formed by Contact of a Liquid with a Cylinder. 841 



Also, when y=h, p = tan^— — cots (vide fig. 1) giving 



h 2 =2a 2 (l—sini)j .... (viii.) 



the usual expression for the height to which a liquid rises 

 against a plane wall. 



Now write (vi.) in the form 



a 2 p dp a 2 V 

 (1 +p 2 )W dy + ~7' %/T+f -ft ' ■• " W 



and substitute in the second term on the left-hand side of 



(ix.) the value of — / given by (vii.). 



V 1 -+ f 



We have at once from (vii.) 



\/4a 2 — y 2 

 2a* -if 



P=±!/ \*2 J > • • • '• • (x.) 



and if the angle of contact be acute y 2 is always less than 2a 2 

 (vide equation (viii.)); also from fig. 1, p is continuously 

 negative. Hence in (x.) above, the negative sign must be 

 chosen, and 



P y \ f ±a 2 — y 



Substituting in (ix.) we have 



a *P d P / y </±a 2 -y 2 \ 

 (H-p 2 ) 3/2 "V 2r )**> 



which, integrating, and remembering that when y = 0, p = 0, 

 gives 



/ 1 \ 4r/ 3 7j 2 1 



4-"vn?)-^=l-67.^ 2 -^ 3/2 - c«) 



As before, when y=h, p= — cot i, giving 



a2( l_ smz) __ = ___^__J . . (X1 .) 



In this equation, 7i, r, and a 2 are capable of experimental 

 determination, and i can therefore be calculated. 



Equation (xi.) can be put into a very simple form by ex- 

 panding the quantity under the radical sign, and neglecting 



