To Mary Somerville   [15 June 1830]

Slough June 15 1830

My dear Madam,

I propose on Saturday morning to call on my way from London to deliver over to you your MS. which I have now detained so very long as to be, I fear almost beyond the reach of apology. The truth is I had hopes to have found leisure to have read more deeply on some of the subjects treated of such as the carrying the approximations to the squares of the masses — the attraction & perturbative influence of the Sun, and the theory of the rotary motion of solids, of which I never possessed more than a superficial knowledge so as to become better qualified to criticize what you have said respecting them. But the hope proved vain, so far from being able to increase my stock of knowledge on these or similar subjects I find is daily sliding from me, and the demands on my attention from less [illegible] quarters become daily more numerous and more pressing so as to take from me not only the hope, but also the wish to penetrate farther into these recesses.

Where I have seen my way clearly I have not spared remark and even where I have thought I perceived room for objection I have considered it my duty to point it out for your own judgement. Such a case arises in your 85^th Page where you treat of the conditions of permanent rotation. There is one part of the theory of perturbations that seems to me to want elucidation [illegible] & you would do a service to many — me among the rest by clearing up an obscurity that hangs about it. I mean the constant part of the effect of perturbation, in permanently altering the elements from what they would be in an undisturbed system, or the destruction of the arc proportional to the time in the series for $\delta v$. In the theory of the moon if I remember right Plana has estimated the permanent effect of the Sun in altering the Lunar period & this I suppose is the analytical translation of what Newton calls the mean effect of the [ablation?] force, & I do not see why the same view should not be taken of planetary action.

The equations of stability $m\sqrt{a}\cdot e^2+m\mathrm{\&\#x2032;}\sqrt{a\mathrm{\&\#x2032;}}\cdot e{\mathrm{\&\#x2032;}}^2+\&c=C$ &c seem to me to have had their importance much overrated. It is quite clear that, taken alone, they prove nothing for the stability of the orbits of the small near planets. For suppose Jupiter & Mercury in which $m\mathrm{\&\#x2032;}:m::2025810:1067$ and $a\mathrm{\&\#x2032;}:a::5.20:0.39$ the equation would be (supposing no other planets) $\frac{e{\mathrm{\&\#x2032;}}^2}{4697}+\frac{e^2}{3244000}=0.000004954$. Now if this alone limits the values of $e$ & $e\mathrm{\&\#x2032;}$ it is clear that $e\mathrm{\&\#x2032;}$ becoming $=0$, $e$ may attain the value $\sqrt{3244000\times 0.000004954}=4.009$ so that, for any thing this equation of stability might say to the contrary, the orbit of mercury might run out into an hyperbola, while that of Jupiter would presume a dignified repose as becomes his god-ships importance. — after reading this, just turn to page 305 vol 1. Book ii. Mec. Cel. 1^st Edition & compare it with Laplace’s words speaking of this equation.

But in fact, is it not by means of perturbative action that the orbit of [symbol]] has attained its actual ugly excentricity[sic].

Mrs H begs to be remembered to you. It is but a few days that we heard of Dr Somerville’s severe loss — which has our hearty condolences.

yours very truly J F W Herschel.