Analyses of Books. 
1883.] 
105 
beings which can adt in it, it is conceivable that such beings may 
be able to tie a knot on a ring-shaped string.” 
This is, perhaps, as clear a representation of the hypothesis of 
poly-dimensional space as can be obtained without the aid of 
transcendental geometry. 
The author propounds a hypothesis which he endeavours to 
follow out to its physical and chemical consequences. It is as 
follows : — “ Our tri-dimensional world, in as far as it is composed 
of ponderable matter, consists of poly-dimensional atoms, 
arranged in a tri-dimensional manner.” 
This hypothesis compels us to the conclusion that every atom 
possesses several magnetic axes, situate in various fixed direc- 
tions in or upon it. Those only which lie with both their poles 
in tri-dimensional space are permanent and incapable of being 
induced. All the others are ordinarily inactive, but owe their 
origin to an indudtive adtion. According to the position of the 
atom sometimes one and sometimes another of these axes comes 
to lie in tri-dimensional space, and furnish then permanent atom- 
magnets. 
This hypothesis, further, according to the author, serves to 
explain how one and the same atom, in different combinations, 
can appear with a different atomicity. 
But, admitting that the hypothesis, if fully followed out, may 
throw a new light upon a multitude of phenomena, we have still 
to ask what are its foundations ? For, if no fourth dimension 
exists, the light thrown by the new hypothesis will be a Will-o’- 
the-Wisp, — an Irrlicht. We must ask, then, for a perfectly 
distindt and decisive proof of the existence of this fourth dimen- 
sion. There have been produced, we are told, certain pheno- 
mena, such as the tying of a knot on a closed string, the passing 
of two wooden rings through each other chain-fashion, the 
passing of a ring upon a pole at either end of which there are 
projections whose diameter exceeds that of the ring, the placing 
of a ring upon a man’s arm whilst he holds his hands clasped 
together, &c. Admitting all this without discussion, — for which, 
indeed, our space is wholly insufficient — there remains a diffi- 
culty which Herr Brosch has not ignored. Whether he has 
succeeded in meeting it is another question. 
Supposing the above-mentioned phenomena verified, are we 
to infer, with the late Professor Zollner, and with our author, 
the existence of a fourth dimension, and of beings capable of adting 
therein ? Or are we to assume, with not a few believers in the 
reality of the phenomena, that there exist superhuman beings 
capable of abolishing temporarily the continuity of an iron ring, 
of a wooden pole, or of a human arm, and then of restoring it to 
its former condition ? We do not find here any answer which 
compels our belief. 
That the work before us is suggestive and that it is worthy of 
a careful study we gladly admit. But we seek to know whether 
VOL. V. (THIRD SERIES). 
I 
