ENGINEER DEPARTMENT, U. S. ARMY. 
 
 ON THE USE OF THE BAROMETER 
 
 ON 
 
 SURVEYS AND RECONNAISSANCES. 
 
 A Compendium, without Plates, of No. 15 
 
 PROFESSIONAL PAPERS OF THE CORPS OF ENGINEERS. 
 
 LIEUT. OOL. E. S. WILLIAMSON, 
 
 CORPS OF ENGINKERS, U. S. A. 
 
 WASHINGTON: 
 
 GOVERNMENT PRINTING OFFICE, 
 
 1878. 
 
ENGINEER DEPARTMENT, U. S. ARMY. 
 
 ON THE USE OF THE BAROilETER 
 
 ox 
 
 SURVEYS AND RECOx\NAISSAXCES, 
 
 IV BEIXG 
 
 A Compendium, without Plates, of No. 15 
 
 OF THE 
 
 PROFESSIONAL PAPERS OF THE CORPS OF ExNGINEERS. 
 
 LIEUT. COL. E. S. WILLIAMSON, 
 
 CORPS OF ENGINEERS, U. S. A. 
 
 WASHINGTON: 
 
 GOVERNMENT PRINTING OFFICE. 
 
 1878. 
 
■N b \ 
 
 i 
 
Offioe of the Chief of Engineers, 
 
 Washington, D. C, August 7, 1878. 
 Sir : Lieut. Col. R, S. Williamson, Corps of Engineers, 
 has submitted to this ofBce a compendium (without plates) 
 of his paper "On the use of the Barometer," &c., Professional 
 Papers, Corps of Engineers, Xo. 15. 
 
 This condensed work contains most of the information to 
 be found in the larger one, with a few tables which are new, 
 the result of further investigation of the subject. 
 
 As this compendium will be very useful and convenient 
 to officers conducting barometric reconnaissances, I have the 
 honor to recommend that it be printed at the Government 
 Printing Ot3ace, and copies furnished upon the usual requi- 
 sition. 
 
 Very respectfully, your obedient servant, 
 
 H. G. Wright, 
 Acting Chief of Engineers. 
 Hon. Geo. W. McCrary, 
 Secretary of War. 
 
 Approved. 
 
 By order of the Secretary of War. 
 
 H. T. Crosby, 
 
 Chief Cleric. 
 War Department, 
 August 10, 1878. 
 
 382800 
 
San Francisco, Cal., 
 
 Ajiril 30th, 1878. 
 General: 1 have the bonor to submit for your consid- 
 eration a condensed copy of my work on meteorology and 
 hypsometry, thinking that a small volume of this kind can 
 easily be carried in the field and be usefully employed there, 
 while the original work with its plates is not in a conven- 
 ent form for that purpose. This little work contains most 
 of the information to be found in the larger one, but 1 have 
 added a few tables which are new, the result of further in- 
 vestigation of the subject. 
 
 In the concluding remarks I have compared the methods 
 of treating meteorological observations with that of Prof. J. 
 D. Whitney as described in his work entitled "Contributions 
 to Barometric Hypsometry,'' and have shown conclusively 
 that there are over forty per cent, more of maximum and 
 mean errors by his method than by mine. 
 
 Very respectfully, your obedient servant, 
 
 R. S. Williamson, 
 Lieutenant Colonel of Engineers. 
 Brig. Gen. A. A. Humphreys, 
 
 Chief of Engineers, U. S. A. 
 

TABLE OF CONTENTS. 
 
 Page. 
 Introduction 11 
 
 Instruments and methods for determining altitudes — The mei- 
 curial and aneroid barometers compared — The barometric 
 formula — The scales in plotting observations. 
 
 Horary and abnormal oscillation 15 
 
 Their periods — Horary corrections — Reduction to level — Re- 
 duction to second level — Rules — Observations — Hourly and 
 at intervals compared — Effect of season, altitude, and lati- 
 tude on horary oscillation — Law of oscillation. 
 
 Variation op temperature 30 
 
 Comparison of barometric and thermometric oscillations — 
 Elimination of effects of temperature — Mean daily temper- 
 ature — Comparisons. 
 
 Hypsometrical results from daily means 38 
 
 Hypsometrical results from monthly mkans 43 
 
 Concluding remarks 45 
 
 Professor J. D. Whitney's method — Comparison of Whitney's 
 and Williamson's methods. 
 
i 
 
LIST OF TABLES 
 
 Page. 
 
 Tahle I. — Showin^j; the (liti'.'reiice between the menu baroiuetric 
 pressure iu the ditferent months as obtained from the mean 
 of 24 hourly observations, and observations at 7 a. m., 2 p. m., 
 and 9 p. m., the former being assumed as the standard 22 
 
 Taiu,e II. — Showing the diftereuce between the daily mean baro- 
 metric pressure as obtained from the mean of 24 hourly obser- 
 vations, and from corrected observations at 7 a. m., 2 p. m., 
 9 p. m., and 7 a. m. the next morning; and also between the 
 first and those obtained from observations at 7 a. m., 2 p. m., 
 and 9 p. m., the first being assumed as the standard 25 
 
 Table III. — Showing the difference between the monthly mean 
 barometric pressure as computed from observations at 7 a. m., 
 2 p. m., and 9 p. m., and 6 a. m., noon, and 6 p. ra., the former 
 being ijsed as a standard 27 
 
 Taijle IV. — Showing the difference between the niaan tempera- 
 ture in the different months as obtained from the mean of 24 
 hourly observations, and those taken at 7 a. m., 2 p. m., and 
 9 p. m., the former being assumed as the standard 35 
 
 Table V. — Showing the difference between the monthly mean 
 temperatures as computed from observations at 7 a. m., 2 p. 
 m., and 9 p. m., and 6 a. m., noon, and 6 p. m., the former be- 
 ing used as a standard 37 
 
 Table VI. — Consolidated table of maximum errors in computing 
 differences of altitude from daily barometric and thermo- 
 metr ic means 41 
 
 Table VII. — Consolidated table of mean errors in computing dif- 
 ferences of altitude from daily barometric aud thermometric 42 
 means 
 
 Table VIII. — Comparison of barometric results by Professor Whit- 
 ney's and Colonel Williamson's methods, from observations 
 taken at 7 a. m., 2 p. m., and 9 p. m., during W days of Au- 
 onst, 1860 49 
 
INTRODUCTION, 
 
 To the large number of engineers, surveyors, and others, 
 who are and will be engaged in developing the geography 
 of this country, so large a portion of which is almost un- 
 known or but partially explored, the best method of treating 
 observations of the barometer and thermometer, so as to 
 obtain the most reliable results in determining diiferences 
 of altitude, is a matter of the first importance. It is well 
 known that the mercurial cistern barometer is the best in- 
 strument for that purpose, for the reason that the spirit- 
 level is out of the question, except within very limited areas, 
 the length of time and amount of labor required for its 
 proper use being far greater than can be devoted to the 
 determination of the vertical element on an ordinary sur- 
 vey. The only instrument, that can be mentioned as at all 
 to be compared with the cistern-barometer is the handy 
 aneroid, the defects of which, however, as compared with 
 the mercurial instrument, are so great as to preclude its 
 being used as a substitute for the latter. Besides the fact 
 that the aneroid is not susceptible of reading closer than 
 one hundredth of an inch, while the mercurial cistern can be 
 read to one-thousandth, the great defect that it is liable at 
 any time to change its zero, particularly in travelling, with- 
 out there being any evidence to show that a change has 
 occurred, makes the instrument entirely unreliable on a 
 survey of any extent. The mercurial cistern barometer is, 
 then, the only instrument that can be used with any satisfac- 
 tion for hypsometrical purposes, and the following few pages 
 will be devoted to show the best method of using it with its 
 accompanying open air thermometer. 
 
12 
 
 I may remark, in tLe first place, tliat whenever tbe read- 
 ings of tbe barometer are referred to in tbe following pages, 
 those of the barometer reduced to 32° Fahrenheit are meant. 
 In the barometric formula of Laplace and others, a term has 
 been introduced to take into account tbe effect of tbe ex- 
 pansion and contraction of tbe mercurial column by beat, 
 in order to reduce tbe readings to what they would have 
 been had tbe temperature of the instrument been always at 
 the freezing point. But it is equally accurate and much 
 more couvenient to reduce each reading in the first i)lace 
 to the freezing point by tbe tables which have been pre- 
 pared for the purpose. By adopting this course, the column 
 so reduced, when plotted, shows the movements of a natural 
 atmosphere, and their peculiarities can be studied with 
 advantage ; whereas tbe readings of the barometer not so 
 reduced give so irregular a curve, the movements being 
 masked by tbe ever-varying temi)erature of the instrument, 
 that it is scarcely possible to discover any law guiding them, 
 if such a law exists. 
 
 1 also wish to point out that, unless special mention is 
 made to tbe contrary, tbe formula used in tbe computations 
 is the one found in Professional Papers of the Corps of 
 Engineers, No. 15, only omitting the special correction for 
 the moisture in tbe atmosphere. It is a translation of tbe 
 formula of Plantamour. This formula differs from the one 
 prepared by Guyot for the Smithsonian Institution, which 
 is, in fact, the formula of Lai)lace, by a very small change 
 in the barometric constant. Plantamour adopts the num- 
 ber 00,384.3, while Guyot gives 60,lo8.G. This slight change 
 causes the dittereuce of altitude to be greater by the former 
 formula than by the latter by a little less than four feet for 
 each thousand feet of difference of altitude. 
 
 1 shall freqaenrly have occasion to refer to the graphic 
 representation of meteorological observations, which opera- 
 tion is called plotting. In order to represent the various 
 
/ 
 
 13 
 
 movemeuts of the atmosphere graphically, and in such a 
 I ^ way that the value of the changes can be measured, it is 
 
 necessary to attach scales to the drawings. In all cases to 
 which I shall refer, the vertical scale is either a scale of 
 inches of the barometric column, or of degrees of the ther- 
 mometer. The horizontal scale is a scale of hours, or days, 
 or mouth, as the case may be. But as I do not propose to 
 illustrate this paper by such drawings, I shall endeavor to 
 give my descriptions in such a way that my reuiarks will be 
 easilv understood without them. 
 
OF THE HORARY AND AUXORMAL OSCILLATIONS OF 
 THE BAROMETER, 
 
 A study of barotnetriu observations, extended over a 
 sufficient period of time, will reveal the existence of two dis- 
 tinct oscillations. These Ijave been called respectivelj' the 
 horary and abnormal oscillations. The horary oscillation 
 lias a period of 24 hours. Within this period it presents, 
 except during barometric storms, two distinct maxima 
 and two minima, easily recognizable. The abnormal oscil- 
 lation, on the other hand, is the result of a steady progress- 
 ive movement of variable period, but usually it passes from 
 one maximum to one minimum in from three to six days. 
 
 When a series of hourly observations of the barometer, 
 taken during ten or more days, is plotted, there appears dur- 
 ing each day a regular movement, more or less marked, and 
 indicating two maxima and two minima in the twenty-four 
 hours. If a table is made by taking separately the mean of 
 the observations at the same hour of each day, thus obtain- 
 ing twenty-four mean readings when the observations are 
 taken hourly and uninterruptedly, and this mean table is 
 plotted, the mean curve so developed shows this double os- 
 cillation very decidedly. If we were to make a grand meau 
 by adding up the twenty-four mean hourly results, and 
 dividing by twenty-four, and if we then subtract each mean 
 result from the grand meau, we have a table in which some 
 of the numbers would be greater and some less than the 
 grand mean, and therefore some would be affected with a 
 
16 
 
 plus and some with a minus sign. This table can be used 
 as a table of corrections, to be ap[»lied to the mean results at 
 each hour separately, in order to reduce each reading to the 
 mean value. This table would represent approximately a 
 true table of horary corrections, but only approximately, un- 
 less the readings of the barometer at the beginning and end 
 of the series happen to be the same, as will become appa- 
 rent further on. Finally, if we api)ly these corrections to 
 the original observations, we Mill have what has been called 
 the "observations reduced." These, when plotted, show a 
 wave-like movement in wjjich uo trace, or but a very slight 
 trace, of the double horary oscillation api)ears. This curve 
 represents very nearly the abnormal osciHation. 
 
 It is very apparent, from the study of such curves plotte<l 
 from observations reduced to 32^ Fahrenheit, that there are 
 two separate forces in .u-tion, one j^roducing an oscillation 
 of regular period, and the otlier an irregular but slowly pro- 
 gressing movement of variable i)eriod. It is apparent, also, 
 that during any twenty four hours, tlie forces being in ac- 
 tion together, the horaiy oscilhition will appear more or less 
 distorted or masked by the action of the abnormal move- 
 ment. But inasmuch as the portion of the abnormal move- 
 ment during one day often shows approximately a uniform 
 rise or fall, the two coexisting movements can be easily sepa- 
 rated. Let us suppose that the barometer during the day 
 had been rising, and that it read two hundred and forty 
 thousandths higher at the end of the day than at tlie be- 
 ginning. If the abnormal oscillation during that day had 
 been such that it could be represented by a right line, then 
 that portion of the movement due to it would show a uni- 
 form vise for each hour. In the case I am sui)[)osing, the 
 rise in one hour would be ten thousandths of an inch ; 
 in the first two hours twenty thousandths, etc. Now, if we 
 were to apply a correction of ten thousandths to the reading 
 of the barometer at one hour after the initial hour, one of 
 
17 
 
 twenty tbousandtbs to that at two liours after the initial 
 hour, etc., the table so resulting would be one representing 
 the movement of the barometer freed (entirely iu this case) 
 from the effects of the abnormal movement. 
 
 But it is very rare that the abnormal movement during 
 the twenty-four hours can be represented strictly by a right 
 line. It is usually, when plotted, more or less curved, being 
 a section of a sweeping curve which requires several days 
 to pass from its maximum to its minimum. Moreover, if it 
 so happens that the time when the abnormal wave reaches 
 its maximum or its minimum iu the middle of the day, 
 a portion of that wave must be deeply concave and the 
 remaining portion convex, and during that day the plotted 
 observations, which represent the combination of the two 
 movements, will show an irregular line different from the 
 normal horary curve, though traces of that will probably be 
 apparent. But it is exceedingly probable that during a se- 
 ries of ten days another day will be found in which a similar 
 movement of the abnormal oscillation will occur, but of such 
 a character that a portion of it will show a concave curve 
 when the observations during a similar portion of the other 
 day showed a convex one, and that the reverse will occur 
 during the remaining portions of those two days. That is 
 to say, the abnormal line will be a convex curve during one 
 day and a concave one during the other. The combination 
 of the observations during two such days would produce a 
 curve approaching to a right line. It has been found from 
 experience that observation s taken for ten days, when treated 
 in this way, generally jiroduce a truthful and characteristic 
 curve. 
 
 This method of treating observations, thereby eliminating 
 the abnormal movements, has been called the "reduction to 
 level." The difference between the reading of the barom- 
 eter at the initial hour of two consecutive days is evidently 
 the correction to level for twenty-four hours, which must be 
 2 u B 
 
called minus when the barometer during the day bas beeu 
 rising, and plus in the reverse case, and the one twenty- 
 fourth part of that is the correction to level for one hour. 
 The correction to level for two hours is twice that for one 
 hour, etc. When the correction to level for twenty-four 
 hours is a multiple of twenty-four, the correction for each 
 hour can be written down without difficulty, but when that 
 is not the case it requires a little calculation to show at what 
 hours the additions or subtractions shall be made. For 
 example, if the correction to level for one hour were three- 
 thousandths of an inch, the correction for the succeeding 
 hours would be G, 9, 12, etc., thousandths ; but if it were a 
 whole number of thousandths and a fraction, as, for 
 example, three and fifteen twenty-fourths, as all the frac- 
 tions less than half are to be thrown away, and all greater 
 than half are to increase the whole number by one, we 
 should have 4, 7, 11, 11, 18, 22, 25, etc., for the number 
 of thousandths to be added or subtracted at 8, 9, 10, 11, 
 12, 1, 2, etc., hours, the barometric day beginning at 7 a. m. 
 Table B of Professional Papers of the Corps of Engineers, 
 No. 15, is intended to facilitate the calculations of the reduc- 
 tion to level by showing at what hours .001 is to be added 
 on account of the fractional part of the correction for one 
 hour. This table I have found convenient, but it is so sim- 
 ple of construction that any one can make it in a few min- 
 utes. 
 
 AVheu the observations reduced to level are continued 
 during several days, and are plotted, they show a series of 
 curves occupying different parts of the paper, because the 
 observ^ations at the initial hour on different days will be 
 different. "When it is desirable, as is often the case in prac- 
 tice, to place them as nearly as possible in a horizontal row, 
 it is best to subtract from each observation so reduced a cer- 
 tain number, which is the same for all the hours of one day, 
 but ditiers in ditlterent days, so as to make the observations 
 
19 
 
 at 7 a. in. all alike. This secoud reduction, called " the reduc- 
 tion to second level," does not change in the slightest degree 
 the character of the oscillation, but simply has the effect 
 that, when i)lotted, the curves are found in a convenient 
 part of the paper. It has been found best to adopt such a 
 subtrahend for each day as will make the observations at 7 
 a. m. a little less than any one in the series. In California 
 29.500 is usually used near the sea-level, as the barometer 
 seldom falls as low as that. 
 
 The following may then be given as a rule for obtaining 
 a table of horary corrections of the barometer and one of 
 the abnormal oscillations freed from the horary movement: 
 
 The observations (reduced to 32° F.) are to be copied in 
 such a way that all at the same hour shall be placed in the 
 same vertical column. 
 
 Each vertical column is to be added up and divided by 
 the number of days in the series. 
 
 If hourly observations during the series are continuous, 
 the grand mean is to be obtained by adding up the twenty- 
 four mean results at each hour, and dividing the sum by 
 twenty-four. If observations are not taken during the uighi 
 hours, then an approximate grand mean is to be obtained 
 by taking the mean of the observations at 7 a. m., 2 p. m., 
 and 9 p. m. 
 
 Subtract the grand mean from the mean at each hour in 
 succession, and we have a table of horary corrections, in 
 which all those greater than the grand mean are to be called 
 minus ( — ), and those less than the grand mean, plus (+). 
 
 The table of horary' corrections being applied to the ob- 
 servations at 32° F., produces the table of observations 
 reduced, which represents the abnormal oscillation. 
 
 It is of great importance, particularly when the series is 
 not long, that the observations should be plotted, in order 
 that any days' observations that are so erratic that they 
 would evidently vitiate the result ii they were combined 
 
20 
 
 witii the otbers cau be detected aud rejected. The reason 
 for this rejection is that we cannot expect the movements 
 of the atmosphere during barometric storms to show its 
 regular normal oscillation. Another advantage in plotting 
 the observations is to afford the means of detecting errors 
 in observations. 
 
 Any hour of the twenty-four may be taken as the initial 
 hour of the barometric day, but it has been found expedient, 
 for several reasons, to adopt 7 a. m. for that hour. Midnight 
 is certainly an inconvenient hour, as observations are sel- 
 dom taken at that time. When observations are taken but 
 three times daily, the Smithsonian hours of 7 a. m., 2 p. m., 
 and 9 p. m. are almost invariably adopted in this country. 
 Full observations taken during all of the twenty-four hours 
 are of great value for certain scientific purposes, particularly 
 in deducing the laws which cause the horary oscillation to be 
 different in different latitudes, altitudes, aud climates. But 
 as barometric observations for hypsometrical purposes are 
 seldom taken during the night, the practical engineer or 
 surveyor seldom cares for them later than 9 p. m., even 
 though he does not obtain the night maximum aud morning 
 minimum, the first of which occurs not far from midnight, 
 and the latter or second between four and five in the morning. 
 
 When the series is a short one aud the horary table is 
 made with the hope of obtaining a type curve, or when it is 
 suspected that the observations, as usually treated, will not 
 give a result fully treed from the abnormal movement, 
 another horary table may be made by treating the observa- 
 tions in the same way, but adopting 7 p. m. as the initial 
 hour instead of 7 a. m. If the series be of teu days' dura- 
 tion, the new table with the new initial hour will produce a 
 nine days' series. A combination of the two mean tables is 
 more likely to produce a good horary curve than either one 
 separately. This would be naturally the case, for, from the 
 very principle of the reduction to level, it is assumed that 
 
21 
 
 the portion of the abnormal wave during each day is a right 
 line, whereas it is only approximately so, and is in reality a 
 curve more or less convex or concave. Now, by adopting 
 another initial hour an additional horary table can be made, 
 and it is more than likely that by the combination of the 
 two the abnormal movement is more thoroughly eliminated 
 When the series of hourly observations is not continuous 
 as, for instance, when the night observations are not taken, 
 we cannot use the method just given, but we must adopt 
 some method of obtaining approximately a grand mean, and 
 it has been found that the mean of 7 a. m., 2 p. m., and 9 
 p. m., gives a close approximation to the mean of the 
 twenty-four hourly observations. It is important to know 
 how close the agreement is. Although the number of sta- 
 tions where I have been able to collect observations is quite 
 small, still they have been sufficient to prove, not only that 
 the difference in obtaining the daily mean pressure by the 
 two methods is not great, but that it varies by a regular 
 law during the months of the year. Tliis is shown by the 
 following table : 
 
22 
 
 « S 
 
 c 
 
 1 
 
 o 
 
 1 
 
 o 
 o 
 o 
 
 
 
 
 o 
 
 1 
 
 o 
 o 
 
 c 
 
 i 
 
 -1 o 
 
 8 8 
 
 o 
 
 1 
 
 c 
 o 
 
 1 
 
 
 Q 
 
 s s § 
 
 o o o 
 
 + + + 
 
 
 
 
 -J. o -- — o 
 o o o o o 
 o c o o o 
 
 + 1 + + 
 
 O 11 
 
 ^^ o 
 o o 
 
 + + 
 
 
 s § s 
 
 o o o 
 
 -f 1 + 
 
 
 
 
 2 S S S g 
 
 o o o o o 
 
 + + + 1 + 
 
 3 8 
 
 O 
 
 § g s 
 
 o o o 
 
 ' + 1 
 
 
 
 
 o o o o o 
 o o o o o 
 
 + + 1 1 1 
 
 o o 
 
 8 8 
 
 
 a . 
 
 § s § 
 l" 1 + 
 
 
 O 
 1 
 
 « (» (N — 1 — 
 
 8 § § § g 
 1* i \ \ \ 
 
 2 S 
 
 o o 
 
 D 
 
 to 
 
 n n o ^ n 
 o o o o o 
 c o o o o 
 
 l' f * l" 1 
 
 O 
 1 
 
 ■«i> •"J- m (M o» 
 
 g § 8 § § 
 
 l" l' l' l' l' 
 
 00 n 
 o o 
 
 l" l' 
 
 1-2 
 
 oooooooooooo 
 oooooooooooo 
 
 l' 1 1* 1 1 1 1 1 1 I f 1 
 
 o o 
 
 1 1 
 
 2 
 
 ■^ ^ rt 
 o o o 
 coo 
 
 l' l' l' 
 
 
 
 
 »r; ^ c« •- "^ 
 o o o o o 
 o o o o o 
 
 l' l" f l" l" 
 
 o o 
 
 1 1 
 
 1 
 
 •j: ■» O 
 
 o o o 
 o o = 
 
 l' l' l' 
 
 
 
 
 s s s § s 
 
 o o o o o 
 
 l' l" l' f + 
 
 § 2 
 
 o o 
 
 l" l' 
 
 <1 
 
 L-5 ffJ t= 
 
 e^ o o 
 o o o 
 
 l' 1 l" 
 
 
 
 
 t- <N (J* r» m 
 
 o o o o o 
 o o o o o 
 
 l' l' l" l' 1 
 
 SI n 
 
 § 8 
 1 l' 
 
 1 
 
 n ffi t» 
 
 o o o 
 o o o 
 
 + + i 
 
 
 
 
 — CJ (» — « 
 
 o o o o o 
 o o o o o 
 
 l' + l' l' l' 
 
 g i 
 
 o c 
 
 1 
 
 
 
 M CO /-> 
 
 § § i 
 
 1 + r 
 
 
 
 
 -^ rt o o — ■ 
 
 o o o o o 
 o o o o o 
 
 + +■ " -f 
 
 8 o 
 
 o o 
 
 + + 
 
 ^2 
 
 o o S S o o 
 o o § o o o 
 
 g g s s § 
 
 c o o O o 
 
 + + + + + 
 
 o n 
 
 2 8 
 + + 
 
 o5 
 
 a 
 2 
 
 z 
 
 < 
 
 1 
 
 z 
 
 c 
 
 E- 
 
 c 
 
 11 
 11 
 
 J 
 
 > 
 
 t- 
 
 !- 
 
 > "i 
 i 1 
 
 H 5 
 
 1 
 
 -. _a 
 > 
 
 ■ c 
 
 •J 
 J c 
 
 c 
 t 
 
 c 
 
 1 
 
 a , 
 
 « : 
 
 a -1 
 
 i i 
 
 C C2 
 
 
 B 
 e 
 
 
23 
 
 By examining the table, it will be seen that out of the 107 
 differences in the monthly results by the two methods there 
 is one amounting to tea thousandths of an inch of the 
 barometric column in the stormy mouth of December, one 
 of seven thousandths, six of six thousandths, four of five 
 thousandths, sixteen of four thousandths, and all the rest 
 are less than that amount. In fact, out of the 107 results 
 there are only twelve in which the differences are so great 
 as five thousandths. The mean results show that the mean 
 of observations at 7 a. m., 2 p. m., and 9 p. m. is less than the 
 mean of twenty-four hourly observations in the months of 
 November, December, January, and February, the January 
 results giving a difference of three thousandths of an inch, 
 and that in the midsummer months it is greater by the 
 same amount. In March and October there is no difference. 
 The yearly mean difference by the two methods is less than 
 one-thousandth of au inch. The above table can be used 
 as a table of corrections to be applied to observations taken 
 in any month in order to reduce them to the yearly mean. 
 
 This table has been deduced from monthly means, and it 
 is not to be supposed that observations taken in a single 
 day, or even a series of a few days' duration, will afford so 
 close an accord by the two methods. There is, however, a 
 method, when the observations are taken at the Smithso- 
 nian hours, which affords a very good value for the daily 
 mean, as compared with the mean of twenty-four observations 
 in a day beginning at 7 a. m. It is to take the mean of 7 
 a. m., 2 p. m., 9 p. m., and 7 a. m, of the succeeding day 
 and apply to it a correction, so as to reduce it to what it 
 would have been had the observations been taken strictly 
 at eight hours apart. From 7 a. m. to 2 p. m. is an interval 
 of but seven hours, and from 7 a. m. to 9 p. m. is 14 hours. 
 Hence the sum of these four observations is too small by 
 the rise, or too great by the fall, between 2 p. m. and 3 p. 
 m., together with the rise or fall between 9 p. m. and 11 p. 
 m,; that is to say, during three hours. But 3 hours is one- 
 eighth of a day, in which day the barometer had au average 
 
24 
 
 rise or fall measured by the amouut which has been called 
 "the correctiou to level for twenty-four hours," aud which 
 is the difference in the readings of the barometer at 7 a. m. 
 on one day and 7 a. m. on the next. Therefore one eighth 
 of that amount should be applied as a correction to the 
 sum of the four observations in question, so as to increase 
 that sum when the barometer for the day had been rising 
 and diminish it when falling. It must be borne in mind, 
 however, that this correction is to be applied to the "ob- 
 servations reduced," or, in other words, to tiie observations 
 after the horary correction had been applied. 
 
 We may therefore have the following rule for obtaining 
 the mean daily pressure from four such " observations re- 
 duced," the barometric day commencing at 7 a. m. Take 
 the sum of the observations so reduced at 7 a. m., 2 p. m., 
 9 p. m., and 7 a. m. the next morning and apply to it one- 
 eighth of the difference between the observations at the 
 beginning of the two consecutive days, calling the difference 
 2)lus (-J-) when the barometer for the day had been rising 
 and mimis (— ) in the reverse case, then divide the result 
 by four, and we have the required daily mean. 
 
 As it is desirable to have a definite idea of the difference 
 between the daily barometric means as computed from 
 twenty-four hourly observations and that given by the last 
 described method, and also between the former and that 
 from observations taken at 7 a. m., 2 p.. m., and 9 p. m., I 
 present a table from ten days' observations at Sacramento, 
 Placerville, Strawberry Valley, and Hope Valley, taken 
 during August, 18G0. The upper line of each group gives 
 the difference between the daily mean as calculated from 
 twenty-four hourly observations aud the mean of 7 a. m., 2 
 p. m,, 9 p. m., aud 7 a. m. the next morning, corrected as 
 above described. The lower line gives the difference between 
 the first and the mean of 7 a. m., 2 p. m., and 9 p. m. It will 
 be seen that the amount of variation from the mean of twenty- 
 four hourly observations is nearly three times greater by the 
 last mentioned method than by the first. 
 
25 
 
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26 
 
 In almost every iustauce it is shown that the second 
 method gives results much nearer the mean of twenty-four 
 hourly observatioDS than the third, which is a simple mean 
 of the observations at 7 a. m., 2 p. m., and 9 p. ra. Taking 
 the mean of twenty-four hourly observations as the stand- 
 ard, and taking the difterence between this standard and 
 the results given by the other two methods, we find that 
 the sum of these differences in a ten days' series by the 
 method of four observations so reduced is only 38 per cent, 
 of the corresponding amount obtained from a simple mean 
 of the observations taken at 7 a. m., 2 p. m., and 9 p.m. 5 and 
 the maximum errors are in proportion, they being at Sac- 
 ramento .007 in. and .032 in., and at Hope Valley .008 in. 
 and .030 in. As this method of obtaining the barometric 
 mean involves very little additional trouble after the obser- 
 vations have been actually taken, it appears to me worthy 
 of being adopted. For, in the field, we cannot tell when 
 the atmospheric conditions which cause the difference 
 between the two methods are in operation, and when the 
 maximum difi'erence will occur ; hence the results are apt 
 to be considered untrustworthy up to the limit of the maxi- 
 mum error. On the other hand, if that maximunj error can 
 be reduced two-thirds or one-half, the results can surely be 
 relied upon within the smaller limit. 
 
 Although observations at the Smithsonian hours have 
 been shown to give a close approximation to the mean of 
 twenty-four hourly observations, still other hours have been 
 adopted that give, also, very good results. The Coast Sur- 
 vey adopted long ago the mean of a. m., noon, and 6 p. 
 m. as a good barometric mean, though latterly they have 
 adopted the hours of 7 a. m., 2 p. m., and 9 p. m. I have 
 obtained from Louis Wilson, tidal observer at Astoria, 
 Oregon, the following table, which explains itself: 
 
27 
 
28 
 
 This table shows nearly as good results as from observa- 
 tions at the Smithsonian hours, but as the latter hours have 
 been so universally adopted, and it is very desirable to have 
 uniformity in the hours of observation, so that comparisons 
 can be easily made, I would recommend that the Smith- 
 sonian hours be adhered to in future observations where 
 they are taken but three times a day. 
 
 Having explained how the horary correction of the barom- 
 eter can be obtained from a short series of observation, I 
 now wish to point out certain facts concerning this oscilla- 
 tion. It has been found that when the stations are near the 
 sea level, the curves for each month at different localities 
 are of the same character, the critical hours occurring at 
 the same times, but varying in range or amplitude, the 
 warmest localities giving the largest curves. Hence, as a 
 general rule, the curves are smaller as the latitude increases. 
 But in the same latitude and climate the curves for the dif- 
 ferent months are different. They vary in the hours of 
 maxima and minima, and also in the amplitude of the oscil- 
 lation. While the hour of the morning maximum does not 
 materially vary during the different months, that of the 
 afternoon varies with the seasons, being usually between 
 2 and 3 p. m. in midwinter and between 5 and G p. m* 
 in midsummer. The consequence of this is, that if the 
 tables representing the hourly observations taken in Jan- 
 uary and July are subtracted the one from the other and 
 this difference plotted, it gives a curve nearly as great as 
 is produced from either set of observations. But as soon 
 as the element of altitude enters into consideration, the 
 curve changes materially, and according to a law which has 
 not yet been discovered. As a general rule, the curves for 
 high altitudes are quite small. At the Grand Saint Ber- 
 nard, that portion of the midsummer curve for the hours 
 when the sun is above the horizon is exceedingly minute, 
 while the night portion of the curve presents an oscillation 
 
29 
 
 of about 0.040 inch. Near the summit of the Sierra Nevada 
 iu July and August, the moruing maximum is at 7 a. m., 
 while in the valley below it is at 11 a. m. There is no sim- 
 ilarity between the Grand Saint Bernard curves and those 
 of the Sierra Nevada, though the altitudes of the two sta- 
 tions do not diifer materially. If we had a series of stations 
 one thousand feet apart, vertically, from the sea level to the 
 summit of the mountain, we would find that the curves at 
 all the stations would be different. 
 
 The amplitude of this oscillation iu the temperate zone 
 usually varies from 0.010 in. to O.OSO in. Near the equator 
 the oscillation is greater, amounting to nearly 0.120 in., 
 and the abnormal oscillation being there very small, the 
 horary oscillation is so regular, that the hour of the day can 
 be ascertained, at least approximately, from the reading of 
 the barometer. But the abnormal oscillation seems to in- 
 crease with the latitude, while the horary movement becomes 
 less, and iu high latitudes the latter is so masked by the 
 former, that a long series of observations is required to ob- 
 tain a reliable horary curve. 
 
 From the above facts it becomes apparent that the effects 
 of this horary oscillation ought to be neutralized in some 
 way. The computed differences of altitude from observa- 
 tions taken at different hours are different on account 
 of the oscillations at the lower and upper stations being so 
 entirely differeut. Now, as a change of 0.001 in. in the 
 barometer at one station will affect the result about a foot, 
 unless a corresponding change occurs at the other station, 
 it is apparent that we should correct the observations before 
 they are used in the determination of altitudes, so as to 
 eliminate the effect of the horary movement. The follow- 
 ing general conclusions are giv^eu in Professional Papers of 
 the Corps of Engineers, No. 15, together with a large num- 
 ber of horary tables and curves: 
 
 1st. As the value of the principal term of the barometric 
 
30 
 
 formula depends upon the difference between the readings 
 of the barometers at an upper and lower station, and as 
 the horary oscillation of the barometer is quite different at 
 the two stations when the difference of altitude is at all 
 considerable, and as its amount is often sufQcient to cause 
 considerable error in hypsometrical calculations if neglected, 
 even when the observations at the two stations are simul- 
 taneous, it is important to eliminate it as far as practicable. 
 
 2d. As the horary curves and tables for any two days, 
 even in a short series, are not identical, the best way to 
 eliminate the effect of this oscillation is to use the mean of 
 observations taken at short intervals, as, for instance, hourly, 
 for one day, or for a number of wJiole days, the day com- 
 mencing at any convenient hour. 
 
 3d. When this is impracticable, and when the horary 
 tables for the station and month are previously known, and 
 the observations are for a portion of a day only, or for por- 
 tions of several days, the horary correction should be 
 applied to them before they are used in estimating differ- 
 ences of altitudes. 
 
 4th. When the horary tables for one or both stations are 
 unknown, and hourly observations cannot be taken, the 
 aim should be to obtain the nearest approximation to a 
 daily mean. For this purpose, the mean of observations 
 taken at 7 a. m., 2 p. m., and 9 p. m., or of 6 a. m., 2 p. m., 
 and 10 p. m., or 6 a. m., noon, and 6 p. m. have been found 
 to afford quite good results. 
 
 ON THE VARIATIONS IN TEMPERATURE. 
 
 While the horary barometric oscillation, when freed from 
 the abnormal movement, does not vary much from day to 
 day at the same station during a short series, it is very dif- 
 ferent with the corresponding thcrmometric oscillation. In 
 the one case it is small as compared with the abnormal one, 
 and so nearly uniform in character that a mean of a few days' 
 
31 
 
 observations, properly treated, will give a characteristic 
 horary table aud curve for that station and month; and, by 
 elimination, the abnormal wave can be represented. In the 
 case of the temperature, the horary movement is very large 
 as compared with the other, and varies so much from day to 
 day that no characteristic horary table can be used in elimi- 
 nating this movement, and obtaining an abnormal ther- 
 mometric wave; though the curve is a simple one, having 
 but one maximum and one minimum in 24 hours, still the 
 range, or vertical amplitude, may be several times as great 
 in one day as in another during a series of ten days. The 
 consequence is that the method of separating the two move- 
 ments, which we have found practicable with the baromet- 
 ric observations, is not applicable to those with the ther- 
 mometer. 
 
 While the barometer gives us a measure of the weight of 
 the whole column of air over the place of observation, the 
 thermometer is local in its character and affected by every 
 pufi' of wind that blows over it. It is true that there is one 
 paramount influence which i)roduces a horary thermometric 
 oscillation with one decided maximum and one minimum, 
 the former usually occurring between 2 and 4 p. m. and the 
 latter about one hour before sunrise; but the amount of 
 variation during the day is greatly modified by many acci- 
 dental causes, such as the clearness or cloudiness of the 
 atmos[)here, the direction and force of the wind, the rapid- 
 ity or slowness of the evaporation or condensation of 
 aqueous vapor, and many other local meteorological phe- 
 nomena. For these reasons the amount of this oscillation 
 must vary greatly from day to day, and this experience 
 shows us to be the case. 
 
 If, in a series of ten days' observations, the horary ther- 
 mometric oscillations are plotted, it will almost always be 
 found, in temperate latitudes, that the vertical range in the 
 curve for some one day will be twice as great as for another 
 
32 
 
 in that short series, aud it is not unusual to find that the 
 difference is three and even four times as great. It is this 
 great difference in range from day to day which prevents 
 us from using advantageously a mean horary thermometric 
 table for hypsometrical purposes. The same reason which 
 makes it necessary to eliminate the effects of the horary 
 oscillation of the barometer applies with still greater force 
 to the varying temperature. It is principally by means of 
 the pressure at the two stations, in connection with the 
 corresponding temperature, that we are to obtain the dif- 
 ference of altitude between them. If the change in temper- 
 ature from hour to hour caused a proper corresponding 
 change in the height of the barometer, we could disregard 
 the effects of the horary oscillations altogether and use the 
 observed pressure and temperature at the two stations. 
 But this is not so. When we take twenty -four hourly ob- 
 servations of the barometer and thermometer at stations of 
 considerable difference of altitude, and estimate the verti- 
 cal distance between these stations by the formula, using 
 successively each pair of corresponding observations, we 
 have a series of twenty-four numbers far from being alike. 
 Again, when we do the same with the next two sets of 
 twenty-four observations taken during the next day, we 
 have another series differing from the first, and it would be 
 very materially different if the horary theimometric oscilla- 
 tions for the two days are quite different, as they are apt to 
 be. For these reasons it is evident that the horary oscilla- 
 tions of both the barometer and thermometer must be elim- 
 inated before the observations can be properly used in esti- 
 mating differences of altitude. Yet I believe it is a common 
 practice with computers to use the observed air tempera- 
 ture. 
 
 When hourly observations of the thermometer are taken, 
 aud the monthly mean for the different months are obtained, 
 it has been found that the range of the horary thermomet- 
 
33 
 
 lie oscillation varies from montli to moutli, the same be- 
 ing greatest in the hottest months and least in the coldest. 
 
 The (litfereuce in these ranges seems to be greatest when 
 the (lilierence between the mean temperatures of the hottest 
 and coldest month is gre;itest. The range is usually great- 
 er ill arid districts than in thu more humid ones near the 
 sea. It has been found from observations at stations vary- 
 ing in altitude from the sea level to the summit of the 
 Sierra Nevada, that in Angust the range at Sacramento, 
 near sea level, was 17 degrees; at Placerville, about 2,000 
 feet high, it was 31 degrees; at Strawberry Yalley, al)out 
 5,700 feet high, it was 33 degrees ; and at Hope Valley, 
 7,000 feet high, it was 17 degrees. In January, at the same 
 stations, the range was 11 degrees at Sacramento, 17.} de- 
 grees at Placerville, 10^ degrees at Strawberry Valley, and 
 17 degrees at Hope Valley. It therefore by no means fol- 
 lows that the range of this oscillation diminishes with the 
 altitude, though it is doubtless samll at exceedingly high 
 places. 
 
 It is evident from the preceding remarks that the ques- 
 tion of how best to obtain the daily mean tem[)erature, in 
 order to secure good hypsoiuetrical results, is of great im- 
 portance. Fortunately, this is not difficult. With the ba- 
 rometer the daily mean can only be ascertained from obser- 
 vations taken during that day at the precise locality, or 
 ai)proximately so, by applying a horary correction But 
 with the thermometer the case is different. As the tempera- 
 ture during a day is nearly the same over a large area in a 
 level country, observations can usually be taken in the 
 field at 7 a. m., 2 p. m., and 9 p. m., and a good mean value 
 to the temperature of the day thus obtained, ahhough the 
 party has been in motion. It the party has been in an un- 
 even or mountainous region, then the only way is to assume 
 that the mean daily temperature varies three degrees with 
 
 each thousand feet of difference of altitude. I am aware 
 3 u B 
 
34 
 
 that this rule gives but a very rude approximatiou to the 
 truth, but, except when the change in altitude from camp to 
 camp is very great, the error from adopting it will be small. 
 The following table gives a comparison between monthly 
 mean temperatures obtained by twenty -four hourly obser- 
 vations and the mean of those taken at 7 a. m., 2 p. m., 
 and 9 p. m. : 
 
35 
 
 ■2 a 
 
 >'V. 
 
 5"-= 
 
 r S 35 
 
 ■2 ^ 
 
 oooooo'oooooocfoooooooooooooooooo 
 I I I I I I I I I I I M I I I I I I I I I I I 1 I I I I I I 
 
 > o o < 
 I I 
 
 10 00 = 
 
 I I I I I 
 
 o o < 
 
 I I 
 
 ) o o 
 
 I i 
 
 oo o oo 
 
 1 I I I I I 
 
 ■c-.c>'Xn~naoo5c;o^f-tocrjm— im-5t-oo-3'Qoino'»(-^t--.c« 
 
 ci?ccM«r^cMro^oc^r:'vc»cocO'^r-'»-^'rrcNcoOi-i5^^: 
 
 I I I I 
 
 oo< 
 
 I I 
 
 >o o o o o 
 
 I I I I I 
 
 oo ; 
 I I 
 
 > o o o t 
 
 I I I 
 
 >oo 
 
 I I 
 
 oo ! 
 
 I I 
 
 H o 
 
 I I 
 
 oi o 
 
 I 1 + 
 
 W^ODi>-OIC4CI-^i--000'^OSrt05t^Oi»n(?»C 
 
 ^c^-Ci^-cccCTP^Tl«c^(c^«coQ^om(7^»o(o^noD■^co■<r(?*c^OT-lccoco 
 >o o 
 
 >o o c 
 
 I I 
 
 > oo oo oc 
 
 I I I I I 
 
 > ooo 
 
 I I I 
 
 oi rH in o irt m « 
 ■<r n 
 
 o 
 
 1 I 
 
 > o o 
 
 I I 
 
 ooo o o o 
 MM + + 
 
 O CO 
 -H O 
 
 7 I 
 
 L'^CllCOO^O^CtO'X'OCMQOCO^ 
 
 M M M M M M M 
 
 > O « O 
 
 I I I 
 
 O O O O O O O 
 
 M M M I 
 
 ooo 
 
 I I I 
 
 -csmocMi^oooom^oi-t^f^^t^ — t'O^QO^oor^oiOTC^Tf^ai 
 
 I co©» 
 
 !0'0 
 I I 
 
 't--(7»OCDt-;OCOf~-^OCO: 
 
 J t-- -r 'V 1-* 1' c. 1 
 
 I I 
 
 ooooo 
 I M M 
 
 --^^^■vt^roxoQOOOcc: 
 
 00( 
 
 ->< o c 
 
 lO O rl 
 I I I 
 
 J -^ tC CO 
 
 :7»C^f-OOf(7^iTJi^Ci:oo-r^ooyra;i 
 
 tHOOOOOOi-hOOOO 
 
 M M M M M M 
 
 tr. TTil^O'Tf-OHOOOICCt- 
 
 IM M 
 
 o o 
 
 I I 
 
 I I 
 
 r- O O O O 
 
 I M I + 
 
 rt O < 
 
 I I 
 
 > O r-( rH 
 I I I 
 
 I I 
 
 O O O OO rM O 
 
 M M I M 
 
 ooo 
 
 I I I 
 
 I 1 
 
 n o 
 I I 
 
 t^occc^c:r^ci:cc:ooeorHQor'(NO».1t-*coOTf^:o«irtc;ioicosQO 
 
 •OC^?trHQCr-«{5«OrtOlrtr-4C:00Or5OOrH- 
 
 > OO ! 
 
 I I 
 
 > I-H O r^O O 
 
 M MH- 
 
 O OrH ■- r-l rH 
 
 M M M 
 
 O O " rl O 1-1 1— > 
 
 M M I M 
 
 ■■c o 
 
 St 
 
 I I 
 
 t^c. o!0^^ir;o--'T0or-t^005<omL^oc:oG0iO5*c:CTm{N-HiftrH 
 Lti^aJm■v^^•^(^^?^cooCToc]OOcc:caLoo^c<'^OGO^iO»-1-tr^ODOoo 
 
 oooooooo 
 I ! I M I M 
 
 ^ o o o o 
 M M + 
 
 o o< 
 
 I I 
 
 > O O T-H 
 
 I I I 
 
 O rl 
 I I 
 
 O O O O O .-I r- 
 
 M I M I I 
 
 OOO 
 
 I I I 
 
 I I 
 
 — " r: cr. X L-: i 
 
 • Gur^iO'^mooi^«ct-'^iftCTt--»-<co^coor'-»j*0 7ioot?j 
 
 ;ot--^ooio<-'^»ro* 
 
 M M M M 
 
 ooooo 
 
 MM 
 
 o o c 
 
 I I 
 
 ) o o 
 
 I I 
 
 m C-. 
 o' o" o' o o' o' o 
 M M M I 
 
 t- Cl (71 
 
 oo'o I 
 
 I I I 
 
 !^'0«M<jioc3toj~oooo»(Nooacoo-'QOi-ixo!(riomQO — »-oo> 
 
 1-1 mo w 
 
 M M M M I 
 
 • 00 — -< O O O 2? ! 
 
 ITv <?» S< -H O 
 
 o o' o o o 
 
 I I I 
 
 o at : 
 
 o o'c 
 
 + 1 
 
 It- o -?■ X m c 
 
 l-lmo^lO^»coo■^c^?c^^^ — ' 
 
 i.O o < 
 I I 
 
 > o o oo o < 
 M M I 
 
 ICO m -v 
 >o'o o 
 
 I I I 
 
 J « ■» -5 
 > o oo 
 [Ml 
 
 cotMcoia^^^irti-^cNOC^ 
 ooooocSoooo I 
 
 M I M M M I 
 
 oo 
 
 I I 
 
 : o X o m r- ^ ^ ■ 
 ^ r:i :n ^T Oi T n ^ i 
 
 o o o o o o o 
 M M M I 
 
 1— o o 
 ooo 
 
 I I I 
 
 ^CiOOOCO::?Xl^*I3'VO-^i^Ot^3St^a!mOOO?J05QO^(?JQOi~-mr-0 
 
 (rj';!Tcoc>r;iu^x — o<i-irr — o<<N'NCJT>coijJCJc»i-icoucoo«i-iO(r< 
 
 ooo'oo" oooooooo o'o'ooooocJooo' ooooo o'o 
 
 M M M M I M M M M M M M M M M I + 
 
 o at 
 
 00 o 
 
 I I 
 
 J) S o c ; . 
 
 .25 = c = 
 
 5 a o o^ >,5 
 il a ^- ft- o ® i 
 .S 2 o o .2 ft- =3 w .. 
 
 O c5 
 
 • : o 2 Sr t; •'; c .^ .3 g cs 
 5 :'5.5 =■<= 5-3 c= B » 
 
36 
 
 It will be seen that tbemeau temperature of 7 a. m., 2 p. m., 
 aud 9 p. m., at almost every station, gives a result too great, in 
 every montb, as compared witli the mean of twenty-four hourly 
 observations ; but the difference is not great, seldom exceed- 
 ing in any one month one and one-half degrees. The mean 
 results show that the mean temperature thus ob tained by 
 the two methods most nearly agrees in December, where the 
 difference is less than one-quarter of a degree, an d that the 
 difference is greatest in June. From December to June the 
 difference increases with much uniformity, and from June 
 to December it decreases in the same manner ; so that if the 
 table "were i^lotted it would show a smooth curve. This 
 table can be used as a table of corrections, to be applied to 
 observations taken at 7 a. m., 2 p. m., and 9 p. m., in order 
 to reduce them to the mean of twenty-four hourly observa- 
 tions. 
 
 I next present a table of comparison between the means 
 of thermometric observations taken at 7 a. ra., 2 p. m., and 
 p. m, aud that of those taken at a. m., noon, and 6 p. 
 m. They were furnished me by Louis Wilson, tidal obser- 
 ver at Astoria, Oreg., and are for three years. 
 
37 
 
 
 5 '^ 
 
 
 S s 
 
 i ^ 
 
 1 
 
 o 
 
 1 
 
 O O i 
 
 1 1 
 
 d 
 1 
 
 
 -^ r- O 
 
 o o o 
 
 1 1 1 
 
 d 
 1 
 
 
 CI c^ o 
 
 o o o 
 
 1 1 1 
 
 d 
 
 1 
 
 
 C» ^ rH 
 
 o o o 
 
 1 1 1 
 
 d 
 1 
 
 s . 
 
 ■<?• CJ o 
 
 o o o 
 
 1 1 1 
 
 d 
 1 
 
 -5 
 
 O CI =5 1 O 
 
 o o o 1 o 
 
 1 1 1 1 1 
 
 •^ 
 
 05 t- O 
 
 O O rn" 
 
 1 1 1 
 
 d 
 
 1 
 
 2 
 ^ 
 
 00 L- 1- 
 
 o o o 
 
 1 1 1 
 
 d 
 1 
 
 CO 
 
 d 
 1 
 
 
 in r^ o» 
 o o o 
 
 1 1 1 
 
 < 
 
 *?" in '^ 
 o o o 
 
 1 1 1 
 
 o 
 
 1 
 
 Maicb. 
 
 — 0.5 
 
 — 0.1 
 
 — 0.2 
 
 n 
 d 
 
 1 
 
 o 
 d 
 
 1 
 
 3 
 u 
 
 c5 o o 
 + i 1 
 
 5 
 
 3 
 
 a 
 
 O ^ St 
 
 o o o 
 
 1 1 + 
 
 o 
 d 
 
 1 
 
 1 
 
 i 
 
 o -^ 
 
 00 TO 
 
 1 
 
38 
 
 It appears from this table that while the winter months 
 give results which agree almost exactly by the two methods, 
 the results in the summer months differ by about three- 
 quarters of a degree, the mean of G a. m., noon, and C p. m. 
 being the greater. As in those months the mean of 7 a. m., 
 2 J). 111., and 9 p. m. gives results too great by about that 
 amount as compared with the mean of twenty-four hourly 
 observations, it follows that the other method must be con- 
 sidered decidedly inferior. 
 
 From an examination of the monthly mean temperatures 
 from year to year at Geneva and the Grand St. Bernard it 
 has been found that when at one station the monthly mean 
 temperature departs considerably from that determined by 
 the mean of a long series, it is not local, for the same depart- 
 ure is found at the other station. 
 
 OF HYPSOMETRICAL RESULTS FROM DAILY MEANS. 
 
 It is presumed that the reader understands the barometric 
 formula, and therefore but few remarks concerning it are 
 necessary here. The most important parts of it are the 
 pressure and temperature terms. The first consists of a 
 constant, multiplied by the difference between the logarithms 
 of two numbers, which are the readings of the barometer at 
 a lower and an upper station. The second term is the pro- 
 duct of the former divided by 900 and multiplied by the 
 sum of two numbers, which sum, when the Fahrenheit scale 
 is used, is the sum of the readings of the open-air thermom- 
 eter at the two stations, diminished by 64, which is twice 
 the temperature at the freezing-point. 
 
 The other terms of the formula are usually comparatively 
 small, though by no means to be disregarded in the com- 
 putations. When the formula is api^lied to observations 
 taken for some time at the same two stations (in wiiich case 
 the true difference of altitude between them will, of course, 
 be constant), the values of these terms should be constant. 
 
30 
 
 With such a series, the mean readings of the barometers 
 and thermometers can be used to compute the mean differ- 
 ence of altitude between them. When this is done, and the 
 value of those small terms is once determined, jf separate 
 computations are made to obtain the difference of altitude 
 from each day's observations, the same value for the sum 
 of these small terms can be used, thus avoiding much use- 
 less labor in computing. When the pairs of stations are 
 different, separate calculations must be made to obtain the 
 values of these terms, which can be conveniently done by 
 the aid of the tables in the appendix to Professional Papers 
 of the Corps of Engineers, No. 15, before mentioned. 
 
 If computations are made from the daily means of ob- 
 servations during every day in a month at the same two 
 stations, each resultjjwill vary more or less from the monthly 
 mean. If a table of wanderings from the mean is made, 
 some of the numbers will, of course, be greater and some 
 less than the mean, and should be written, some with a plus 
 (-f) and some with a minus ( — ) sign. If all these errors 
 or wanderings are added together, without regard to sign, 
 and divided by the number of days in the month, the 
 resulting number will give the mean error; and it may be 
 confidently assumed that if similar observations at those 
 two stations are taken during the same month of another 
 year, very similar results will be obtained. But it can be 
 shown from a large number of^computed differences of alti- 
 tude from daily means that the amounts of the maximum 
 and mean errors in different months at the same two stations 
 vary considerably, being least in mid-summer and greatest 
 in mid-winter. 
 
 As a general rule, when the difference of altitude between 
 the two stations is at all considerable, the amounts of the 
 maximum and mean errors vary with the difference of alti- 
 tude. This is quite natural, for, in the first place, when the 
 difference of altitude is great the horizontal distance between 
 
40 
 
 tliem must also be coin[)aratively great, and tbe errors are 
 apt to be greater tbau when the stations are close together ; 
 but, in the second place, the temperature term of the form- 
 ula is the i)rodact of the approximate difference of altitude 
 given by the pressure term multiplied by a variable depend- 
 ing upon the temi)erature. Now, the value of this variable 
 being different from day to day, the wanderings from the 
 mean value of the temperature term are inevitable, and 
 must be proportional to the value of this variable, as well 
 as to the difference of altitude. This last cause of error, 
 however, does not materially affect the result when the 
 difference of altitude is quite small, in which case the errors 
 are apt to vary with the horizontal distance between the 
 stations. 
 
 The following tables of maximum and mean errors in com- 
 l)utiug differences of altitude from daily means are now 
 presented. They are the result of great labor, as every two 
 corresponding numbers are the result of as many different 
 computations as there were days in the month ; but they 
 give a clear idea of the j)robable amount of error to which 
 such results are liable. 
 
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43 
 
 From the examiuatiou of a large lumiber of observatious 
 and computed results from daily means, I have come to the 
 conclusion that there is no relation between the height of 
 the barometer at the lower or upper station and the value of 
 the differences of altitude. That is to say, the wandering 
 from the monthly mean may be a maximum or a minimum 
 with either a high or a low barometer. 
 
 The cause of erratic results from daily means must be 
 attributed to the fact that the atmosphere is seldom, if ever, 
 in a state of equilibrium, and hence the wanderings cannot 
 be controlled by any law, and must be incident to all 
 measurements of this kind. 
 
 OF THE VARIATIONS IN HYPSOMETRICAL RESULTS 
 FROM MONTHLY MEANS. 
 
 When observations of the barometer and thermometer 
 have been continued for a number of years at two stations, 
 and the mean monthly readings are used in computing 
 the difference of altitude between them, it has been ascer- 
 tained that these computed results from observations taken 
 in the different months differ. If we take the series of 25 
 years at Geneva and the Grand St. Bernard as affording us the 
 best tj'pe series available, we find that the computed differ- 
 ence of altitude for the month of December and July differ 
 by 101 feet, and that those for the different months vary by 
 a definite law, so that when plotted they show a smooth 
 curve. We can only ascertain what this law is bj' compar- 
 ing results from observations taken in different latitudes, 
 altitudes, and climates. Unfortunately, extensive series of 
 reliable observations at high and low altitudes are seldom 
 to be found. But I shall make use of such as I have had 
 access to, and from which some important facts can be de- 
 duced. 
 
 Going back to the observations at Geneva and the Grand 
 St. Bernard, the first fact of importance is, that while the 
 
44 
 
 25 years' series gives a good curve, the observations taken 
 in any one year do not, and the plotted results from monthly 
 means of observations taken during a single year are so 
 irregular that it would be difficult to develop from them 
 a law in this variation. This fact shows that even with 
 these stations, if a table of corrections were made to reduce 
 the results taken during each of the mouths to the mean 
 for the year, and if that table of corrections were applied 
 to observations taken in any year, the correction would not 
 with certainty be applied advantageously, though of course 
 the chances are that they would be so applied. 
 
 It is now necessary to ascertain if this variation in hypso- 
 metrical results is peculiar to the climate of Switzerland, or 
 whether it is applicable to other countries. The observa- 
 tions taken in the Sierra Nevada, though not as numerous 
 as are desirable, at least indicate that the same general law 
 holds good in California; but while observations in mid- 
 winter give the least results, and those in midsummer the 
 greatest, the range is twice as great, which may be attrib- 
 uted to the higher temperature of this country. The mean 
 temperatures in the hottest and coldest months at Geneva 
 and the Grand St. Bernard are respectively 64° and 31° at 
 the former, and 43^ and 15^ at the latter. In the Sierra 
 Nevada we have, in July, at Sacramento, 70-.0, and at the 
 summit, about 7,000 feet high, 5o°.o, and in January they 
 are 48^.9 and 26^.3, respectively. 
 
 But unfortunately for the development of any law of 
 practical importance that can be of use in making a table 
 of corrections to be applied to results obtained in different 
 months so as to reduce tliem to the yearly mean, the range 
 in the variation of these results seems to depend more u[)on 
 the temperatures of the stations than upon the difference of 
 altitude between them. For example, the range between 
 the winter and summer results, as develoi)ed from observa- 
 tions taken at Sacramento and Fort Churchill, is 200 feet. 
 
45 
 
 while the diiference of altitude is about 4,200 feet, and that 
 from observations at Sacramento and summit of the Sierra 
 Nevada at Hope Valley, about 7,000 feet, is 118 feet. This 
 last result, however, is from observations in the single 
 months of July of 1860 and January of 1804. 
 
 From all that has been previously pointed out on this 
 subject, we are certain that hypsometrical results generally 
 give results which are considered greater in midsummer 
 than in midwinter, but the amplitude of this variation de- 
 pends so much upon the climate of the two stations that no 
 definite rule can be given concerning it. 
 
 COiNCLUDlNG REMARKS. 
 
 In the previous pages I have explained the method which 
 I have recommended to be adopted in i)roduciug the best 
 hypsometrical results, the essentic^l points of which are to 
 prepare the barometric observations beforehand by correct- 
 ing them for the horary oscillation of the barometer, and 
 then to use the mean daily temperature during the period 
 in which the observations were taken, whether it be short 
 or long. 
 
 Prof. J. I). Whitney, formerly the State geologist for the 
 State of California, with a full knowledge of my method as 
 explained in Xo. 15 of the Professional Pa[)ers of the Corps 
 of Engineers, has adopted another method, and has explained 
 it in a work entitled "Contributions to Barometric Hypsom- 
 etry, with tables for use in California." In the first chapter 
 the distinguished professor gives an able and learned dis- 
 cussion of the various forms of the barometric formula 
 which have been used, and comes to the conclusion that no 
 change in any of the constants is advisable. He says, in 
 the beginning of his third chapter, that my formula, or that 
 of Guyot (which is almost identical with it, and one or the 
 other of which was used by him and his assistants during 
 the geological survey of California), " is the one which leads 
 
46 
 
 most directly to practical results, and upou which the chief 
 dependence is to be placed/' 
 
 Tbe third and last chapter of this work is also interesting, 
 but the second one is the onl^- one which explains his method 
 of treating barometric and thermometric observations. He 
 had obtained observations during three years at Sacra- 
 mento, near the sea-level; at Colfax, on tbe slope of the 
 Sierra Nevada, at an altitude of 2,414 feet; and at Summit 
 Station, at an altitude of 6,951 feet. The altitudes were as- 
 certained during the leveling for the railroad. Tbe obser- 
 vations were taken at 7 a. m., 2 p. m., and 9 p. m. From 
 the monthly means of the barometer and thermometer at 
 those three hours, he ascertains how much the mean hypso- 
 metrical results at each of those hours in each month at each 
 of the three stations differ from their altitudes as given by 
 the level. He then forms a table of corrections to be ap- 
 plied to such results from observations taken in tbe field 
 during those months and at those hours, and by a simple 
 interpolation assumes corrections for the intermediate hours 
 between 7 a. m. and 9 p. m. He uses the actual observa- 
 tions of the barometer and thermometer without other cor- 
 rection than that of reducing the barometer to 32° F. From 
 tbe monthly menu i)ressure and temperature at each of the 
 three hours, he deduces bis table of corrections to be ap- 
 plied to each hour of the day and month of the year. 
 
 My method is to eliminate beforehand all causes of error, 
 as far as possible, by first applying a correction to the bar- 
 ometric readings so as to get rid of the effects of the 
 horary oscillation, and then to eliminate the effects of the 
 horary movement by using, instead of the observed tem- 
 perature, the mean daily air temperature for tbe period 
 during which the barometric observations were taken. 
 
 It is evident to me that Professor Whitney's method must 
 produce more "maximum errors" than mine; because tbe 
 periods of the barometric and tbermometric observations, in 
 
47 
 
 the field are not the same as the monthly })eiiods of obser- 
 vations nsed by him in preparing his table of corrections. 
 Observations in the field are usually for a short period ; his 
 table of corrections is from the monthly means. During a 
 barometric reconnaissance, the altitudes of most of the sta- 
 tions on the line are approximately determined from single 
 observations. In forming his table he has used the monthly 
 mean of the thermometer at the three observed hours. 
 Xow it is well known that during a month the range of the 
 thermometer during the twenty-four hours may be twice, 
 three times, and even four times as great in one day as in 
 auother. If observations of the barometer had been taken 
 during one day only, it might have happened that the ther- 
 uiometric curve (if the observations had been plotted) for 
 that day was a maximum or a minimuai, and the horary 
 thermometric curve from the actual observatiotis would be 
 quite different from that obtained from the thermometric 
 monthly- mean. With regard to the barometer, its horary 
 oscillations from day to day during a month at the same 
 place are so nearly alike that no material error is made by 
 adopting either the horary oscillation for the month or that 
 for the period of observation. 
 
 Within the limits of the State of California almost every 
 variety of climate is to be found. There is the moist and 
 uniform climate of the coast, and the arid and tropical cli- 
 mate of the Mohave and Coiorado deserts. There are vast 
 plains near the sea level, and a number of mountain peaks 
 between fourteen and fifteen thousand feet above it. When 
 we consider the greaL change of temperature during twenty- 
 four hours in a considerablj portion of the State, the great 
 variation in the range of that temperature in different days 
 and in different localities, and the totally different character 
 of the horary oscillations of the barometer at an upper and 
 lower station, varying as these do with altitude, latitude, and 
 climate, and, more than all, local peculiarities of climate, it 
 
48 
 
 can be easily umlerstood that it is impossible to adopt, with 
 good results, a table of corrections suitable to every part of 
 such a State as California, or even to a considerable portion 
 of it. 
 
 My method is quite as easy of api)lication as that of Pro- 
 fessor Whitney, except that itre<iuires a certain amount of 
 intelligence in the computer, who has to i)repare the obser- 
 vations and apply the corrections before the numbers are 
 used in computing the difference of altitude. This might be 
 considered by some to be a disadvantage, for with bis 
 method any ignorant man, possessed of a small amount of 
 knowledge of arithmetic, can become a baroujetric compu- 
 ter, by following certain prescribed rules. But I take it for 
 granted that all persons engaged in barometric reconnais- 
 sances of any importance are endowed with quite enough 
 intelligence to properly prepare barometric and therrao- 
 metric observat:ions for computation by my method. 
 
 It is of the utmost importance on a barometric reconnais- 
 sance that we should know as nearly as possible the probable 
 maximum error, because the results are only to be fully 
 trusted up to that limit. The method which produces the 
 least maximum error must then be considered the best. I 
 wish now to show, from the computed results of observa- 
 tions at my command, that the method adopted by Pro- 
 fessor Whitney does actually produce more maximum error 
 than mine. 
 
 For that purpose I have used ten days' observations at 
 Sacramento, Placerville, Strawberry Valley, and Hope Val- 
 ley, in August. Observations at those four stations are the 
 only ones at my command which are suitable for the i>urpose 
 where full hourly observations were taken. I calculated 
 for each of the three hours during the ten days the differ- 
 ence of altitude by the two methods. 1 then made fiom 
 them a table of maximum and mean errors, which is here- 
 with submitted. 
 
49 
 
 It will be seen that the amount of error in hypsometrical 
 results is over forty per cent, more by Professor Whitney's 
 method than by mine, and any intelligent man who has 
 carefully studied the two methods can easily appreciate the 
 reason. 
 
 Table VIII. — Comparison of barometric 7'esuJt.s by Professor Whttneifs and 
 Colonel lilUiamson's methods, from observations taken at 7 a. m., 2p.m., 
 and 9 jj. ni., during ten days of August, 1860. 
 
 SACRAMENTO AND HOPE VALLEY. 
 
 
 Max. error. 
 
 Max. error. 
 
 Mean error. 
 
 Grand mean. 
 
 Whitney's method 
 
 Williaiusou's method 
 
 + -249. 7 
 + 155.7 
 
 — 214. 5 
 
 — 144. 2 
 
 61.6 
 54.5 
 
 6, 976. 9 
 6, 961. 7 
 
 
 + l.CO 
 
 — 1.49 
 
 1.13 
 
 
 
 
 SACRAMENTO AND PLACERVILLE. 
 
 
 + 
 + 
 
 37.9 
 
 •21.9 
 
 — 36.8 
 
 — 24.6 
 
 13.5 
 13.0 
 
 1, f97. 
 
 Williamson's method 
 
 1,918.4 
 
 
 + 
 
 1. 36 
 
 — 1. 50 
 
 1.04 
 
 
 
 
 PLACERVILLE AND STRAWBERRY VALLEY. 
 
 Whitney's method 4-194.4 
 
 Williamson's method -|- 143.0 
 
 + 1.36 
 
 — 94. 1 
 
 — 51. 5 
 
 — 1.66 
 
 42.1 
 20.1 
 
 3, 715. 
 3, 731. 6 
 
 STRAWBERRY VALLEY AND HOPE VALLEY. 
 
 
 + 64.5 
 + 49.2 
 
 — 4.5.3 
 
 — 41.0 
 
 21.3 
 21.0 
 
 1,362.3 
 
 Williamnon's tuethod 
 
 1, 368. 6 
 
 Ratio ... 
 
 + L31 
 
 — 1.10 
 
 l.Ol 
 
 
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