sulphuric Anhydride 
 
 S|O 3 
 
 2.763 
 
 39.87 
 
 40.00 
 
 1.6021 
 
 Tantalic Chloride 
 
 TaCl s 
 
 12.8 
 
 184.70 
 
 179.70 
 
 2.2546 
 
 Titanic Chloride 
 
 TiCl t 
 
 6.836 
 
 98.65 
 
 96.00 
 
 1.9823 
 
 Zinc Ethide 
 
 ( C 2 H 3 ) 2 =Zn 
 
 4.259 
 
 61.46 
 
 61.60 
 
 1.7896 
 
 Zirconic Chloride 
 
 ZrlC7 4 
 
 8.15 
 
 117.60 
 
 115.80 
 
 2.0637 
 
LOGARITHMS AND ANTILOGARITHMS. 
 
LOGARITHMS OF NUMBERS. 
 
 II 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 Proportional Parts. 
 
 
 
 j 
 
 6 7;8 9 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 '1 
 
 3 
 
 4 5 
 
 10 
 
 0000 0043 
 
 0086 0128 0170 
 
 0212 
 
 0253 
 
 0294 
 
 0334 
 
 0374 
 
 4 
 
 8 
 
 12 
 
 17 2 
 
 25 29 33 37 
 
 11 
 
 04140453 
 
 049205310569 
 
 0607 
 
 0645 0682 
 
 0719 
 
 0755 
 
 4 
 
 8 
 
 11 
 
 15[ 
 
 23 26 30 34 i 
 
 12 07920828 
 
 0864 0899 0934 
 
 0969 1004 
 
 1038 1072 
 
 1106 
 
 3 
 
 7 
 
 10 
 
 14 
 
 
 21 24 28 31 i 
 
 13 
 
 1139 
 
 1173 
 
 1206 
 
 1239 1271 
 
 1303 
 
 1335 
 
 1367 1399 
 
 1430 
 
 3 
 
 6 
 
 10 
 
 13 
 
 
 19 23 26 29 | 
 
 14 
 
 1461 
 
 1492 
 
 1523 
 
 1553 1584 
 
 1614 
 
 1644 
 
 1673 
 
 1703 
 
 1732 
 
 3 
 
 6 
 
 9 
 
 12 
 
 
 18 21 2- 
 
 27 
 
 15 
 
 1761 
 
 1790 
 
 1818 
 
 1847 
 
 1875 
 
 1903 
 
 1931 
 
 1959 
 
 1987 
 
 2014 
 
 3 6 
 
 8 
 
 11 
 
 
 17 20 22 25 j 
 
 16 
 
 2041 2068 
 
 2095 
 
 2122 214S 
 
 2175 
 
 2201 
 
 1227 
 
 2253 
 
 2279 
 
 3 5 
 
 8 
 
 11 
 
 
 16 18 21 24 
 
 17 
 
 2304 2330 
 
 2355 
 
 2380 2405 
 
 2430 
 
 2455 2480 
 
 2504 
 
 2529 
 
 2 5 
 
 7 
 
 10 
 
 
 15 17 20 22 
 
 18 
 
 2553 2577 
 
 2601 
 
 2625 2648 
 
 2672 
 
 26959718 
 
 2742 
 
 7765 
 
 2 5 
 
 7 
 
 9 
 
 
 14 16 1< 
 
 21 
 
 19 
 
 2788 2810 
 
 2833 
 
 2856 2878 
 
 2900 
 
 2923 
 
 2945 
 
 2967 
 
 2989 
 
 2: 4 
 
 7 
 
 9 
 
 
 13 16 18 20 ij 
 
 20 
 
 30103032 
 
 3054 
 
 30753096 
 
 3118 
 
 3139 
 
 3160 
 
 3181 
 
 3201 
 
 i 4 
 
 G 
 
 8 
 
 
 13 15 17 19 
 
 21 
 
 3222 3243 
 
 326332843304 
 
 3324 
 
 3345 3365 
 
 3385 
 
 3404 
 
 2 4 
 
 6 
 
 8 
 
 
 
 12 14 
 
 16 18 
 
 22 
 
 3424 3444 3464 
 
 3483 3502 
 
 3522 
 
 3541 
 
 3560 
 
 3579 
 
 3598 
 
 2 4 
 
 6 
 
 8 
 
 
 
 12 14 
 
 15 17 
 
 23 
 
 JJ617 
 
 3636 
 
 3655 3674,3692 
 
 3711 
 
 37293747 
 
 3766 
 
 3784 
 
 2 4 
 
 6 
 
 7 
 
 
 11 
 
 13 
 
 15 17 i 
 
 24 
 
 38023820 
 
 3838 3856 3874 
 
 3892 
 
 3909 3927 
 
 3945 
 
 3962 
 
 2 4 
 
 5 
 
 7 
 
 p 
 
 11 12! 14 16 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 25 
 
 3979:3997 
 
 4014 
 
 4031 4048 
 
 4065 
 
 4082 
 
 4099 
 
 4116 
 
 4133 
 
 2 3 
 
 5 
 
 
 f 
 
 10; 12 14 15 
 
 26 
 
 41504168 
 
 4183 
 
 42004216 
 
 4232 
 
 4249 4265 
 
 4281 
 
 4298 
 
 2 
 
 
 5 
 
 7 
 
 1 
 
 10 11 
 
 13 15 ; 
 
 27 
 
 4314 4330 
 
 4346 4362 4378 
 
 4393 
 
 4409 4425 
 
 4440 
 
 4456 
 
 2 3 
 
 5 
 
 i 
 
 | 
 
 9 11 13 14 
 
 28 
 
 4472 4487 4502 
 
 4518 4533 
 
 4548 
 
 4564 
 
 4579 
 
 4594 
 
 4609 
 
 2 3 
 
 5 
 
 6 
 
 | 
 
 9 11 12 14 
 
 29 
 
 46-24 4639 
 
 4654 
 
 4669 4683 
 
 4698 
 
 4713 
 
 4728 
 
 4742 
 
 4757 
 
 1 
 
 3 
 
 4 6 
 
 ~ 
 
 9 10 12 13 | 
 
 30 
 
 4771 4786 4800 4814 
 
 4829 
 
 4843 
 
 4857 
 
 4871 
 
 4886 
 
 4900 
 
 1 
 
 3 
 
 4 6 
 
 - 
 
 9 
 
 10 11 
 
 13 
 
 31 
 
 4914;49-28|4942 4955 
 
 4969 
 
 4983 
 
 4997 
 
 5011 
 
 5024 
 
 5038 
 
 1 
 
 3 
 
 4 6 
 
 - 
 
 8 
 
 10 11 
 
 19 
 
 32 
 
 5051 5065 '5079 5092 
 
 5105 
 
 5119 
 
 5132 
 
 5145 
 
 5159 
 
 5172 
 
 1 
 
 3 
 
 4 5 
 
 7 
 
 8 
 
 9 11 
 
 li 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 33 
 
 5185 '5198,5211 
 
 5224 
 
 5237 
 
 5250 
 
 5263 
 
 5276 
 
 5289 
 
 5302 
 
 1 
 
 3 
 
 4 5 
 
 6 
 
 8 
 
 9 10 
 
 if ri 
 
 34 
 
 5315 5328 ! 5340 
 
 5353 
 
 5366 
 
 5378 
 
 5391 
 
 5403 
 
 5416 
 
 5428 
 
 1 
 
 3 
 
 4 5 
 
 6 
 
 8 
 
 9 10 
 
 11 
 
 35 
 
 5441)5453 '5465 
 
 5478 5490 
 
 5502 
 
 5514 
 
 5527 
 
 5539 
 
 5551 
 
 1 
 
 2 
 
 4 ! 5 
 
 6 
 
 7 
 
 9 10 
 
 11 
 
 36 
 
 5563 5575 >587 5599 5611 
 
 5623 
 
 5635 
 
 5647 
 
 5658 
 
 5670 
 
 1 
 
 2 
 
 4 5 
 
 6 
 
 7 
 
 8 
 
 111 
 
 11 
 
 37 
 
 5682 5694 5705 5717 5729 
 
 5740 
 
 5752 
 
 5763 
 
 5775 
 
 5786 
 
 1 
 
 2 
 
 3 5 
 
 G 
 
 7 
 
 8 
 
 9 
 
 10 
 
 38 
 
 57985S095821 
 
 5832 5843 
 
 5855 
 
 5866 5877 
 
 5688 
 
 5899 
 
 1 
 
 2 
 
 3 5 
 
 G 
 
 7 
 
 8 
 
 9 
 
 10 
 
 39 
 
 5911 
 
 59-22 5933 5944 5955 
 
 5666 
 
 5977 
 
 5988 
 
 5999 
 
 6010 
 
 1 
 
 2 
 
 3 4 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 40 
 
 6021 6031 6042 6053 6064 
 
 6075 
 
 6085 
 
 6096 
 
 6107 
 
 6117 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 6 
 
 8 
 
 9 
 
 10 
 
 41 
 
 6128 6138 6149 6160 6170 
 
 6180 
 
 6191 
 
 1201 
 
 6212 
 
 6222 
 
 1 
 
 2 
 
 3 4 
 
 5 
 
 6 
 
 7 
 
 8| 9 
 
 42 
 
 6232 
 
 6243 6253 
 
 6263 6274 
 
 6-284 
 
 6294 
 
 6304 
 
 9314 6325 
 
 1 
 
 2 
 
 3; 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 43 
 
 6335 6345 6355 6365 6375 
 
 6385 
 
 6395 6405 
 
 6415 
 
 6425 
 
 1 
 
 2 
 
 3 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 44 
 
 G435 6444 '6454 
 
 6464 6474 
 
 6484 
 
 6493 6503 
 
 6513 
 
 6522 
 
 j 
 
 2 
 
 3 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 45 
 
 6532654-26551 
 
 6561 6571 
 
 6580 
 
 6590 6599 
 
 6609 
 
 6618 
 
 1 
 
 2 
 
 3 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 g 
 
 46 
 
 66-28 6637 6646 6656 6665 
 
 6675 6684 
 
 6693 
 
 6702 
 
 6712 
 
 1 
 
 2 
 
 3 4 
 
 5 
 
 6 
 
 7 
 
 7 
 
 8 
 
 47 
 
 67-21 6730 6739 6749'e758 
 
 6767 
 
 6776 6785 
 
 6794 
 
 6803 
 
 1 
 
 9 
 
 3 4 
 
 5 
 
 5 
 
 G 
 
 7 
 
 8 
 
 48 
 
 6812 6821 ! 6830 6839 6848 
 
 6857 
 
 68666875 
 
 6884 
 
 6893 
 
 1 
 
 2 
 
 3 4 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 49 
 
 690-2 6911 6920 
 
 69286937 
 
 6946 
 
 6955 
 
 6964 
 
 6972 
 
 6981 
 
 1 
 
 2 
 
 3 4 
 
 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 | 50 
 
 699069987007 
 
 7016 7024 
 
 7033 
 
 7042 
 
 7050 
 
 7059 
 
 7067 
 
 1 
 
 2 
 
 3 3 
 
 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 51 
 
 7076 7084 7093 7101 
 
 7110 
 
 7118 
 
 71267135 
 
 7143 
 
 7152 
 
 1 
 
 2 
 
 3 3 
 
 4 
 
 5 
 
 G 
 
 7 
 
 8 
 
 52 
 
 7160 7168 3177 
 
 7185 
 
 7193 
 
 7202 
 
 7210 7218 
 
 7226 
 
 7235 
 
 1 
 
 2 
 
 2 3 
 
 4 
 
 5 
 
 G 
 
 7 
 
 7 
 
 53 
 
 724372517259 
 
 7267 
 
 7275 
 
 7284 
 
 729-2 7300 
 
 7308 
 
 7316 
 
 1 
 
 2 
 
 2 3 
 
 4 
 
 6 
 
 6 
 
 G 
 
 7 
 
 54 
 
 i' 
 
 73-24 7332 7340,734817356 
 
 7364 
 
 737-27380 
 
 7388 
 
 7396 
 
 1 
 
 2 
 
 2 3 
 
 4 
 
 5 
 
 6 6 
 
 7 
 
LOGARITHMS OF NUMBERS. 
 
 11 
 
 I 
 
 55 
 
 
 
 1 
 
 7412 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 7459 
 
 8 
 
 9 
 
 7474 
 
 Proportional Parts. 
 
 I 
 
 2 
 
 3 4)5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 7404 
 
 7419 
 
 7427 
 
 7435 
 
 7443 
 
 7451 
 
 7466 
 
 
 2 3 
 
 
 5 
 
 5! 6 
 
 7 
 
 56 74827490 
 
 7497 
 
 7505 7513 
 
 7520 
 
 7528 
 
 7536 
 
 7543 
 
 7551 
 
 i 
 
 2 i 
 
 
 5 
 
 6 6 
 
 * t 
 
 57 755975667574 
 58 7634 7642 7649 
 59 7709! 7716 7723 
 
 7582 
 7657 
 7731 
 
 7589 
 7664 
 6738 
 
 7597 
 7672 
 7745 
 
 7604 
 7679 
 7752 
 
 7612 
 7686 
 7760 
 
 7619 
 7694 
 7767 
 
 7627 
 7701 
 
 7774 
 
 i 
 
 i! 
 i 
 
 2 3 
 
 2 3 
 2 3 
 
 
 5 
 
 4 
 
 4 
 
 5 6 
 5 6 
 5 6 
 
 r 
 
 60 7782 
 61 S 7853 
 
 7789 
 7860 
 
 7796 
 
 7868 
 
 7803 
 
 7875 
 
 7810 
 
 7882 
 
 7818 
 7889 
 
 7825 
 7896 
 
 7832 
 7903 
 
 7839 
 7910 
 
 7846 
 7917 
 
 ) 
 
 
 2 3 
 2 3 
 
 
 4 
 4 
 
 5 6 
 
 5 
 
 6 
 6 
 
 62 7924 
 
 7931 7938 7945 
 
 7952 
 
 7959 
 
 7966 
 
 7973 
 
 7980 
 
 8987 
 
 i 
 
 2 
 
 
 
 4 
 
 6 
 
 6 
 
 63 < 7993 
 
 8000 8007 
 
 8014 
 
 8021 
 
 8028 
 
 8035 
 
 8041 
 
 8048 
 
 8055 
 
 i 
 
 2 3 
 
 
 4 
 
 5 
 
 
 6 
 
 64 8062 
 
 8069 8075 
 
 8082 
 
 8089 
 
 8096 
 
 8102 
 
 8109 
 
 8116 
 
 8122 
 
 i 
 
 2 
 
 
 4 
 
 5 
 
 6 
 
 65 8129 
 
 8136 8142 
 
 8149 8156 
 
 8162 
 
 8169 
 
 8176 
 
 8182 
 
 8189 
 
 i 
 
 
 2 3 
 
 
 4 
 
 5 
 
 6 
 
 66 8195 
 67 8261 
 
 8202 8209 8215 8222 
 
 8267827482808287 
 
 8228 
 8293 
 
 8235 
 8299 
 
 8241 
 8306 
 
 8248 
 8312 
 
 8254 
 8319 
 
 i 
 i 
 
 
 2 3 
 2 
 
 
 4 
 4 
 
 5 
 5 
 
 6 
 6 
 
 68 8325 
 
 8331 8338 8344 8351 
 
 8357 
 
 8363 
 
 9370 
 
 8376 
 
 8382 
 
 i 
 
 
 2 3 
 
 
 4 
 
 4 o 
 
 6 
 
 69 S388 
 
 8395 8401 
 
 8407 8414 
 
 8420 
 
 8426 
 
 8432 
 
 8439 
 
 8445 
 
 i 
 
 
 2 2 
 
 
 4 
 
 4 
 
 6 
 
 70 8451 
 
 8457 8463 
 
 8470 
 
 8476 
 
 8482 
 
 8488 
 
 8494 
 
 8500 
 
 8506 
 
 i 
 
 
 2 
 
 
 
 4 
 
 4 
 
 6 
 
 71 8513 
 
 8519 8525 
 
 8531 
 
 8537 
 
 8543 
 
 8549 
 
 8555 
 
 8561 
 
 8567 
 
 i 
 
 
 2 
 
 
 
 4 
 
 
 
 5 
 
 72 8573 
 
 8579 8585 
 
 8591 
 
 8597 
 
 8603 
 
 86098615 
 
 8621 
 
 8627 
 
 i 
 
 
 2 2 
 
 
 4 
 
 
 
 5 
 
 73 8633 
 
 8639 8645 
 
 8651 
 
 8657 
 
 8663 
 
 8669 
 
 8675 
 
 8681 
 
 8686 
 
 i 
 
 
 
 
 
 4 
 
 
 
 5 
 
 74 8692 
 
 8698 
 
 8704 
 
 8710 
 
 8716 
 
 8722 
 
 8727 
 
 8733 
 
 8739 
 
 8745 
 
 i 
 
 
 
 
 
 4 
 
 
 
 5 
 
 75 8751 
 
 8756 
 
 8762 
 
 8768 
 
 8774 
 
 8779 
 
 8785 
 
 8791 
 
 8797 
 
 8802 
 
 i 
 
 
 
 
 
 a 
 
 
 
 5 
 
 76 8808 
 77 8865 
 
 8814 
 8871 
 
 8820 
 8876 
 
 8825 
 8882 
 
 8831 
 8887 
 
 8837 
 8893 
 
 8842 
 8899 
 
 8848 
 8904 
 
 8854 
 8910 
 
 8859 
 8915 
 
 i 
 i 
 
 
 
 
 
 3 
 
 3 
 
 
 
 5 
 
 78 8921 
 
 8927 
 
 8932 
 
 8938 
 
 8943 
 
 8949 
 
 8954 
 
 8960 
 
 8965 
 
 8971 
 
 i 
 
 
 
 2 
 
 
 3 
 
 
 4 
 
 5 
 
 79 8976 
 
 8982 
 
 8987 
 
 8993 
 
 8998 
 
 9004 
 
 9009 
 
 9015 
 
 9020 
 
 9025 
 
 i 
 
 
 2 
 
 2 
 
 
 a 
 
 
 
 5 
 
 80 9031 
 
 9036 
 
 6042 
 
 9047 
 
 9053 
 
 9058 
 
 9063 
 
 9069 
 
 9074 
 
 9079 
 
 i 
 
 
 
 
 2 
 
 
 
 
 
 4 
 
 5 
 
 81 
 82 
 83 
 84 
 
 85 
 86 
 87 
 88 
 89 
 
 9085 9090 
 9138 9143 
 9191 9196 
 92439248 
 
 92949299 
 9345:9350 
 9395,9400 
 94459450 
 94949499 
 
 9096 
 9149 
 9201 
 9253 
 
 9304 
 9355 
 9405 
 9455 
 9504 
 
 9101 
 9154 
 9206 
 9258 
 
 9309 
 9360 
 9410 
 9460 
 9509 
 
 9106 
 9159 
 9212 
 9263 
 
 9315 
 9465 
 9415 
 9465 
 9513 
 
 9112 
 9165 
 9217 
 9269 
 
 9320 
 9370 
 9420 
 9469 
 9518 
 
 9117 
 9170 
 9222 
 9274 
 
 9325 
 9375 
 9325 
 9474 
 9523 
 
 9122 
 9175 
 9227 
 9279 
 
 9330 
 9380 
 9430 
 9479 
 9528 
 
 9128 
 9180 
 9232 
 9384 
 
 9335 
 9385 
 9435 
 9484 
 9533 
 
 9133 
 9186 
 9238 
 9289 
 
 9340 
 9390 
 9440 
 9489 
 9538 
 
 i 
 
 i 
 i 
 
 i 
 i 
 
 
 
 
 
 
 2 
 
 2 
 
 
 3 
 3 
 
 4 
 
 
 
 5 
 5 
 5 
 5 
 
 5 
 
 5 
 4 
 4 
 4 
 
 i 
 
 2 
 
 3 
 
 3 
 
 4 
 
 4 
 
 1 
 
 
 cy 
 
 
 
 
 
 
 2 
 
 2 
 
 3 
 3 
 3 
 
 <- 
 
 4 
 
 4 
 4 
 
 90 
 91 
 92 
 93 
 
 954219547 
 9590 9595 
 96389843 
 
 96859689 
 
 9552 
 9600 
 9647 
 9694 
 
 9557 
 9605 
 9652 
 9699 
 
 9562 
 9609 
 9657 
 9703 
 
 9566 
 9614 
 9661 
 9708 
 
 9571 
 9619 
 9666 
 9713 
 
 9576 
 9624 
 9671 
 9717 
 
 9581 
 9628 
 9675 
 9722 
 
 9586 
 9633 
 9680 
 9727 
 
 
 
 
 
 o 
 
 
 
 2 
 2 
 2 
 9 
 
 2 
 
 a 
 
 3 3 
 3 3 
 3 3 
 3 3 
 
 4 
 4 
 4 
 4 
 
 4 
 4 
 4 
 4 
 
 94 
 95 
 
 9731 9736 
 9777 9782 
 
 9741 9745 
 9786 9791 
 
 9750 
 9795 
 
 9754 
 9800 
 
 9759 
 9805 
 
 9763 
 9809 
 
 9768 
 9814 
 
 773 
 
 818 
 
 o 1 
 
 
 
 
 
 2 
 2 
 
 2 
 2 
 
 3 3 
 3 3 
 
 4 
 4 
 
 4 
 4 
 
 96 
 
 9823 9827 
 
 9832 
 
 9836 
 
 9841 
 
 9845 9850 
 
 9854 
 
 9859 
 
 863 
 
 
 
 
 
 2 
 
 2 
 
 3 3 
 
 4 
 
 4 
 
 97 
 
 9868 9872 
 
 9877 
 
 9881 
 
 9886 
 
 9890 9894 
 
 9899 
 
 9903 
 
 908 
 
 
 
 
 
 2 
 
 2 
 
 3 3 
 
 4 
 
 4 
 
 98 
 
 9912'9917 
 
 9921 9926 9930 
 
 9934 9939 
 
 9943 
 
 9948 
 
 952 
 
 
 
 
 
 2 
 
 2 
 
 3 3 
 
 4 
 
 4 
 
 99 
 
 9956 9961 9965 9969 9974 
 
 9978 9983 
 
 9987 
 
 9991 
 
 996 
 
 o 
 
 
 2 
 
 2 
 
 3 3 
 
 3 4 
 
ANTILOGARITHMS. 
 
 41 
 
 
 
 
 
 
 
 
 
 
 Proportional Parts, 
 
 "56 
 
 
 
 < 
 
 
 4 
 
 
 
 
 
 9 1. 
 
 
 
 
 
 I 
 
 
 M- C 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 3 4 
 
 5 
 
 6 
 
 f 
 
 s 
 
 9 
 
 .00 
 
 000 
 
 1002 
 
 1005 
 
 1007 
 
 1009 
 
 1012 
 
 014 
 
 1016 
 
 1019 
 
 1021 |0 
 
 
 
 i i 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 .01 
 
 023 
 
 1026 
 
 1028 
 
 1030 
 
 1033 
 
 1035 
 
 038 
 
 1040 
 
 1042 
 
 10451 
 
 
 
 i i 
 
 
 i 
 
 2 
 
 2 
 
 2 
 
 .02 
 
 1047 
 
 1050 
 
 1052 
 
 1054 
 
 1057 
 
 1059 
 
 1062 
 
 1064 
 
 1067 
 
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 9661 96839705 
 
 9727 
 
 9750 
 
 2 
 
 4 
 
 7 
 
 9 
 
 11 
 
 13 
 
 16 
 
 18 
 
 20 
 
 .99 
 
 9772 9795|9817 9840 9863 
 
 9886 '9908 9931 
 
 9954 
 
 9977 
 
 o 
 
 5 
 
 7 
 
 9 
 
 11 
 
 14 
 
 ie|i8 
 
 20 
 
CONSTANT LOGARITHMS. 
 
 Loga- Ar. Co. 
 
 rithms. Log. 
 
 Circumf. of circle when R = 1, (| = 1.5708) 0.1961 9.8039 
 
 " " " " D = 1, (re = 3.1416) 0.4971 9.5028 
 
 Area of circle when 1P=1, (n = 3.1416) 0.4971 9.5028 
 
 " " " " 1)2=1, (J = 0.7854) 9.8951 0.1049 
 
 " " " " C*= 1, Q^ = 0.0796) 8.9008 1.0992 
 
 Surface of sphere when .R 2 = 1, (4^=12.5664) 1.0992 8.9008 
 
 " " " Z> 2 =1, (TT = 3.1416) 0.4971 9.5028 
 
 " "' " " C*=l, (-^ = 0.3183) 9.5028 0.4971 
 
 Solidity of sphere when R 3 = 1, (|?r= 4.1888) 0.6221 9.3779 
 
 " " " 1> 3 = 1, (~ = 0.5236) 9.7190 0.2810 
 
 " " " " C 3 =l, (g^= 0.0169) 8.2275 1.7724 
 
 Weight of one litre of Hydrogen (0.0896 grammes) 8.9522 1.0478 
 
 Air (1.293 " ) 0.1116 9.8884 
 
 (14.43 criths ) 1.1594 8.8406 
 
 Per cent of Oxygen in air by weight (0.2318) 9.3651 0.6349 
 
 " " "Nitrogen" " " (0.7682) 9.8855 0.1145 
 
 Mean height of Barometer (76 c. m.) 1.8808 8.1192 
 
 Coefficient of expansion of Air (0.00366) 7.5635 2.4365 
 
 Latent Heat of Water (79) 1.8976 8.1024 
 
 " " Free Steam (537) 2.7300 7.2700 
 
 To reduce 0p.(J$r. to S P- Gr., or reverse, add to log. 1.1594 or 8.8406 
 
 " " Sp. Gr. toSp.Gr.," " " " " 6.9522 or 3.0478 
 
 0p.<5r. to Sp. Gr., " " " " " 7.1 116 or 2.8884 
 
 grammes to criths, " " " "" 1.0478 or 8.9522 
 
 " " 
 
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