404 Mr. T. Proctor Hall on New Methods of 



the increase of weight is p times the volume of cylinder and 



of liquid raised above the level surface. If r be the radius of 



the cylinder and w the increase of its weight, in grams, then 



(fig. 6) for unit length of the cylinder, 



wg = 2T sin a + %rpyg sin a + r 2 pgu — r 2 pg sin a cos a, 



or f c 2 ~] 



W = P \ 2" sina + 2r3/sina + r' 2 a — r 2 sinacosa f , . . (4) 



where a? y is a point of contact of the cylinder and the surface 

 film. 



Fig. 6. 



'<X 



-X 



We have also (fig. 6) 



h=y+r— r cos a, . . . . 



•'• h =y+-!jy 2 • • • • fr o m ( 2 )> 







(5) 



■••■^^(vV + Sf*-*) (6) 



Equations (4), (5), and (6) are sufficient to determine iv 

 when h, r, p, and T are given. 



The condition that w shall be a maximum is that dw/dh = 0. 

 Now 



dw # d* 

 'dA 



dA 



da 



da r 



= d7/\ 



c «~ r a . « crsina 



5- cos a + 2ry cos a + 2t* sin a — . \- 2r 2 sin 



J 4y 



in 2 aV 



