434 Different “ Rates” of Pennington’s Astronomical Clock, 
Such would be the ratio of the lengths of a pendulum to vibrate 
seconds at the two assumed stations: and from this it follows, 
that if at the temperature 50°, 39-136 inches be the length of a 
second pendulum at Woolwich Common, its length at the spot 
assumed for the experiment in the isle of Balta would be 39°1724 
inches; and this result, Ihave no doubt, is exceedingly near the 
truth. 
But before a result of this kind can be classed with others, in 
order for application to the question of the earth’s figure, the 
deductions from the respective series of observation must be re- , 
duced to the same level. Such reduction I shall make conform- 
ably with the principles usually adopted, although I am _per- 
suaded (and could easily show, would it not extend this paper to 
too great a length) that it often introduces a greater error than 
that which it is intended to correct. In the case before us, where 
the difference between the levels of the two stations is eighty feet 
and 2101,0000 feet the earth’s radius, we have € : tow), : 
or 1:000007615, for the factor by which the last term of the 
above ratio must be multiplied. The multiplication being ef- 
fected, we have when reduced to the level of the sea, 
Length pend. at /Voolwich: length at Balta :: 1 : 1-0009379. 
This ratio is the only independgnt result as to the lengths of 
pendulums at the two places furnished by the apparatus com- 
mitted to my charge. 
To judge to what extent confidence may be placed in this ul- 
timate deduction, let us consider what will follow, supposing the 
difference in the rates at the two stations to be appreciated within 
only half a second of the truth. ‘Then, since (+d)? —n*= 
2Qnd+d°, n being =86400, and d less than 4, 2nd is less than 
es — of 72, that is, the difference between the lengths of two 
pendulums that shall vibrate seconds at the respective stations, 
is, by such an experiment, ascertained to within the 2220th part 
of an inch. 
I have no conception that any result which depends upon ac- 
tual measurement, and still more upon measurement and com- 
putation conjointly, can go beyond this degree of accuracy ; if, 
indeed, it can attain it. 
If it were true that the terrestrial meridians were similar el- 
lipses, and if it were at all philosophical to attempt to infer the 
“¢ compression ”’ of the earth, as it is technically termed, from 
{wo observations upon the pendulum ; it would f ollow from those 
which have been here described, adopting the well known me- 
thod by means of two similar equations: 
m=A+d sin. L 
m=AaA-+ da sin? L’: and, 
