Feb. 17, 1870] 
NATURE 
I do not know if this be similar to that Mr. Grove has seen, 
but it evidently corresponds with the appearance Mr. Newall 
describes in your journal for January 27th. The next mention 
of inner rainbows is in the Phil. Trans. for 1749, p. 193, when 
Mr. Dayal, the then secretary of the Royal Society, corroborates, 
from his own experience, Dr. Langwith’s description, Dr. Thos. 
Young next refers to the phenomenon in order to give his explana- 
tion of it in the Phil. Trans. for 1804, and he also twice alludes 
to it in his published Jectures on Natural Philosophy. Further, 
at p. 374 of his ‘‘ Optics,” Brewster describes supernumerary 
bows that, at different times, he has seen within the primary 
rainbow; and, also, he mentions an analogous appearance ob- 
served without the secondary, a fact previously surmised by Dr. 
Young. * 
An explanation of the phenomenon is first attempted by Dr. 
Pemberton (Phil. Trans. 1722), who classes it with the colours of 
thin plates, according to the theory of ‘‘fits.” Dr, Young, in 
his paper on Physical Objects (Phil. Trans. 1804), disputes Dr. 
Pemberton’s explanation, and shows that the appearance is 
readily explicable by the interference of two pencils of light, 
regularly reflected from the posterior surface of the drops of rain. 
The drops must, in this case, be between ‘5th and sth of an 
inch in diameter. Evening appears to be the time these super- 
numerary bows are generally seen, and invariably they are ob- 
served beneath the wpfer part only of the primary bow. Hence, 
I presume, the phenomenon is similar to the diffraction colours 
seen in the cloud that is precipitated when the first portions of 
air are promptly removed from a receiver. 
I have, in conclusion, to thank Mr. Grove for pointing out, 
in his second letter, that the word ‘‘ correlation” implies too 
much when applied to the relationship of colour and music. 
“* Analogy ” is certainly far more appropriate to express what is 
merely a parallelism, and not a necessary or complementary 
relationship between light and sound. 
Woodlands Grove, Isleworth, Jan. 29 W. F. BARRETT 
P.S.—Since the foregoing letter was written,—which was sent 
to your office on the date it bears,—several contributions on the 
subject of my ‘‘note”’ have appeared in your journal. I will 
not now yenture to intrude further upon your space, but, with 
your permission, shall reply to your other correspondents in a 
subsequent letter. Warkia Bs 
February 12 
Sensation and Perception 
HAVING in the Journal of Mental Science tried to show how 
Sensation and Intellect are distinguished from each other, allow 
me to state, in regard to Dr. Bastian’s views on this head, that 
Dr. Lockhart Clarke, after a careful review of what has been 
written on Sensation, rejects Sir W. Hamilton’s statement that 
“it is manifestly impossible to discriminate, with any rigour, 
sense from intelligence.” ‘‘ Although, in the lowest animals, 
there is this apparent identity of sense and intelligence, which 
seem as it were to be fused into one common state of conscious- 
ness, yet when we find them in the course of development, either 
in the foetus or in the scale of animal life, emerge each in a distinct 
and different form out of that common or indifferent state, are 
we to ignore the distinction, and assert with Sir W. Hamilton 
and others, that sensation is simply a function of the intellect? 
It might with equal reason be maintained that there is no real 
difference between any other two organs of the body, because in 
the ovum they are developed out of one homogeneous tissue or 
common germinal mass.”’ + According to Von Baer’s law, it 
seems that while in the lower animals sense and intelligence 
are fused into one, in the higher they become differentiated, 
each having a separate seat. When Dr. Bastian, then, 
contends, with the metaphysicians, for the identity of sense 
and intelligence, he seems to be reversing the method of 
evolution, and going back to the medley out of which well- 
defined organs with zmfroved functions were evolved. He 
would make us believe that as the sense-ganglia become more de- 
fined and eliminate the rudiments of intelligence, they assume a 
lower function than they had before, one not to be distinguished 
in kind from that of the excito-motor system previously differ- 
entiated. Is this likely? As to the impossibility of discrimin- 
ating sense from intelligence there are the following facts indicat- 
* Sir David Brewster, moreover, refers to the occurrence, spoken of by 
Mr. Newall, of a dark-coloured zone between the primary and secondary 
bow : a somewhat similar dark fringe is, on @ frior¢ grounds, apparently 
predicted by Dr. Young, at p. 369 of his ‘* Lectures on Natural Philosophy,” 
1845 edition. 
+ Medical Critic and Psychological Journal, vol. il. p. 574, e¢ seq. 
ing the contrary. Physiology shows that the external object of 
the many must be revealed in a seat that is not at the periphery; 
but such an object is not an idea or notion; therefore, there is a 
marked distinction between an external object in sense and an 
idea of one in intellect. A sense-object may be common to two 
distinct sets of ideas, as when it is now interpreted to be a ghost, 
now the stump of a tree. A sense-object is antecedent to an 
ideal object, for the latter only exists as a representation of the 
former. <A feeling in sense may cause coughing or sneezing, é.¢., 
in spite of the veto of the intellect. A feeling in sense may be so 
intensely painful as, for the time, to paralyse intellectual energy. 
But what about the following argument? What is known at 
first hand is known as 7¢ zs, for if you say not as it is; but as it is 
not, you imply that it is not known at first hand, but through 
something which does not even represent it, which is absurd. 
Therefore, as sense and intelligence must be known at first hand, 
and, as thus known, are distinguishable from each other in mazzy 
respects, pre-eminently, the one as the sphere of objects at first 
hand, the other at second hand; the one as pertaining to ¢/e 
organic ego, the other to the zon-organic ego—each must be 
known as it 7s, not as 7 as not. 
Abergavenny. W. G. DaviEs 
Transcendent Space 
In Nature for January 13 I was permitted, as it were, to 
speak the prologue to the correspondence on ‘‘ Kant’s View of 
Space,” now happily, if not satisfactorily, closed. I now ask 
permission to speak the epilogue, in strict reference to the sub- 
ject of my first letter. 
The most interesting period of incubation in Sir William 
Rowan Hamilton’s discovery of Quaternions was October 15, 
1843. On that day, as he relates in a letter to a friend, he was 
walking from his Observatory to Dublin with Lady Hamilton, 
when, on reaching Brougham Bridge, he ‘‘ felt the galvanic cir- 
cuit of thought c/ose ; and the sparks which fell from it were the 
fundamental equations between 1, 7, k; exactly such” as he used 
them ever since (North British Review, September, 1866, p. 57). 
Two days after he wrote a letter to his friend and coadjutor, Mr. 
J. T. Graves, a brother of the present Bishop of Limerick, giving 
a most interesting narrative of his transition from 777A/ets to 
Quaternions. Ut is here that I found, after much search and re- 
search, the confirmation of a notion which had floated for years 
in my mind, that Hamilton’s speculations had borne a very re- 
markable relation to Transcendent Space of Four Dimensions 
The letter in question is printed in the supplement to vol. xxv. 
(third series) of the L. E. and D. Philosophical Magazine, and ot 
late years has escaped the notice of mathematical students, en- 
grossed, as many are, in the geometrical and physical applications 
of Quaternions. It seems that after Hamilton had completed 
his Theory of Conjugate Functions, he endeavoured to obtain an 
Algebra of Pure Space, and for this purpose employed, after the 
Germans, the symbol 7 to express one root of negative unity, and 
introduced a new symbol, 7, to express another root of negative 
unity. Further, he employed an operant, 4; and with these 
elements he worked out a theory of Triplets in which 7*=7*= ~1, 
and i= —7i, while £ remained ambiguous. Assuming, at length, 
that 77=4, and ji= —%, and leaving it still undecided whether 
#=0 or not, there dawned on him, as he phrases it, ‘‘ the notion 
that we must admit, in some sense, @ fourth dimension of Space 
for the purpose of calculating in triplets.” 
Now this curiously interesting phase in the generation of 
Quaternions is an admirable instance of what I mean by affirming 
Quadridimensional Space to be a mathematical figment springing 
out of an otherwise uninterpretable formula. Observe, in this 
case, what was the effect of the completion of the theory. So 
soon as Hamilton had passed from 777p/ets to Quaternions, and 
he had made his /a third root of negative unity, ¢Azs trazscen- 
dent space vanished out of thought. The ghost of a fourth 
dimension, which had haunted Hamilton’s Triplets, was imme- 
diately laid ; and thenceforth his system was, what he originally 
sought, an Algebra of Pure Tridimensional Space. ‘The haunting 
notion, thus banished from Triplets, took refuge in Quinaries 
and other transcendent algebraical formulisations. To me it is 
a spurious product of “*mental activity,” not, even possibly or 
potentially, a form of mental receptivity, and @ /ortiorz externally 
denied to experience. 
In conclusion, I protest that in denying (for Kant) to Space 
and Time the title of Forms of Thought, I do of restrict the term 
Thought to the technical limits of Kant, but use it as synony- 
mous with mental activity in general. 
Ilford, Feb. 14 C. M, INGLEBY 
