70 CapUlary Attraction. 



Fx Fy Fz ^ , ■ ^ -^ . \ 



rections of ooj y, Zj gives — > — ? — ? for the force of k m those di- 



Fx Fy Fz 



rections; put — =-Xj — = — Y, y=~Z; hence Xx+Yy-^-Zz 



-|-Fr=:0, (c) ; X5 Y, Zy being fictitious forces, which are equal res- 

 Fa: Fy Fz , . , ■ . 



pectively to — 5 — ? — ? and acting directly opposite to them, so that 



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



d^x d^'y d^z 



(c) given at page 332 of the last Journal; by changing -^9 ^^j' -^p 



into Xj Y5 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, XV+YY+ZV+FV=0, {&) ; and so on for the 

 forces F'^, F'^^, &:c. to any number offerees w^hatever; by accenting 

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

 y, Zy x% y', z', he. being rcspecnvely parallel to each other. Now 

 by adding (c), {&), &:c. and taking the variatlonj fee. as at pages 332, 

 333 of the last Journal, I have (X+X^+ &c.)'5x+(Y+Y'+ &c.)5y 

 + (Z-!-Z^+ &c.)oz + F^r+F%^+ &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 j hence (G) becomes, by the omission of the fic- 

 titious forces, FoV+F^cV-f. &:c. =0, (H) ; which is the formula of 

 statics in the case of tlie 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; by Prof- Theodoke Stbong 



TO PROFESSOR SILLIMAK. 



New Brunswick, Jan. 27, 1830. 



Dear Sir — Should yoti think die 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 



\ 



