Mr Galbraith's Barometric Measurements of Heights. 319 



H = {48400+ 60 (i! + }/5«— (2.42 4-3(j^'} ('• — ■'') • • (12.) 

 The terms of s will be readily obtained for heights exceeding 2000 or 3000 

 feet when they begin to become sensible, by deducing them from each other. 



Thus j> 1 , = /5, whence is derived /3', and — "5 ~ >'> 

 Multiply by g>\ . ^= S, 



- = e, &C. 



Hence y + 'S+i + Sec. = s = the decimal by which the first approximation 



must, when necessary, be multiplied to obtain the correction for great heights, 



where alone they are required. 



The formula in my last paper may be deduced from (12) by rejecting s, 



t + t' 180° , . , . 



and assumuig g^^ = g^ = 0.6, which gives 2.4 + 0.6 = 3, the coefficient 



of (t — 7'). It is obvious that 180° for the sum of the temperatures, or 90° 

 for the mean, will generally be too great. Indeed, -^^ will at a medium be 



about 300"= 0.3% and 2.42 + 0.33 = 2.75 feet, about a quarter of a foot less 



than 3 feet, so that the error from this source must be small. By making 

 these changes, formula (12) will become nearly the same as formerly, or 



H = {48400+ 60(< + <')} B^— 3(r — t') . (13.) 



In the former paper 48000 was obtained partly by being derived from Roy's 

 expansion of aii-, and partly by rejecting the three last significant figures, 

 from a desire to select round numbers easily recollected. However, if the 

 figures 48 be repeated, thus making the constant 48480, it would be as easily 

 recollected, and the results, if under 3000 or 4000 feet, would be sufficiently 

 correct for most purposes, if the computer finds it inconvenient to use the 

 more complete formula (12). 



General Rule. 



This rule is derived from formula (13), and is intended for those only wlio 

 are not very conversant with algebraic symbols. 



Those who are, will, in all considerable heights, prefer formula (12). 



1. Take the sum of the temperatures of the air at both stations, as shown 

 by the detached thermometers, and multiply that sum by CO. 



2. To this result add the constant number 48400, (or even 48480 as men- 

 tioned above), the sum will be the correct coefficient. 



3. ISIultiply the correct coefficient just found by the difference of the 

 heights of the mercurial columns in the barometers at the two stations, and 

 divide the product by their sum, the quotient will lie the approximate height. 



4. Take the difference of the temperatures of the mercury at the top and 

 bottom indicated by the attached tliermometers, which multiplied by three, 

 will give the correction to be subtracted, if, as is gcneraUy tlie case, the tem- 

 perature of the upper station be the colder, otherwise it must Ijc added, and 

 the result will be Ihc true height. 



