W. Skey. — On FmnklamVs Paper on Two Dimensions. 101 



true (whatever this may mean), and that, of these geometricians, 

 LobatcheAVsky has, by assuming the twelfth axiom of EuchcT to be untrue, 

 " Avorked out the conception of a space in which the ordinary laws of 

 geometry do not hold good." From this and other assumptions at vari- 

 ance with the axioms of Euclid respecting distance relations, it is assumed, 

 as a fact, that geometry is only a particular branch of a more general 

 science, and that " the conception of space is a particular variety of a wider 

 and more general conception." To this wider conception is applied the 

 term " manifoldness," and the full meaning of this term is very lucidly 

 explained. 



The author then adverts to "the existence" of a particular manifold- 

 ness, which has been treated by Professor Clifford in a lecture on the 

 postulates of space ; then he describes how this space is analytically con- 

 ceived, with the object of putting us in a position to apprehend certain dis- 

 coveries of his own, which relate to its very singular properties ; these 

 discoveries communicated to us, he closes his paper with a quotation from 

 Professor Clifford imputing finiteness to the Universe as a result of certain 

 conclusions he has arrived at, which pertain to, or are deducible from, this 

 wider conception, and indicate, on his part, a belief therein, a belief 

 which we may fairly infer is shared in by Mr. Frankland himself. 



Such is a fair synopsis of Mr. Frankland's paper, and no one who con- 

 siders it as a whole, can avoid the conclusion that its prime object is to 

 spread and support the views of the metaphysical school ; i. e., it is working 

 for the absorption of science in metaphysics by endeavouring to show that 

 for one of its sections — geometiy — there is a transcendental geometry, which 

 not only stultifies it, but swallows it whole, and ultimately assimilates it to 

 itself. This view is supported by the fact, that just recently this gentleman 

 has read before us a very able and profound paper entitled " Mind Stuff," 

 and which is evidently of a highly metaphysical character. 



This, however, by the way, has nothing to do with the objections which 

 I here restrict myself to detail and support, and I therefore proceed by 

 premising, that these objections do not extend, at least in a dkect manner, 

 to the results of the original researches which are embodied in this paper. 

 Whether these are valid or not is a matter to be only properly tested by ex- 

 amining, as I have, what they rest upon ; but this I will say now, (so that 

 the position I take in respect to this matter, may be apprehended at the out- 

 set) — that all which this paper treats of, which is distinctly antagonistic 

 to geometry (as understood by geometers of the Euclidian school, or intended 

 to be conveyed by them), I take exception to, and now I proceed to show 

 cause. For this I shall, in order to keep myself within due limits, adhere 

 as much as possible to the text of Mr. Frankland's paper, conceiving as I 



