248 Dynamics. 



Reciprocally, if two points are so chosen, or so adjusted to 

 each other by moveable weights, that the pendulous body shall 

 vibrate in the same time when suspended from one as when sus- 

 pended from the other, these points are alternately the centres 

 of oscillation and points of suspension, and the distance asunder 

 is the length of the pendulum in question, and equal to that of a 

 simple pendulum vibrating in the same time. The above proposi- 

 tion was demonstrated by Huyghens, the original author of the 

 theory of the pendulum, but it was not till very lately applied to 

 any useful purpose. Captain Kater was the first, to perceive 

 that it furnished a very simple aud accurate method of deter- 

 mining the length of the compound pendulum. 



Figure 179 represents Captain Rater's pendulum. The axes 

 jF, O, were adjusted by means of intermediate moveable weights 

 C, D, and with so much accuracy that the number of oscilla- 

 tions made in twenty four hours, F being uppermost, differed from 

 those performed in the same time with O uppermost, less than 

 half a vibration ; and the mean of twelve sets of observations with 

 first one then the other uppermost, differed from each other less 

 than the hundredth of a vibration. The length of the pendulum, 

 as thus obtained, is stated to be 39,1386 inches. This is for the 

 latitude of London, or 51 31' 08",04 JV, and on the supposition 

 of the arcs of vibration being infinitely small, taking place in a 

 vacuum, and at the level of the sea, the temperature being 62 

 by Fahrenheit's thermometer. This determination exceeds what 

 was considered the most accurate result of the methods previous- 

 ly in use by 0,00813 or nearly one hundredth of an inch, a very 

 important difference in researches where the ten-thousandth of 

 an inch is appreciable quantity. 



It may be observed, moreover, that if the two axes of the 

 pendulum be cylindric surfaces, the points of suspension and 

 oscillation are truly in these surfaces, and the length sought is 

 rigorously the distance between these surfaces. This second 

 property, so necessary to the completeness of the method, when 

 actually applied to practice, was discovered by Laplace. See 

 Ed. Rev. vol. 30, p. 407. Phil. Trans, for 1818. 



