MEASUREMENT OF HEIGHTS. 547 



supposing a = «' = ^ ; if a different value be supposed for a. 

 and «', log (« + «') must be added. Hence is obtained the ar- 

 gument of Table IL, which contains log V. Table III., with 

 the argument ip = the latitude, contains 



lo!? G = l02" 



« ^ 1 - 0-0026257 cos 2?)' 



which formula rests on the value of the increase of the length of 

 the seconds pendulum from the Equator to the Poles, deduced 

 by Mr. Baily from the combination of all the known pendulum 

 observations. Trans. Ast. Soc. vol. vii. page 94. 



The sum of B and of the numbers taken from the three Tables, 



is = log -Ih' — h 1 >; to obtain from hence h' — h, 



we must add — and subtract — , which are both given by Table 

 IV., which is to be entered with A' and with h. 



It may be convenient to recapitulate the notation and rules : 



b, b' are the heights of the barometer, read off on a scale divided 

 into Parisian lines. 



t, t' are the heights of the centesimal thermometer attached to 

 the barometer. 



T, t' are the heights of the centesimal thermometer in the free 

 air. 



a, a! are the degrees of saturation of the atmosphere with aque- 

 ous vapour. 



The calculation of the difference of height of the points where 

 these observations have been made, requires 



1. log ^», = log i - ^ . 0-00007 ; log bj = log b' - t' . 0-00007. 



2. B = log {log ^, - logb/}. 



3. log V and log W, which, with the argument t + t', are to be 



taken out of Table I. 



4. log V, which is given in Table II., with the argument 



5. log G, which is given in Table III., with the argument of the 



latitude = (p. 



6. The log of the approximate difference of height = B + log V 



-f logV' + logG. 



