$g8 Don J. Rodriguez’s Observations on the 
into the calculation by assuming a false estimate of the sph®- 
roidity of the earth, or of other elements employed in the 
calculation, it is very evident that the zenith distances of stars 
taken at Arbury Hill are affected by some considerable error, 
wholly independent of these elements. 
It was not till the date of the measurement of the meridian 
in France, that M. Delambre published and explained, with 
admirable perspicuity and elegance, all the formulae and me- 
thods relative to the calculation of spheroids, and put it in the 
power of astronomers in general to make use of the elliptic 
elements in verifying the results of their observations. In the 
present state of science these elements are well known, and 
the errors that can arise from any uncertainty in them, are 
not so considerable as is generally supposed. The oblateness 
and the diameter at the equator are the only elements want- 
ing in the calculation ; for the purpose of seeing what effect 
our present uncertainty respecting them can have on the sub- 
ject in question, I have employed three different estimates of 
the oblateness T |-, and . With respect to the radius 
of the equator, that is ascertained with sufficient precision by 
the mean of the arc extending from Greenwich to Formen- 
tera, corresponding to latitude 45 0 4' 18". The value of the 
degree in toises is 57010,5, and it is highly probable that in 
this estimate the error does not amount to so much as half a 
toise, as it is deduced from an entire arc of 12 0 48' between 
the two extremities, the latitudes of which have been deter- 
mined with extreme care, and by a great number of obser- 
vations. 
The following are the logarithms of radius at the equator, 
which I have employed as adapted to each degree of oblateness. 
