Answer to Sir John Herschel's letter

No 4[I beg to acknowledge your letters of the 10th & 13th. If you will permit me I shouldlike to send the Athenaeum2 to M. Comte as from yourself, with a copy of your lastnote,3 which I think would be more agreeable to him, or to any man, than the directcommunication of your animadversions could be disagreeable.]
The question raised by your criticism on M. Comte appears to me,I confess, to be one which a mere reference to his book would
decide. It is simply this. In saying (as he does) that a theorem
compounded of Huyghens' & Newton's laws leads directly to the lawof Kepler, does he represent this as a verification of the nebular
hypothesis ? In your address you say he does. I continue to thinkthat if you refer again to his book you will see that he does not,& moreover that he does, elsewhere, represent that same logicalsequence, as a verification not of the nebular hypothesis, but of
the law of gravitation.
What may be the value of what he does bring forward as anumerical verification I cannot pretend to say; I am notacquainted with what he has written expressly on the subject;& if I were, it would become me to express myself much moremodestly on that question. The verification would of course consist
in the agreement of the periodic time of each planet, with what
would be the period of the sun's revolution if it were suddenly
expanded so as to touch the planet. For computing that period
the elements would be, the present period of the sun's rotation, thesun's equatorial radius, the mean distance of the planet fromthe sun, and ―― Kepler's law. Therefore I presume that M. Comte
must either prove or assume ( as stated in your letter ) that
Kepler's law applies to the successive states of the sun itself,& not merely to the planets when detached from it. On what grounds
he does so, his own dissertation must shew.
Admitting however the impossibility of proving the proposition
stated in your letter, still it cannot be considered a mere arbitrary
assumption; & if it can be shewn that the present rotation of
the sun takes place in the same time in which it ought to takeplace supposing that proposition and the nebular hypothesis to1

be true, would not that be of considerable weight as an additional
argument in favour of the nebular hypothesis ? A proof, it would notbe; but M. Comte, you will observe, distinctly disclaims thepretension of having proved the hypothesis.
And now, without troubling you further on this subject, permit
me to say, that I thankfully accept your offer4 with respect tomy own book. I am well aware that any one, not a mathematician
by profession, is likely in going over such a field as I have done,to have committed many such errors as those you propose pointing
out; & for myself, though I formerly went quite through theusual course mathematics & its applications, & haveoccasionally revived my recollection by recurring to partsof it, I do not pretend to have retained any accurate memoryof more than the outline. I have therefore always hoped that
if my book had any success, some of those who possess therequisite knowledge would take the trouble to free it fromerrors of this description, & I shall endeavour to profit
to the utmost by every indication you may give.
14 July 1845
注 1 宛先：Sir J. F. W. Herschel Bart. / Collingwood / Hawkhurst / Kent. 消印：W / PAID
/ 14 JY 14 / 1845, and STA ... HURST / JY 15 / 1845.王立協会所蔵自筆書簡、7 月 16 のハーシェルの返書も同じ。
[2 先の書簡、注 3 を見よ。][3 ハーシェルがミルに、『アシニーアム』Athenaeum をコントに送付する際に自分の名前を挙げないよう要請した 7 月 13 日の書簡。
「いかなる場合でも、不運にも彼をして、言及したそのとおりの言葉（ipsissima verba）の所有者に早くからしてしまうことなく、著者の著作について言及することはきわめて不当なことであると私は考えております。しかも、個人的性質に関して不必要に攻撃するものであってはなりません。」（In all such cases
I consider it highly unjust to remark on the writings of an author unfavorably without
putting him early in possession of the ipsissima verba of the remarks, but then it should
be so done as to give no unnecessary offence of a personal nature.）]4

7 月 10 日の書簡においてハーシェルはミルの『論理学』の話をして次のように記した。

" the general high opinion I have formed and expressed of it in a philosophical point ofview" but thought "the least felicitous portions of it, those in which points of physicalscience and mathematics are touched upon. I should have no objection if you desired it2

to specify some particular instances which have occurred to me inter legendum to which
this remark applies. ..."

3