MEASUREMENT OF HEIGHTS. 523 



where /3 = 0-0067407 



a = 0-0279712 

 c — 0-0000625826. 



If we now multiply the differential equation (8.) bv 



JL fdJL 



jq/V e 



we can integrate the product, namely, 



Laplace's assumption of the law of the change of temperature 

 between two elevations, at each of which the temperature is given 

 by observation (Art. 2.), is 



^pr =— -^ at. 

 E I 



If we substitute this, and also the expression above given of 



(j9,), we have 



c=;. . io~ '^' ^ ^^iiiiii^ Ao(" - K> " ^%^ 



fx.1' A J 

 By this equation we obtain the relation between the pressures of 

 the atmosphere P and P' at the heights h and A', namely, 



P. 10 "^^-PMo "^ 



wl' i J „ 



,. -, X.. dt. 



If we write T for g^ (t + t'), and T + s for t, then the integral 

 still to be sought is changed into 



-10' .Kf''-'^''' 10^ " ^ dz. 



J -i(^-T') 



If, for brevity, we write 



u = - j^—. — 10 f lu az, 



We have thus, 



2 k 2k ^ 2 * 



P. 10 '' - P'.IO ' ' = — 10 ' • , 



