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Recueil de travaux offerts par les auteurs à H. A. Lorentz à l'occassion du 25me anniversaire de son doctorat le 11 décembre 1900

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Wlience by determiuants tlie condition tliat the accelerations of [i»,2] [£ and [», v2] should vanish gives

[(X, + li)2] , 0 , m, [p]

\wi 2]: Kï + PL '"2W

2[(jr,4-/f)(A',—«)], W

[(A', + 7i')2] > — [?i + p] > '"i M

= [»V>22]: [(A2—tf)2] , <> , '"»H

2[(A, + «)(A2— A)], [p] + «iKj + p]

[(A, + -ft)2] ,— [*,+#>], 0 = hi)j]: [(A2 — -ft)2] , 0 ,-[?2+p]

2 [(A, -f- ii) (A2 — -ff)], [p] • [p]

— [5, +p], 0 , «,[/>] = 1 : 0 , — [5, + p]» «>M

[p] , [p] , W'2 [?l + p] m\ ^ C')

Tf wc write these equations in the abbreviated form

[mx vt 2] [m2 t'22] __ [('i y-i] __ 1

A ~ B 11 C

tlien for any value of >. we obtain

A tti- {- 2 /. m, »w2 11 -\- t' M m.L [(•», + *■» ''•-)■]= £

and since the left hand side is essentially positive the condition for energy-equilibrium to be possible is tliat the right hand side must be essentially positive. Hence

(I) A and li must be of the same sign as (',

(II) AH > «, m2 li1.