in reply to Mr. Riddle. 49 
the whole demonstration hinges) is a function of the latitude 
by account, of the time nearest noon, determined by means of 
that latitude and of the middle time connected with it; and 
must evidently partake, in any future combination, of the in- 
exactness to which each of these quantities may be subject ; 
and that inexactness, we have seen, may be very considerable. 
Weask then, how is it possible that any combination or trans- 
formation of 7 can lead to an exact result, or to the correction 
of an inexact one? But to prop this, it is gratuitously sup- 
posed that, t—rit—c:i:nel, 
Or, t—c:ec—r:i:lin—1], 
Or, t-c= ree 
n—i 
Now, this implicitly supposes that a certain fixed relation 
must always subsist between t, r, and c, and that they will con- 
stantly bear the same invariable relation to x, With such an 
order of latitudes, the correction certainly may sometimes suc- 
ceed; but is such order to be always expected in practice? 
We may with as much truth suppose, 
Pmt ti—creg: 1, 
Or t~c:r+ec—2t::lin—1, 
Oy sOrps LOH Ewe" 
oT mit 2 
Or ¢= ~7+"£*; which would considerably 
n+l 
change the Doctor’s final equations, ¢ = ¢ + = - , &e. Ke. 
It is evident, therefore, that the correction derived from the 
Doctor’s reasoning will be conditionally true, and at best but 
very uncertain in practice. Hence J am not at all surprised 
that this mode of correction has imposed on Mr. R. Even 
Douwe’s solution, simple as it is, seems to have presented 
stumbling blocks, which he has not been able to get over. In 
his first paper, explaining what he calls the times A.M. and 
p.M., he says “ they are not 7ntended to represent the true ap- 
parent times of observation, but to determine the elapsed in- 
terval !—and to find with the aid of the estimated longitude 
the approximate Greenwich time for determining the declina- 
tion.” Now, without meaning any disrespect, was it possible 
he did not know that the times A.M. and P.M. do really repre- 
sent the true apparent times, not in the latitude sought, but 
* Hence would arise some curious paradoxes; as when xn = 0, (=r; 
as < , &c. 
Vol. 67. No. 333. Jan. 1826. G in 
and if n=1, t= 
