1 90 Mr. W. G. Homer's Considerations relative to 

 result would be a cubic, complete in all its terms. In fact, 

 merely say x m — , and we have 



a — b a—c 



f a — o a — c \ _ , A x 



U+l — j— + ) z = ... (4.) 



v 1 — bz \—czi v 



which, when cleared of fractions, will be an equation of three 

 dimensions. 



If the parenthetic portion of (4.) is made = 0, and re- 

 duced, the result will be a quadratic agreeing w 7 ith Mr. Mose- 

 ley's. But here is, besides, a third root, z as 0, which gives 



1 M 



x = — and — = in each equation (1.), (2.). Q. E. D. 

 a 



Again, this infinite x not only solves both the original 

 equations, it does so to the exclusion of any other infinite x 

 presumed to be deducible from any relation incident to a, b, c. 

 For it reduces (1.) (2.) (3.) to simple and dependent equations, 



3 ^ b + c _■ Sa — b—c , . , „ 



viz. — = 0, = 0, = 0, which all merge in 



XX x 



— = ; the condition 3#— b~ c = being quite superfluous 

 x 

 and nugatory. 



M 



In some views of the equation — = 0, upon which the in- 

 finity of x depends, physical and analytical considerations are 

 inseparable, and results are obtained which confirm what has 

 just been alleged; e.g, it distinctly announces either that 

 the mass M has absolutely no weight, or else that the standard 

 moment of pressure a is infinite. The latter is of course the 

 alternative to be preferred, as it cannot be Mr. Moseley's de- 

 sign to discuss the relations of weight and pressure in masses 

 absolutely destitute of weight. But if a is infinite, what be- 

 comes of its constancy ? " Let a represent a constant quan- 

 tity." Or, granting that, what becomes of the quantities 



A = — , B = r, C = ? Can they be severally af- 

 ar x—b x—c J < 



firmative and infinite, although their sum is = the finite 

 quantity M ? If not, x must have been infinite from the first, 

 and irrespectively of a 9 b 9 c. 



After all, the only way of arriving at conclusions perfectly 

 satisfactory is by regular elimination ; the labour of which, 

 even by the easiest methods, is in this instance considerable. 

 I have, however, undertaken it, not only for the sake of epi- 



