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the mathematical arguments required for testing their truth by the explana- 
tions they give of natural phenomena. In this difficult and indispensable re- 
search, in which I have made some advances, I might have expected the aid 
of some of my junior contemporaries ; but unhappily those who would be 
capable as mathematicians of taking this part have so let their imagination 
run wild on “doors,” and “demons,” and “vortex-atoms,” that they have no 
thought left for sober theoretical reasoning. In my opinion, nothing so much 
at this time stands in the way of the progress of true physical science as the 
propensity of physicists to disregard the strict rules of philosophizing, and 
betake themselves to those creations of the imagination which Newton calls 
“ somnia” It is a little hard that, having laboured much to counteract this 
tendency, 1 should be charged with advocating an imaginative course of 
philosophy. 
With respect to the remarks in the concluding part of Mr. Brooke’s speech, I 
beg to say that I have ascribed gravitating attraction, and magnetic and electric 
attractions and repulsions, to action of the ethereal medium only so far as by 
mathematics I arrive at consequences of my hypotheses which are counterparts 
of the observed effects of these forces. One word in addition respecting 
Mr. Brooke’s reference to the phenomena of crystallization. I make a dis- 
tinction between an atom and a molecule, considering a molecule to consist 
of a congeries of atoms, having sometimes, but not generally, an arrangement 
in accordance with strict geometrical figures. Such arrangement is the 
theoretical basis of crystallography. The aggregate of the ethereal forces 
emanating from the atoms so arranged, may well be conceived to give rise, 
simply by reason of the arrangement, to the existence of molecular forces 
having axes of maxima or minima, and therefore poles, in two or three rect- 
angular directions, and consequently recognizable experimentally by spheroidal 
or ellipsoidal forms. But all this is quite consistent with a spherical form of 
the individual atoms. . 
The remarks by Mr. Walter Lea are mainly concerned with defending a 
passage in The Unseen Universe, in the censure of which I am supported by the 
opinion of Prebendary Row. I think I may appeal to views which I have 
expressed in communications to this Institute and elsewhere, that I can quite 
agree with the position maintained by Mr. Lea that there is no real incom- 
patibility between religion and natural philosophy, but the philosophy of 
which this is affirmed must be trice philosophy, which, I believe, cannot be said 
to be the character of much that passes for philosophy in the present day. 
S 2 
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