166 Mr. Galbraith on the Figure of the Earth. 
lums by the means of a number of observations near those 
points; so that any small change or error of the total variation 
from the equator to the pole, when substituted in the formula 
may have little effect on their absolute lengths when reduced 
through a small are by that formula. Thus at 70° N. Cap- 
tain Sabine finds 39'"*19452 for the length of the pendulum 
by grouping those within 10° on each side of it. Now by re- 
ducing this to the pole, it becomes 39°21816, differing little from 
what we have already found it. The equatorial pendulum 
has, by nearly a similar manner, been found to be 39:01259, 
though Captain Sabine’s group gives 39:01604. But if those 
at St. Thomas and Ascension he rejected as being on a ba- 
saltic basis, it will be 39°01308, differing little from the general 
mean of a number of places and different observers, and which 
we regard as the more decisive. Taking the polar pendulum 
at 39:21816, and the equatorial at 39:01259, the excess of the 
polar above the equatorial will be 0°20557, and hence the ellip- 
ticity will become 0-008608 —0:005270 = = very nearly. 
Hence, if we set out from the equator, the formula for the 
length of the pendulum at any latitude will be 
1 = 39:01260 + 0°20557 sin?'a .... (A) 
or, commencing at the parallel of 45° N. 
1 = 39°11540 — 0°102785 cos2A.... (B) 
From the foregoing results it appears that even if the quan- 
tities determined by Captain Sabine himself be substituted in 
the corrected formula for deducing the compression, it be- 
comes considerably different from the fraction expressing the 
ratio of the centrifugal force to gravity at the equator, and still 
more so if the quantities which we have selected be adopted, 
as in our opinion best entitled to confidence. 
By these remarks, it is by no means intended to set a light 
value upon Captain Sabine’s labours. They will be highly 
estimated by all capable of appretiating their merit; but so 
much we are afraid cannot be said for the formule he has em- 
ployed for deducing his final results. Approximations which 
might have been supposed sufficiently correct about a century 
ago, cannot now receive that appellation. What we have said 
is therefore rather intended to direct the attention of mathe- 
maticians to this subject, and to reconsider the degree of ac~ 
curacy which may be conceded to the usual formulae, than a 
critique on the labours of this distinguished officer, whose 
abilities and acquirements do so much honour to himself, and 
credit to his profession. 
It is hoped Mr. Ivory, who is now examining with so much 
ability 
