Ansiver to Olject'ions against Mr. Horn's Theory of Fision. 273 



it will not ap])ly in those cases where more than two payments 

 are concerned; by first equating for two, then a third, and so on, 

 a difficulty which the advocates for it have never attempted satis- 

 factorily to explain ; yet it is said the equated time may be found 

 for any number of payments when the question is propounded in 

 numbers; but that it would be difficult to give a general theorem 

 for such cases : analytically, indeed, the thing is I believe hardly 

 possible to be effected. 



From the preceding discussion I feel persuaded it will appear 

 that tlie old rule is the true, and Malcolm's the false one ; and 

 I have been the more soHcitous to point out the distinction be- 

 tween tbe rules, as well as to explain on what head I conceive 

 the ambiguity in Malcolm's to rest, because several eminent 

 writers who rank high on the score of science have indiscri- 

 minately one after another adopted it in their works, under the 

 impression of its being the only true rule : but if this mode of 

 reasoning be just, they must have rendered, and so will all suc- 

 ceeding v.riters (who give the rule admission jnto their works) 

 at least render them erroneous in this respect. But if otherwise 

 it can be shown that what is herein advanced is not consonant 

 to the truth, as I am always open to the conviction of errors, so 

 I shall be thankful, on my part, for the candid correction of them. 

 I am, sir. 



Your very obedient humble servant, 

 Halierdashors Place. IIo\ton, Jas. Benj. BenwelL. 



April 12, 1317. 



LXVIII. Answer to Ohjectiovs nsninst Mr. Horn's Theory of 



Vision. 



To Mr. Tdloch. 



Sir, — -L PERCEIVE by your last Number, that the opponents 

 to my theory have increased : — still I am neither appalled by their 

 inimber nor arguments. I am disposed to draw a broad line of 

 distinction between Mr. Pater and your correspondent J. Q. R. 

 The latter gentleman's argument assumes something like a tan- 

 gible shape ; though I have to complain of his ex parte decisions. 

 As my principles arc already before the pul)lic, it is rather prepo- 

 sterous to ask, "What foundation has Mr. Horn for his theory ?" 



Your correspondent L.S. has partly avoided this inconsistency. 

 Being in possession of my pamphlet, he has also corrected some 

 of the errors into which Mr. P. and J. Q. R. have fallen. But 

 while he does this with an apparent regard for justice, in order 

 to render my optics ridiculous, he grossly misrepresents the de- 

 scription I have given of a phsenomcnon, whicli he found could 



Vol. 'Jf). No. 228. AprU 1817. i> not 



