294 ON CAPILLARY ACTION; 



the base of the space the two parallelopipedons leave be-^ 



/ X (c-i-c') 



tween them will be : thus, h being the mean 



height of the fiuid raised, we shall have V=h lx ■■■ ■ , and 



consequently h~q. We may determine too from the pre- 

 ceding principles what will take place, if the prisms be 

 immersed wholly or partly in a vessel filled with any num- 

 ber of fluids, and in the case of their being inclined to the 

 horizon. 

 Where they are " The data being the same as in the preceding theorem, 

 maS s ent if the tW0 P aral3elo P i P edons be °f different materials, put-- 

 ^ for the force of attraction which that of the greater has 

 for the fluid, and?, for the attractive force of that of the 



smaller, we shall have, V=-^-^ — — x c-f- ? ' — — xc': 

 g D gD 



so that, if we put q and q , for the elevations of the fluids 

 in two very narrow cylindrical tubes of the same interior 

 radius /, formed of these two materials respectively, we 

 shall have V=\lx (qc-\-q J c") 



This theorem too is demonstrable in the same manner as 

 the first. It is easy to perceive, that by the same princi- 

 ples we shall obtain the volume of fluid raised above the 

 level in a space included between any number of vertical 

 planes of different materials. 

 Attraction on It follows from the preceding theorem, that the volume 

 V of the fluid raised by capillary attraction exteriorly to a 

 prism immersed in a fluid at its inferior extremity, is equal 



2e — e' 

 to — ~-jj — xc=f/ qxc; c being the outer circumference 

 g Lf 



Hence increase °* tne P rism « The increase of weight of the prism, owing 



of weight, to capillary attraction, is equal to the weight of this volume 



-ar diminution, of fluid. It changes to diminution, if q be negative, and 



then the prism is raised by capillary action. If the base of 



the prism be a very narrow rectangle, of which a is the 



longer side, and I the shorter, putting i for its height, its 



solidity -will be a i I, and its circumference, c, will be 



2 a-\-<2l; and the volume V of fluid depressed by capillary 



action "will be a q lx ( l-\ ) Putting k then for the 



ratio 



the outside of 

 a prism 



