526 



NATURE 



[^April 1, 1884" 



to tell us whether it is in use in the Orkneys and the Hebrides, 

 or elsewhere, where the people still spin their own wool. 



Cosmopolitan 



MEASURING HEIGHTS ' 

 'X'HE system of barometric hypsometry described in 

 -'■ this treatise — first communicated in 1877 to the 

 PhilosophicLil Society of Washington — was suggested bv 

 the needs of the geographical surveys conducted by the 

 Government of the United States in the mountainous 

 region lying between the Great Plains and the Pacific 

 Ocean. The system proposes a ne.v method of observa- 

 tion and computation. It is not of universal application, 

 but the range of work to which it is adapted is large and 

 deserving the attention of the geographer. 



The method of obseiiuiiion is as follows : — Two base 

 stations are established — one high, the other low. Their 

 difference in altitude is made as great, and their horizontal 

 distance as small, as practicable. Each station is fur- 

 nished with a barometer only, and observations are made 

 at frequent intervals through each day. At each new 

 station a barometer is observed, ani no other instrument. 

 The difference in altitude of the two base stations is 

 determined by spirit level, and forms a vertical base by 

 which all other intermediate altitudes are coinpitted as 

 follows: — The readings, being corrected for inde.x error 

 and te nperature of instrument, are collected in groups of 

 three, each observation at a new station being accom- 

 panied with the simultaneous observations at the two base 

 stations. The resulting difference of heights of the lover 

 and the new station is then computed by the following 

 formula, in which if L, U, N represent the height of the 

 lower, upper, and new slations respectively, and /, n, n 

 the simultaneous corrected barometric readings at the 

 same stations, and also let B — U - L, A — N — L, and 

 B — A = U - N ; then it is found approximately that — 

 jl =B log I - log « , A(B - A) 

 log I -\ogu D ■ 



where D ^ 490,000, if A and B are rec'<oned in feet ; or 

 149,349 if in metres. This formula consists of two terms 

 — the first, or logarithmic term, is the principal one ; the 

 second, or thermic term (so callei), is always very small 

 in comparison with the first — so that it suffices to substi- 

 tute for A in the second term the value of the first. The 

 following e.\ample of computation further illustrates the 

 formula : — 



In August 1872 the simultaneous mean pressures at 

 Sacramento, Colfax, and at Summit were 29 S79, 27'475, 

 and 23'336 inches respectively, and the altitude of Summit 

 above Sacramento is 6989 feet. Required the altitude of 

 Colfax above Sacramento. In this case : — 

 /= 29-879 loT / = 1-47537 



n = 27-475 'og « = i'43**94 



" ~ 23 -336 Ijg u =. 1 -36S03 



log / - log « = 0-03643 

 log / - l.>- I, = 0-10734 

 log (0-03643) = - 2-56146 

 log (0-10734) =- - 1-03075 



Difference = - I -53076 



log j9 =3-04441 69S9 =/)' 



sum = log (first term) = 3-37511 ..2372-o = ru-rtt term = ^ nearly 



[mately) 



log (B - A) = 3-6644 ...46J7 = (Z> - A) (ipproxi- 



colog (490000) = - 6-3098 ... 



Siiui = I '3493 = log 22 4 ..the second ter.n 



Requir&l difference of altitude = 2394 4 feel. 



^ " A New Method of Measuring Heights by Means of the Barometer." 

 By G. K. Gilbert. Extract from the Annual Report of the Director of llie 

 U.S. Ge.ilogical Survey, i88o-8i. (Washington: Government Printing 

 Office, 18S2.) 



The author, considering the direct calculation of the 

 second term inconvenient, has calculated a table of 

 double-entry showing the value of this term as a correc- 

 tion of the first term for every 100 feet of B and of the 

 approximate value of A, which is appended. A graphic 

 table is also appended (plate Ixii.) for computation of this 

 therijiic correction. However, as the table of logarithms 

 must be to hand, the direct calculation does not seem to 

 present any particular inconvenience. 



By thus abandoning the thermometer and psychrometer, 

 and employing the barometer alone, the author reverts 

 to elementary principles upon wdiich all barometric 

 measurements depend, and presents in his first chapter a 

 review of the purposes and conditions of barometric hyp- 

 sometry in general, and although not presenting anything 

 new, is yet very interesting. The principle which under- 

 lies the measurement of heights by the barometer is 

 exceedingly simple, but its application is fraught with 

 difficulty. The law of the relation of altitude to atmo- 

 spheric pressure is consequent on the law of the com- 

 pressibility of gases, and is simply a certain multiple of 

 the logarithm of the air-pressure. But there are numerous 

 modifying conditions which must be considered in the 

 application of this law. After describing the construction 

 of barometers, of which the mercurial is both the oldest 

 and the most accurate, the author passes to the con- 

 sideration of the modifying conditions of the tempera- 

 ture and humidity of the atmosphere which are ever 

 varying, so that the static order of densities is broken, 

 currents are set in motion, and the circulation and 

 the inequalities of temperature conspire to produce 

 inequalities of moisture. Every element of equilibrium is 

 thus set aside, and the air is rendered heterogeneous in 

 composition, temperature, and density. Moreover, the 

 disturbing factors are so multifarious and complex that 

 there is infinite variety of combination and infinite variety 

 of result. Approximate solutions of the problem are 

 therefore only expected ; and the author, after describing , 

 the disturbing factors — gradients, temperature, humidity— 

 and the various devices for the elinrination of the errors 

 due thereto, and other general devices for diminishing 

 hypsometric errors and the relative importance of different 

 sources of error, arrives at the conclusion that the diffi- 

 culties which inhere in the use of the barometer for the 

 measurement of heights are so numerous and so bafiling 

 that there is no reason to hope they will ever be fully 

 overcome. The best that can be done is to mitigate 

 them, keeping in mind that the barometric method must 

 not be so elaborate that its cost will approach that of the 

 use of the spirit level. The problem, therefore, which 

 occupies the attention of those who have occasion to use 

 the barometer in extended surveys is how to secure the 

 best result from a single observation at a new station 

 combined with a series of observations at one or more 

 base stations. 



The author next proceeds in the second chapter to 

 develop his tiew method, as explained above, and deter- 

 min s a mean value of the thermic constant, D. In 

 Chapter III., on " Co;nparative Tests," various tables are 

 given of the coaiparative results obtained by means of 

 the new method and the ordinary and other empirical 

 methods in use. This compirison shows the advantage 

 of the new method in a reduction of one-half the error 

 of the ordinary method, and one-fourth that of the 

 empiric method. Nevertheless there is a considerable 

 range of special cases in which the ordinary method can 

 never be superseded. 



Having shown that the new methoi is theoretically 

 plausible and practically successful, the author considers 

 in the fourth chapter the nature of pissible improvements. 

 This chapter, and the following fifth chapter on the limits 

 of utility, and the sixth on the work of others, are more 

 specially addressed to the students of hypsometry. This 

 interesting work closes with a short chapter, the seventh. 



