No 1My dear Sir

To Sir John Frederic William Herschel, Bart.
The correspondence which took place between

us, two years ago,2 must be my warrant, if the object I havein view requires any, for taking the liberty of writing to you
respecting a passage in the address which you delivered to theBritish Association for the Advancement of Science at its firstevening meeting on the 19th of last month.3
In that discourse you spoke of a recent publication of minein so handsome a manner as would have more than satisfied
a much greater degree of vanity than I possess. But mypurpose in writing to you is not to make acknowledgments
for your politeness nor to express my gratification at yourfavourable opinion, but to call your attention to an actof injustice which you have, I am sure unintentionally,
committed against the scientific reputation of a distinguishedman. You have publicly imputed to M. Auguste Comte,
not only a gross blunder in reasoning, but one inconsistent
with the most elementary knowledge of the principles
of astronomical dynamics. If M. Comte had been capableof such a blunder, he would have been quite incapableof writing any one chapter of the Cours de Philosophie
Positive : and I am sure, nothing is necessary but amore careful reference to that work, to convince youthat he never was guilty of it.
You say that for the purpose of giving a numericalverification to the hypothesis of the nebular originof the solar system, M. Comte computes the time ofrotation which the sun must have had about its axis
so that a planet situated on its surface should not press
upon that surface. That as the basis of this calculation
M. Comte employs "the elementary Huyghenian theorems"for the evaluation of centrifugal forces, in combination"with the law of gravitation ―― a combination which,"I need not explain to those who have read the first"book of Newton, leads direct to Kepler’s law," And1

then you accuse him of “gravely turning round upon us"and addressing the coincidence of the resulting periods"compared with the distances of the planets with"this law of Kepler, as being the numerical"verification in question." Well may you add "where"is there a student to be found who has graduated as"a Senior Optime in this university, who will not"at once lay his finger on the fallacy of such an argument,"& declare it a vicious circle." But that M. Comte
has fallen into this vicious circle is a statement
only to be accounted for by supposing that you have not readthe astronomical portion of M. Comte’s work, but only referred,
and that cursorily, to a single passage of it.
It would be difficult for even the shallowest person
to have attempted to give a philosophical outline ofastronomy without being aware that the evidence bywhich Newton proved the law of gravitation was the factof its leading demonstratively to Kepler’s laws; & that
Kepler’s law of the relation between the distances & theperiodic times, was deduced from the law of gravitation
combined with the Huyghenian measure of the centrifugal
force. Accordingly if you refer to an earlier chapter inthe same volume of M. Comte, being that in which he unfolds theevidence of the law of gravitation, you will find (pp. 227-231)
that all which you so contemptuously bring forward in condemnationof M. Comte, is brought forward by him. You will find the same
exposition repeated in the corresponding chapter of his very
striking "Traite Philosophique d’Astronomie Populaire." It
was impossible that the accordance of Kepler’s law with thepremises from which he knew and said that it demonstratively
followed, could appear to him to be a "numerical verification,"
not of those premisses, but of something quite unconnectedwith them, viz. the nebular hypothesis.
And if you only refer again to the very passage, towhich I venture to think that your former reference2must have been a very hasty one, I am confident that you
will see how completely you have mistaken its import. It was
not the coincidence of the resulting periods of the planets"with this law of Kepler" that M. Comte considered as anumerical verification of their nebulous origin; it was thecoincidence (within certain limits of error) between the periods,
as resulting from the calculation, and the actual periodic timesof the planets, as known by observation. The reference to Kepler’s
law is only incidental, and the sole use made of it is, todispense with the necessity of performing the calculationseparately for each planet, since, when it has been madefor any one, Kepler’s law gives the correlative result forevery other.
I speak without any knowledge of the Memoir or Memoirs
on the subject, which M. Comte read before the Academy ofScience, and with which you appear to be equally unacquainted.
A reference to them would doubtless shew both "the steps"
and "the data of his calculations," which could not havebeen given with any propriety in the Cours. I also write
without communication with M. Comte, who is probably quite
unaware of the attack made upon him. But on the faceof the Cours itself and of the very passage from which you quote,
it is evident to me that the attack has been made under amisapprehension, & I cannot doubt that your love of justicewill induce you to reexamine the subject.
A judgment from you, delivered with preparation, andon an occasion of so much publicity, must have a serious
effect upon the scientific reputation of any author: and you
cannot be unaware how little chance any one, who may
dispute its justice, would have of obtaining, from thescientific or from the general public of this country, even ahearing, against your authority. So great a power involves a
proportional responsibility; and when it has been inadvertently
exercised to the injury of any one, I cannot doubt your being
most desirous that the error should be pointed out.
3

I remain

Yours very truly

J. S. Mill

9th July 1845.
注 1 〔ロンドン〕王立協会所蔵自筆書簡。ハーシェルの 6 月 10 日の返書も同じ。更にハーシェルの 7 月 13 日書簡はイェール大学にある。
2 書簡 397 を見よ〔
『全集』13 巻、583-584 頁〕。
3 ケンブリッジにおける協会第 15 回会合でのハーシェル総裁演説は、公刊されている。

Athenaum for June 21, 1845, pp. 612-17.

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