328 Don J. Rodriguez's Observations on the 
be affected, without a possibility of discovering such an error 
in this mode of operating. It is consequently necessary, in 
such a case, to employ some other method, which may serve 
as a means of verifying the observations themselves, of de- 
tecting their errors, if there be any, or at least of shewing 
their probable limits. 
My object therefore is to communicate the result of calcu- 
lations that I have made, from the data published by Lieut. Col. 
Mudge in the Philosophical Transactions; and I hope to make 
it appear, that the magnitude of a degree of the meridian, 
corresponding to the mean latitude of the arc measured by 
this skilful observer, corresponds very exactly with the results 
of those other measurements that have been above noticed. 
In M. Delambre's method nothing is wanting but the sphe- 
rical angles, that is to say, the horizontal angles observed, 
corrected for spherical error. Moreover, for our purpose, we 
have no occasion for the numerical value of the sides of the 
series of triangles, but only for their logarithms. Thus the 
logarithm of the base measured at Clifton, as an arc gives us 
that of its sine in feet or in fathoms, so that by means of this 
latter logarithm, and the spherical angles of the series of tri- 
angles, we obtain at once, and as easily as in plane trigonome- 
try, the logarithms of the sines of all their sides in fathoms. 
After this, it is extremely easy to convert them into loga- 
rithms of chords or of arcs, for the purpose of applying them 
to the computation of the arcs on the meridian or azimuths. 
I give the preference to taking the logarithms of the sides as 
arcs, because the computations become in that case much more 
simple and expeditious. 
Near to Clifton, which is the northern extremity of the arc. 
