7 Capillary Attraction. 



Yx Yy Yz 

 rections of x, y, z, gives — ? — > — > for the force of F in those di- 



Yx ^ Yy Yz 



rections; put — = — X, — = — Y, — = ~Z; hence Xx-{-Yy-\-Zz 



4-Fr=0j (c) ; X, Y, Z, being fictitious forces, which are equal res- 

 Fa: Yy Yz 

 pectively to — ' — ' — ' and acting directly opposite to thera, so that 



the particle is kept at rest by these opposing forces ; (c) is similar to 



d^x d-y d^z 

 (c) given at page 332 of the last Journal; by changing -r-^ -7:7' -777' 



into X, Y, Z, respectively, that formula becomes (c) given as above. 

 In like manner for another force F' acting on the particle, I have a 

 similar formula, 'X.'x' -\-Y'y' -\-7a'z' -\-Y'r' ~Q, [d) ; and so on for the 

 forces F^', Y'", &;c. to any number of forces whatever ; by accenting 

 the letters once for F', twice for Y", and so on ; the co-ordinates x, 

 y, z, x', y', z', &1C. being respectively parallel to each other. Now 

 by adding (c), {&), he. and taking the variation, he. as at pages 332, 

 333 of the last Journal, I have (X+X'-[- &c.)5^^+(Y+Y'+ &c.)<5?/ 

 + (Z+Z'+ &LC.)5z+YSr-i-Y'Sr'+ &c. =0, (G) ; this is the equa- 

 tion of connexion between the actual and fictitious forces in the case 

 of the equilibrium of the particle. Hence supposing that the parti- 

 cle is kept at rest by the actual forces alone, the fictitious forces must 

 destroy each other ; hence (G) becomes, by the omission of the fic- 

 titious forces, YSr-\-Y'Sr'-\- he. =0, (H) ; which is the formula of 

 statics in the case of the equilibrium of one particle of matter. (H) 

 can be extended to the equilibrium of a system of particles in the 

 same manner that (B) has been extended to the motion of a system 

 of particles m, ,m, etc. 



Art. XIII. — On capillary attraction; 5?/ Prof. Theodore Strong. 



TO PROFESSOR SILLIMAN. 



New Brunswick, Jan. 27, 1830. 

 Dear Sir — Should you think the following method of considering 

 the phenomena of capillary tubes of any importance to the cause of 

 science, you will oblige me by giving it a place in the Journal. 



Yours respectfully, T. S. 



I suppose the internal surfaces of the tubes to be either cylinders, 

 or right prisms, made of the same kind of glass, and immersed in a 

 given fluid of indefinite extent. I also suppose the internal surfaces 



