352 



The mode of suspension adopted by Capt. Kater was the knife- 

 edge, of which he points out the various advantages and disadvan- 

 tages, and the methods he took for overcoming the difficulties of the 

 inquiry. By employing the method of coincidences he found that 

 the number of vibrations made by the pendulum in twenty-four 

 hours might be obtained to within half a second of the truth in the 

 space of eight minutes : and he then applied the usual correction 

 for the extent of the arc of vibration, and also for the height of the 

 place of observation above the level of the sea. 



5. This paper was followed by another, " On the length of the 

 French Metre estimated in parts of the English Standard :" in de- 

 termining which he employed the same micrometer microscopes as 

 were used in the pendulum experiments, bringing them alternately 

 over the metre and over the standard scale, placed in the same plane 

 parallel to and in contact with one another ; care being taken that 

 their temperatures were the same. 



6. In the following year (1819) Capt. Kater gives an " Account of 

 experiments for determining the Variation in the Length of the Pen- 

 dulum vibrating Seconds, at the principal stations of the Trigonome- 

 trical Survey of Great Britain :" a paper which is full of laborious 

 calculations, founded on the observations therein detailed. The in- 

 vestigation of the diminution of terrestrial gravity from the equator 

 to the 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 2§ 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 

 various degrees of density : instances of the occurrence of which 

 are given in this paper. 



7. In the 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 efFeet of these differences on the figure of the earth. 



