Mr. Davies on Mr. Herapath’s Demonstration. 53 
«25> ; EF EF — 
In a similar manner we find amie vain icsmeeh teed and 
therefore, dividing by EF we get 
L Symorsbnd ee gel 1 
AE DE EB. [oodkGs Tse 
Cor. AE+ED:EB+EC:: AE. ED: EB. EC. 
Postscript on P. Q.’s Second Defence of * Mr. Herapatu’s 
Demonstration.” —(Phil. Mag. vol. \xvi. p. 354.) 
I cannot close this short paper without rectifying a slight 
mistake into which your learned correspondent P. Q. has fallen 
' respecting one or two points in my last communication. 
In the first place, I did not “‘ abandon” the arguments em- 
ployed in my first paper on Mr. Herapath’s demonstration. 
They still remain opposed to the view which I then took of 
the process in question: and my second paper was intended 
to show the inefficiency of that demonstration, also under 
P. Q.’s interpretation of it; and to prove that under “ either 
view the same fallacy was involved, the same gratuitous’ as- 
sumption employed.” It could only be by an oversight that 
P. Q. could call my second paper an abandonment of the 
principles of the first. They are totally distinct arguments, 
and are directed against the two distinct views which I con- 
ceive may be taken of Mr. Herapath’s meaning. 
Secondly, the objection to my magical “ comparison be- 
tween the independence of 7 and v, and that.of an angle and 
its complement” appears also to have been too hastily made. 
For the addition of an indeterminate number of units to the 
Jraction in Mr. Herapath’s demonstration is exactly similar to 
the addition of an zndeterminate number of circumferences to 
any fractional portion of a circumference. The truth is, that 
the inquiry does not call for the consideration of indeterminate 
integers: these may be dropped; and the question would be 
stripped of its ambiguity by the adoption of two proper frac- 
tions as the values of r and v. If, however, the indeterminate 
integers be still contended for, I must still submit that an in- 
determinate number of circumferences will afford a complete 
parallel. As subjects of analytical investigation they are of 
precisely the same character. 
I own I was surprised to see so much confidence placed in 
the argument of P. Q. to establish the triple condition of Mr. 
Herapath’s equation, p. 354. When 7 + v =” = indeter- 
minate integer [7 = const. ], it cannot be for a moment dis- 
puted that Av = An. But are we therefore to admit that 
gentleman’s interpretation of the consequences which flow fi pea 
this 
