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ME. C. W. MEEEIEIELD ON A NEW METHOD OE APPEO XTM ATTON 
tion of this equation in respect of z, and still less do they solve the more general form 
It may suggest processes of reduction in some cases to remark, that there are many 
other functions of and (p(z), which will approximate to <p(z) as m increases, besides 
the simple product or quotient of <p{z) by y^. 
There is one point about these higher approximants, of which a solution, even if 
accompanied with considerable restrictions, would be extremely desirable, — I mean the 
resolution of the denominators into factors. I do not suppose that the problem, in its 
perfectly general form, admits of a compact solution ; but any class of cases, of even 
moderate generality, for which it could be elegantly solved, would probably have very 
useful applications. The criterion of convergence and the measure of approximation 
would also have their interest. 
