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For the function of elements C, we obtain the following approximate expression C1 for that function, of the form supposed by our theory:  1 (λ1 − p1 )2 + (λ2 − p2 )2 (λ3 − p3 )2   C1 = − +   2t µ2 ν2    t 1 − {(λ1 − p1 )p1 + (λ2 − p2 )p2 + (λ3 − p3 )(p3 − 3 gt)}  2    3 4 5  t t t  2 2 2 2 2 2 2 2  + {µ (p1 + p2 ) + ν p3 } − ν gp3 + ν g . ) 2 δλ3     2 2 2   δC δC δC 1 t  2 2 2 2 2 2 − +µ +ν µ dt. ) 2 2 2 = − {(λ1 − p1 ) + (λ2 − p2 ) + (λ3 − p3 ) }   3     t3 2  2 2  + {µ p1 (λ1 − p1 ) + µ p2 (λ2 − p2 ) + ν p3 (λ3 − p3 )}    24    4 5  t 2 t  4 2 4 2 4 2  − ν g(λ3 − p3 ) + (µ p1 + µ p2 + ν p3 )   45 240    6 7  t 4 t 4 2   − ν gp3 + ν g .

We may therefore, theoretically, consider the problem as solved; but it must remain for future consideration, and perhaps for actual trial, to determine which of all these various processes of successive and indefinite approximation, deduced in the present Essay and in the former, as corollaries of one general Method, and as consequences of one central Idea, is best adapted for numeric application, and for the mathematical study of phenomena.

32. ) for H into the two following parts,  m m H1 = Σ . )  M   mi mk  + (xi xk + yi yk + zi zk − M fi,k ) + · · · ,  M 42 of which the latter is small in comparision with the former, and may be neglected in a first approximation.  dt m δz M dt m δζ δζ These equations arrange themselves in n − 1 groups, corresponding to the n − 1 binary systems (m, M ); and it is easy to integrate the equations of each group separately. ) with five other analogous, for the five other elements λ, µ, ν, τ , ω, in any one binary system (m, M ).