268 Prof. Potter on some properties of the Air Thermometer. 



Again, the adhesion between the surfaces of the liquid and 

 the tube, which is proportional to those surfaces, 



= Jc.27rr(a-\-b — x), 



if k is the adhesion of unity of the surfaces. 



Taking this adhesion as a retarding pressure, and putting for 

 k its value in terms of the pressure at a depth z of the liquid, as 

 in hydrostatics, or 



k=gpz } 



and also putting ~=ft, which must be a known number, we have 



whence, since a = 7rr-, 



jjg._ gx /-. h — a\ 2irgzr 

 dp ~~a + b-x\ + T+~cc) ~aT • 



d*x ( f h — a\ /. h — a\ a + b \ 

 Multiplying each side by 2 -=- and integrating, we have 



j-„.^j{ 2 , + (,4)-(i + ^}*, 



=&{(2» + (l+ J))*'+(l + J)(«'+6) log, (a + i-*)} +0, 

 and v = when x = a; 



.-. 0=2 i7 {(2» + (l + J))«+ (l+ J) (a + J) log, (5)} +C, 

 and .'. generally, 

 v*=2 S {(2n+(l+fyy*-a) +(l +.J)(a+J) log.(i±^)}. 



Prom the correction of the integral we have in all cases v — 

 when x = a; and the other value of x, where v is again =0, 

 is obtained by trial and successive approximations from the 

 equation 



, (a + b—x\ / 2n \{a—x\ A 



It will be seen that this equation differs from the one correspond- 



