-recommendations authoritative, 
brethren a striking example of patient, persevering in- 
dustry in trying to keep pace with the rapid progress of 
oe 
, ‘) 
‘uly 24, 1873] 
natural proclivity to sarcasm, and his impatience of 
routine constraints. With the view of trying to leaven 
the dead mass around him, and to awaken some interests 
apart from everyday life, he gave popular lectures to the 
upper classes, which ultimately resolved themselves into 
that very attractive—if slightly prolix—résumd of his 
_ knowledge, observations, and speculations, which we know 
under the title of “ The Cosmos.” And while he laboured 
assiduously to exercise his influence for the endowment 
of scientific institutions of all kinds, and the encourage- 
ment of learning and learned men, not only in Germany, 
but in every country where his reputation made his 
he set his scientific 
inquiry,and of humblereadiness in renouncing old opinions 
whenever he found that they had been superseded by 
more correct views. 
To the English reader interested in tracing the progress 
of scientific and social development in Germany and 
other parts of the Continent during the close of the last 
and the first half of the present century, the “ Life of A. 
von Humboldt, by Bruhns and Lassell,” cannot fail to 
_ prove at once instructive and suggestive. 
STIRLING’S “ PHILCSOPHY OF LAW” 
Leatures on the Philosophy of Law. Together with 
Whewell and Hegel, and Hezel and Mr. W. R. Smith, 
a Vindication in a Physico-Mathematical regard. By 
James Hutchinson Stirling, F.R.C.S, and LL.D. Edin. 
(London: Longmans, 1873 ) 
HIS volume contains certain lectures on the Philo- 
sophy of Law, delivered to the Juridical Society of 
Edinburgh in November 1871, together with a discussion 
of Hegel’s opinions concerning gravitation and the differ- 
ential calculus. Of the lectures we may say, that if the 
members of the Juridical Society understood them, they 
must be much more clever than we profess to be. The 
first lecture is an introduction to philosophy in general, 
that is, the philosophy of Hegel. It expounds the doc- 
trine of the #o¢ion, and discloses in the briefest possible 
space the “secret of Hegel.” Mr. Stirling has already 
written a work of two substantial octavo volumes, entitled 
“The Secret of Hegel.” A friend of the author being 
found reading it, and being asked what he thought of the 
* Secret,” answered, “ Why, I think the author has kept 
it.” If then the secret cannot be disclosed in two volumes, 
how did Mr, Stirling hope to make it plain in a lecture 
occupying only fifteen printed pages? In reading this 
lecture we did not enjoy for a single moment the feeling 
of solid ground. We had an impression that we under- 
steod what logic was until we met with the following 
passage :— 
“ Hegel’s system, as is now pretty well known, is con- 
tained in three great spheres—the Science of Logic, the 
Philosohpy of Nature, and the Philosophy of Spirit. 
Here we see at once that what we have before us is the 
Notion. Logic is the universal ; Nature is the particular ; 
and Spirit is the singular. Logic, having developed into 
full Zdea, passes into the particular as the particular, into 
externalisation as externalisation, in Nature ; and Nature, 
rising and collecting itself, through sphere after sphere, 
‘from externality itself in the form of space, up to natural 
NATURE 
241 
internality in the form of organic life, passes into the Soul, 
which is the first form of Spirit. The instrument of the 
evolution all along, we are to understand, is the Vo/ion, 
in its three Moments” (p. 15). 
So long as Hegel and his satellite Stirling kept to the 
notion and its three moments in the abstract, they are 
impregnable and unapproachable, like those fishes which 
are said to make the water muddy all around when an 
enemy is near. It was when Hegel ventured out of his 
own mists that he showed his extreme fallibility. Having 
applied his “notion” to the theory of gravitation, he dis- 
covered that Newton was wrong in asserting the curve of 
motion of a gravitating particle to be any conic section, 
“‘Hegel’s idea certainly is that the ellipse is a necessary 
outcome of ¢ke notion on this the stage of free motion 
according to the relations of time and space as moments, 
If planets do move in circles, or even if planets might 
move in circles, Hegel would here have to confess a 
failure. It would be his metaphysic that in that event 
would suffer, however, rather than his knowledge of 
physics. In the meantime, the fact is that the curve of 
movement still remains an ellipse, and Hegel so far is 
not in error” (p. 99). 
Now, inasmuch as the circle is only the extreme case 
of an ellipse possessing no eccentricity, it is just as likely 
that a planet would move ina circle as in any one definite 
ellipse ; but astronomers could never discriminate with 
certainty between a circle and an ellipse of very slight 
eccentricity ; and so far Hegel escapes absolute conflict 
with fact. Unfortunately, however, it is known that cer- 
tain comets move in hyperbolic paths (see Chambers’ 
“ Handbook of Descriptive and Practical Astronomy,” p, 
203, 1861), and as the ellipse is the wecessary outcome of 
Hegel’s notion, we think he must suffer both in his meta. 
physics and his physics. ; 
In Mr. Stirling’s controversy with Mr. W. R. Smith 
concerning Hegel’s notion of the differential calculus, we 
also think that Hegel suffers. The critical statement of 
the necessary outcome of Hegel’s philosophy is as follows 
(p. 113) :— 
“ The limit of a qualitative relation is that in which it 
both is and is not, or, more accurately, that in which the 
quantum has disappeared, and there remains the relation 
only as qualitative relation of quantity.” 
Now the very essence of the differential calculus con- 
sists in the fact that quantities, although indefinitely 
decreasing, or vanishing, as the expression is, preserve all 
their quantitative relations. Mr. Stirling says (p. 114) :— 
“ What is called infinitely /¢¢/e is only qualitative, and 
is neither little nor great, nor quantitative at all.” 
On the contrary, the very principle of the calculus is 
that infinitely little magnitudes are still comparatively 
little or great, and preserve all their quantitative relations, 
so that differential co-efficients, or the ratios of such 
infinitesimals, are definite numbers. 
As Hegel’s “notion” here again comes into conflict 
with all that is best established in abstract mathematical 
science, we must decline to follow Mr. Stirling through 
his generally incomprehensible vindications of Hegel. 
When Hegel's philosophy breaks down so sadly at the 
slightest touch of fact, can we waste our own time, or that 
of our readers, with endeavouring to attach a meaning to 
pages of this kind of philosophy ?— 
“ The outside darvshauung being viewed as the con- 
