Mécanique Céleste Vol.4

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p = ^II-^ . (1 + constant). [8295ciJ When r=a, and p:=(p), this becomes, log.( P) = ^S)-{pU A _|_ constant) ; [8295e] subtracting this from the preceding expression of log.p, we get, log.f = ^^".f^-lV [8295/] (P) (P) \r j Multiplying the second member of this expression by log.c=l [8290'], and then reducing to natural numbers, it becomes as in [8296].
* (3872) The weight (p) of the homogeneous column of air /, is found by multiplying its heiglit / by the gravity (^), and by the density (p); hen
...ce we get (jj) = (^).(p)./, as in [8298]. From this we get -2_i_ =: — j and by multiplying it by a.f^ — Ij =—as [8284], we obtain [°-. —If a. ^?^ = —J- Substituting this last expression in [8296], we get [8299].
f (3873) In order to develop the radica' in tlie denominator of [8286], we shall put / _ »£\ [8300a] for brevity D^^cos.^e — 2a. \I — c '/-j-2i.sin.^e ; and we shall get by development, using the value of -~ [8299], if ) I— s \/cos.2e— 2a.('l— -^^ + (2*— s^) \ (f )/ 1 s.{D — ^5.


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