at the Island of Balta, and at Woolwich Common. 435 
; ‘ ‘ 5 1 d , 
i = 
and, taking the compression = =64 aa met that the said 
: c © : 1 : 
compression is expressed by the fraction jpe> agreeing nearly 
with the result of a comparison between the measurements of de- 
grees at the equator and in America. But the ouly use to which 
two or three results thus obtained by one observer can be legiti- 
mately applied, is to make them parts of a series obtained by 
different persons in different places, and reduce the whole to 
computation by the ‘* method of least squares.” aRe general 
result would in such case probably agree nearly with = aa the de- 
duction from'the lunar theory. 
So long, however, as the investigations are conducted upon the 
hypothesis that the meridians are similar ellipses, or even ellipses 
at all, they proceed upon a petitio principii, and must involve 
error, while they are employed to elicit truth. For, as Horsley 
remarked when speaking of this very hypothesis+, ‘* Plausible as 
it may seem, I must say that there is much reason from expe- 
riment to call it in question. If it were true, the increment of 
the force which actuates the pendulum as we approach the poles, 
should be as the square of the sine of the latitude; or, which is 
the same thing, the decrement, as we approach the equator, 
should be as the square of the cosine of the latitude. But who- 
ever takes the pains to compare together such of the observa- 
tions of the pendulum in different latitudes, as seem to have been 
made with the greatest care, will find that the increments and 
decrements do by no means follow these proportions ; and in 
those which I have examined, I find a regularity in the deviation 
which little resembles the mere error of observation. The un- 
avoidable conclusion is, that the true figure of the meridians is 
not elliptical. If the meridians are not ellipses, the difference 
of the diameters may, indeed, or it may not, be proportional to 
the difference between the polar and the equatorial force ; but it 
is quile un uncertainty what relation subsists betiveen the one 
guantily and the other: our whole theory, except so far as it 
relates to the homogeneous spheroid, is built upon false assump- 
tions, and there is no saying what figure of the earth any observa- 
tions of the pendulum give.” 
In reference to the irregular figure of the earth, Laplace, when 
speaking of the irregularities of its meridians, as proved by ac- 
* It should not, moreover, be forgotten in this inquiry, that new and cor- 
rect experiments on pendulums at the equator, and a more correct. appre. 
ciation of the equatorial radius of the earth, may change the fraction g}y, 
and all which depends upon it.— See Clairaut’s elegant disquisitions Su - 
la Théorie de la Figure de la Terre, part U. § 20. 
+ Letter to Captain Phipps. 
Ee2 tual 
