. Mécanique céleste . X, ij, z ; these partial forces will be, by the preceding article,! s.Çfn^; ^.fc^; sr-^- (Pi-, ]-, s s s \ox J \àyJ \ùz [13] [12a][13o] Partial Diftoren- lials. * (13i) Let jfiTbe the origin of tlie co-ordinates, ! ,-X( A the origin of the force S, c the place of tlie pointM. Draw, as in tlie last note, tlie lines AD, Dd, dc,parallel to the axes x, y, z, represented by KX, KY,KZ, respectively, and complete die parallelopipedABCD abed. Continue the lines bn, BA, cd,CD, tin they meet die plane YKX, in die pointse, E, f, F. Draw die lines fF, e E, to meet diea
. Mécanique céleste . X, ij, z ; these partial forces will be, by the preceding article,! s.Çfn^; ^.fc^; sr-^- (Pi-, ]-, s s s \ox J \àyJ \ùz [13] [12a][13o] Partial Diftoren- lials. * (13i) Let jfiTbe the origin of tlie co-ordinates, ! ,-X( A the origin of the force S, c the place of tlie pointM. Draw, as in tlie last note, tlie lines AD, Dd, dc,parallel to the axes x, y, z, represented by KX, KY,KZ, respectively, and complete die parallelopipedABCD abed. Continue the lines bn, BA, cd,CD, tin they meet die plane YKX, in die pointse, E, f, F. Draw die lines fF, e E, to meet dieaxis KX perpendicularly in H, G. Then, by dieabove notation, die co-ordinates of tlie point A areKG=^a, GE=^b, EA = c. The co-ordinatesof tlie point c are KH=x, Hf^=y, fc^z, and Ac = s. From this conslrucdon itfoUows that AD = EF^GH=^KH—KG=x — a; Dd=Cc = Ff^Hf—HF=Hf—GE^y — b; DC^OTdc=fc—fd^fc — EA = z — c, substituUng these values in A c = V A D^ ^ D d^ -{- d c^, found as in the last note, it becomes. s = ^/{x — af-\-{y—bf-\-{z—cf, as in [12]. f (13c) If the line A c represents the force S, it niiglit be resolved, as m note 13«, intotlii-ee forces, AD, D d, dc, pai-allel to the axes x, y, z, respecdvely ; consequently diese du-ee forces will be represented by S Ac S. —r— ; ; which, by substituting the values of Ac, AD, Dd, dc, given in the last note, become S. -«), S {y-b). S. {Z-C) s s s respectively, as in [13]. They may be put under a different form, by means of die partialdifferentials or variations of s. The jntrtial differendal of a quantity denotes its differentialsupposing only part of the quantities of which it is composed to be variable. Thus the partial differential of s ^V ÇIx—a]dx IS ? ^T ^~ (y — ^T ~H (^ — ^) taken relative to x. x only being considered variable, this is usually denoted by f — j dx including the quantities considered as variable between the parentheses. Li the same I. i. .^^O COMPOSITION OF FORCES. (~
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