282 
NATURE 
it. When a cart with a butcher’s man came into the place where 
the dogs were kept, although they could not see him, they all 
were ready to break their chains. A master-butcher, dressed 
privately, called one evening on Paris’s master to see the dog. 
He had hardly entered the house before the dog (though shut in) 
was so much excited that he had to be put into a shed, and the 
butcher was forced to leave without seeing the dog. The same 
dog at Hastings made a spring at a gentleman who came into the 
hotel. The owner caught the dog and apologised, and said he 
never knew him to do so before, except when a butcher came to 
his house. The gentleman at once said that was his business. 
So you see that they inherit these antipathies, and show a great 
deal of breed.’ “ WitLtraAmM Huccins” 
The unreasonable 
My attention has directed itself to a letter by Dr. Ingleby 
in your last number, containing two curious but inconsistent 
misrepresentations of my words, and therein something that, if 
the writer were not Dr. Ingleby, might be called an instructive 
instance of cynophatnism or doggimangerness—the behaviour of 
one who will neither understand a thing himself, nor allow other 
folk to understand it. As, however, the writer is Dr. Ingleby, 
I feel sure that a less cursory contemplation of the matter will 
modify his. views. 
The following doctrines are in the A7vitik :— 
1. At the basis of the natural order is a transcendental object. 
“Das ¢ranscendentale Object, welches den aiisseren Erschei- 
nungen, ingleichen das, was der inneren Anschauung 
zum Grunde liegt, ist weder Materie, noch ein denkendes 
Wesen an sich selbst, sondern ein uns unbekannter 
Grund der Erscheinungen, die den empirischen Begriff 
yon der ersten sowohl als zweiten art an die Hand 
geben,” (1Vth Paralogism, of Ideality ; Hirst Edition.) 
2. The transcendental object is wsreasonable, or evades the 
processes of human thought, 
(a) OF the sensibility :— 
‘*Dienichtsinnliche . .. Ursachedieser Vorstellungenist uns 
ginzlich unbekannt, und diese _kénnen wir daher nicht 
als Object anschauen.”. . . (VIth section of Antithetic.) 
(4) OF the understand ng :-— 
‘* Unser Verstand .. Dinge an sich selbst (nicht als Ersch- 
einungen betrachtet) Vowmenanennt. Aber er setzt sich 
auch sofort selbst Grenzen, sie durch keine Kategorien 
zu erkennen, mithin sig nur unter dem Namen eines 
unbekannten Etwas zu denken.” (Ground of distinction 
between Phenomena and Noumena.) 
3. The doctrine of the contradictions is one means by which 
we know this. 
“Mann kann aber auch umgekehrt aus dieser Antinomie 
.. . die transcendentale Idealitit der Erscheinungen. . . 
indirect... beweisen,” &c., (VIIthsection of Antithetic. ) 
The Kantian theory had two legs to stand upon; one the 
alleged necessity of mathematical axioms, the other these alleged 
necessary contradictions in our ideas of the natural order. How 
completely the first has been amputated I hope to have shortly 
an opportunity of showing in a course of lectures at the 
Royal Institution. The doctrine, that we may infer the exist- 
ence of an unknowable from supposed contradictions in the 
knowable, ‘has been developed and extended by the great suc- 
cessors of Kant;” and when in ‘‘a later form” these contra- 
dictions were set forth from an ultimately empirical standpoint 
(not that of Hamilton, but of Spencer, as stated in my note) the 
doctrine became fit for notice ina scientific lecture. Only the 
contradictions themselves, however, could be criticised, and not 
the step from them to the existence of the unknowable, or the 
unknowability of the existent. And Kant’s name coud only be 
mentioned as the historical starting-point of the doctrine ; whose 
importance for the empiricist is mainly due to the modifications 
it has undergone since his time, 
| three points in space. 
If Dr. Ingleby will kindly look at my lecture (A/acmillan’s | 
Magazine, October 1872) again, he will see that I have attri- 
buted to Kant no more than the above-quoted doctrines ; that I 
never pretended to expound Kant’s form of them, or their relation 
to the rest of his system ; and that I never said nor accused any- 
body of saying either that the antithetic was unreasonable, or 
that any natural order of thought or things was unreasonable, 
In regard to the other misrepresentations he speaks of, I shall 
be very glad indeed to be told of them, and to he set right, pro- 
vided only they exist in my words, and not in the exuberant 
imagination of my critic. 
London, Feb. 9 W. K. CLirrorD 
P.S.—There is an important error in p. 508 of the lecture in 
question. The surface-tension of camphor and water is /ess than 
that of water, not greater, as there stated. The general argu- 
ment depends only on there being a difference. 
Prof. Clifford on Curved Space 
THE friend, who (as I stated in my letter in NATURE, Feb. 6) 
called my attention to Prof. Clifford’s address in A/acmillan’s 
Magazine for October last, asked me certain questions respecting 
curved space, which I was quite unable to answer: and another 
friend, occupying the foremost place among English philoso- 
phers, has since communicated to me the great discomfort which 
Prof, Clifford’s views had occasioned him, and suggested that I 
should comment upon them in Nature. I am not sure that 
what I have to say will prove to be helpful either to my discom- 
forted friend, or to truth : yet the doctrine of curved space is so 
extraordinary in itself, and so momentous in its consequences, if 
it be true, that it is a fair subject for sceptical scrutiny. More- 
over, I do not conceive that in commenting upon it Iam going 
ultra crepidam ; for the nature of space is not a subject on which 
the mathematician can claim a monopoly. Jz imine allow 
me to express my regret that Prof. Clifford should have 
selected such a topic for the entertainment of a popular audi- 
ence. It is quite incredible that any of his hearers could have 
apprehended his meaning. There was assuredly no need for the 
lecturer to have cast a glamour on their mental eye by the inyo- 
cation of those awful names, Lobatchewsky and Gauss, Riemann 
and Helmholtz. : 
The principle, in exemplification of which Prof. Clifford ex- 
pounded the doctrine in question, was this: that a law can be 
only provisionally universal (7.e. as ‘‘ we find that it pays us to 
assume it’’), but that it is theoretically universal, or true of all 
cases whatever, ‘‘is what we do not know of any law at all” 
p. 504. I fancy he would not include numerical formule under 
the term ‘‘law:” else arithmetic and algebra would afford an 
infinity of examples of sucha law. Be that as it may, he does 
not select an example from either of those sciences, but from 
Euclidian geometry. He takes the proposition established by 
Euclid, that in any plane triangle the three angles added together 
are equal to two right angles. This he asserts we do not know 
as a universal truth, I now quote his own words: ‘* Now 
suppose that three points are taken in space, distant from one 
another as far as the sun is from a Centauri, and that the shortest 
distances between these points are drawn so as to form a 
triangle : and suppose the angles of this triangle to be very 
accurately measured and added together ; this can at present be 
done so accurately that the error shall certainly be less than one 
minute. . . . Then I do not know that this sum [? apart from 
the question of error] would differ at all from two right angles; 
but also I do not know that the difference would be less than 
10°.” If, then, after a sufficient number of observations it were 
found that the deviation were greater than the assigned limit of 
error (less than one minute), it would follow that the Euclidian 
law is not universal, and that for triangles of such dimensions 
it isnot true. Tne conclusion would be, then, that our Tri- 
dimensional space is not ahomaloid. We need not run our heads 
against the ghost of a fourth dimension ; for the refinements of 
the geometer enable him to investigate a curved tridimensional 
space, just as he inves igates a homaloidal tridimensional space. 
But all the same, it is absurd to attempt the interpretation of the 
results without supposing that fourth dimension as tbe conditio 
sine qué non. 
Now we will suppose that the triangle in question has been 
surveyed, and that the sum of its three angles have been found 
to deviate from 7 far beyond the assigned limit of error: what 
have we really got thereby? The triangle, says Prof. Clifford, 
is formed by drawing ‘‘ lines of shortest distance” between the 
Is observation through a telescope draw- 
ing such a line? Be it so, for the sake of argument. Then, if 
the conclusion to be drawn is that space is curved, I ask does it 
or does it not follow that the sides of the triangle are themselves 
curved? Observe that i! those seemng (to us) straight lines are 
really curves of an exceedingly small curvature, the Euclidian 
law is not touched. Of course, then, Prof. Clifford did not 
mean to assert that in a case in which the sides of a ttiangle are 
