From Mary Somerville   [11 February 1831]

Chelsea 11 Feb [1831] [Original sent to Sir W. Fairfax Bart July 1885]

From Mrs Somerville To J. F. W. Herschel

My dear Sir,

I think it would be a great improvement to integrate the differential equations of the perturbations of the planets by the method of indeterminate coefficients. I have applied it to the radius vector and as I have arrived at the same result with La Place I cannot see an objection. I avoid the terms having the mean anomaly as a coefficient which answers better since I determine the secular inequalities by the variation of the constant quantities. Should you approve of this plan I shall employ the same method for the perturbations depending on the other powers of the excentricities. This also saves the trouble of transforming the equation.

0=d2rδrdr2+urδrr3+2dR+r(dRdr)

into a similar equation in function of u (see LaPlace vol 1st pages 260, 261)

I beg my kindest wishes to Mrs Herschel who I hope is quite well. Ever my d[ea]r Sir

sincerely y[ou]rs

M. Somerville

Please cite as “Herschel2650,” in Ɛpsilon: The Sir John Herschel Collection accessed on 28 March 2024, https://epsilon.ac.uk/view/herschel/letters/Herschel2650