Royal Society. 15% 
tothe pole is pursued by the comparison of determinations of the 
length of the seconds pendulum at various stations: and is founded 
on the theorem demonstrated by Clairaut, that the sum of the two 
fractions expressing the ellipticity and the diminution of gravity 
from the pole to the equator is always a constant quantity, and is 
equal to 24 times the fraction expressing the ratio of centrifugal 
force, and that of gravity at the equator. The extreme degree of 
accuracy with which the force of gravitation may be determined by 
the apparatus employed by Capt. Kater, suggested to him the possi- 
bility of ascertaining by its means minute variations in this force 
observable in passing through a country composed of materials of 
yarious degrees of density: instances of the occurrence of which 
are given in this paper. 
7. Inthe year 1823, Capt. Kater communicated to the Royal Society 
an account of experiments made with an invariable pendulum be- 
longing to the Board of Longitude, by Sir Thomas Brisbane and 
Mr. Dunlop, at Paramatta in New South Wales, and thence deduces 
the fraction expressing the terrestrial compression. 
8. In a paper which appeared in the Phil. Trans. for 1821 (p. 75.) 
Capt. Kater gives an account of the comparison which he instituted 
of various British Standards of Linear Measures for the purpose of 
accurately examining the standard yard employed by General Roy, 
in the measurement of a base on Hounslow Heath, as a foundation for 
the trigonometrical operations carried on by the Ordnance through- 
out the country. He found material differences to exist between the 
standards of Sir George Shuckburgh, of Bird, of the Royal Society, 
of General Roy’s, and of the one constructed by Ramsden, which 
was used in the trigonometrical survey. Capt. Kater then proceeds to 
investigate the effect of these differences on the figure of the earth. 
9. Sir George Shuckburgh Evelyn kad, in the course of his inquiries 
respecting a standard of weights and measures, examined with great 
care the weights of a standard cube, cylinder, and sphere, and the 
methods employed for this purpose had been minutely described ; 
but the mode of ascertaining the dimensions of these bodies had not 
been so fully detailed. Capt. Kater was accordingly desirous of re- 
investigating this latter branch of the subject before the Commis- 
sioners of Weights and Measures should make their final report. The 
apparatus he employed for this purpose, and the results of his ex- 
periments, are stated in a paper also published in the Philosophical 
Transactions for 1821. 
10. These researches were continued by Capt. Kater in the year 
1825; and the details are given in a paper published in the Phil. Trans. 
for 1826, and entitled «‘ An Account of the construction and adjust- 
ment of the new standards of weights and measures of the United 
Kingdom of Great Britain and Ireland.” 
11. The series was completed in 1830 by the account he gives of 
the detection of a source of error in estimating the standard of linear 
measure, arising from the thickness of the bar, on the surface of 
which the lines are traced, and of the means he took to obviate it. 
12. The attention of Capt. Kater was at one time directed to the 
Third Series. Vol. 8. No. 45. Feb. 1836. 
