. 
ADDRESS. XXXIX 
siderations of the law of cooling, the change of spheroidical form, the internal 
distribution of density, the probable non-circulation of the internal and ex- 
ternal shells in the same periodic time, on which alone it is possible to execute 
such a calculation correctly ; and avowedly, as a short-cut to a result, using 
as the basis of his calculation “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 ;—and if we find him then 
gravely turning round upon us, and adducing the coincidence of the result- 
ing periods compared with the distances of the planets with this law of Kepler, 
as being the numerical verification in question,—where, I would ask, is there 
a student to be found who has graduated as a Senior Optime in this Uni- 
versity, who will not at once lay his finger on the fallacy of such an argu- 
ment*, and declare it a vicious circle? I really should consider some apo- 
logy needed for even mentioning an argument of the kind to such a meeting, 
were it not that this very reasoning, so ostentatiously put forward and so 
utterly baseless, has been eagerly received among us+ as the revelation of a 
profound analysis. When such is the case, it is surely time to throw in a 
word of warning, and to reiterate our recommendation of an early initiation 
into mathematics, and the cherishing a mathematical habit of thought, as the 
safeguard of all philosophy. 
A very great obstacle to the improvement of telescopes in this country has 
been happily removed within the past year by the repeal of the duty on glass. 
Hitherto, owing to the enormous expense of experiments to private indivi- 
duals not manufacturers, and to the heavy excise duties imposed on the 
manufacture, which has operated to repress all attempts on the part of prac- 
tical men to produce glass adapted to the construction of large achromatics, 
our opticians have been compelled to resort abroad for their materials— 
purchasing them at enormous prices, and never being able to procure the 
largest sizes. The skill, enterprise and capital of the British manufacturer 
have now free scope, and it is our own fault if we do not speedily rival, and 
perhaps outdo the far-famed works of Munich and Paris. Indeed, it is hardly 
* M. Comte (Philosophie Positive, ii. 376, &c.), the author of the reasoning alluded to, 
assures us that his calculations lead to results agreeing only approximately with the exact 
periods, a difference to the amount of one-forty-fifth part more or less existing in all. 
As he gives neither the steps nor the data of his calculations, it is impossible to trace the 
origin of this difference,—which, however, must arise from error somewhere, if his funda- 
mental prince le be really whathe states. For the Huyghenian measure of centrifugal force 
2 
( F acy ) “combined” with “ the law of gravitation” ( oo a =), replacing V by its 
é R 
equivalent, = can result in no other relation between P and R than what is expressed in the 
Keplerian law, and is incompatible with the smallest deviation from it. 
Whether the sun threw off the planets or not, Kepler’s law must be obeyed by them when 
pare fairly detached, and the sun concentrated into a spherical nucleus, such as we now 
nd it. 
In the above reasoning, the consideration of the sun’s varying oblateness has been omitted 
as complicating the argument. It is easily taken account of, but with no benefit to the 
theory contended against. It should moreover be noticed that the actual time of rotation 
of the sun on its axis stands in utter contradiction with that theory. 
~ How, then, can their actual observance of this law be adduced in proof of their origin, one 
way or the other? How is it proved that the sun must have thrown off planets at those 
distances and at no others, where we find them,—no matter in what times revolving ? 
That, indeed, would be a powerful presumptive argument ; but what geometer will venture 
on such a ¢owr d’analyse? And, lastly, how can it be adduced as a numerical coincidence 
of an hypothesis with observed fact to say that, at an unknown epoch, the sun’s rotation 
(not observed) must have been so and so, if the hypothesis were a true one? 
+ Mill. Logic, ii. 28.—Also, ‘ Vestiges of the Creation,’ p. 17. 
d2 
