106 CELESTIAL MECHANICS. I. i. 3. 



{(;>+(-D^+'}(-^)^'-''T-"^ 



ex, z — c 

 7 * P 



— ; . ; and i/— 5,and z — c afford, in a similar man- 



ner, the terms /3d?/ and ydz.] ** We obtain, therefore, the 

 value of (]/>, whatever may be the form of the equation of 



the surface, from the equation dj?zzdM : s/\ ( —j^ + ( J~)^ 



+ (— V f , calling «dj: + i3dy + ydz=: dii, which must be ad- 

 missible, since the differential equation of a surface must 

 be a complete fluxion: and employing the usual mode of 



notation for the partial fluxions, in which -r-=:a, — zi^and 

 ^ d:c di/ 



— — y\ and Pdp, the efficacy of the force P, will be ex- 

 dz 



pressedbyPd«:v{(g)^ + (J-P^ + ©^}," the .8„ 



of the Mecanique Celeste.] 



[255. Definition. The rotatory pressure 

 of a given force, with respect to any axis, is 

 the product of its magnitude into the distance 

 of its Hne of direction from that axis.] 



9<oQ, Theorem. The rotatory pressure of 

 the result of any number of forces is equal to 

 the sum of the rotatory pressures of the same 

 forces taken separately, with respect to the 

 same axis. 



