1818.] Proceedings of Philosophical Societies. 219 



Article XI. 



Proceedings of Philosophical Societies. 



ROYAL SOCIETY. 



Feb. 5. — An abstract was read of Capt. Kater's paper on the 

 length of the pendulum vibrating seconds in the latitude of 

 London. 



Those who have attempted the solution of this problem, with 

 the exception of Whitehurst, have proceeded on the assumption 

 that the place of the centre of oscillation might be determined 

 by calculation. But, the truth of this depending on the regular 

 figure and uniform density of the body employed as a pendulum, 

 the difficulties attending this mode of inquiiy, may, perhaps, be 

 considered as insurmountable. Capt. Kater having satisfied 

 himself of the inadequacy of this method, endeavoured to dis-? 

 cover some property of the pendulum of which he might avail 

 himself, with a better prospect of success ; and was so fortunate 

 as to perceive, that the theorem of Huygens, of the reciprocity of 

 the axes of suspension and oscillation, afforded a principle on 

 which to construct a pendulum exempt from all errors resulting 

 from unequal density, or irregular figure. 



It is demonstrable that if a pendulum be made to vibrate on its 

 centre of oscillation, its former point of suspension becomes the 

 centre of oscillation ; and the number of vibrations on each will 

 be the same in equal times. The pendulum was made of plate 

 brass ; two knife edges were passed through it at the distance of 

 about 39*4 inches, and firmly secured. The distance between 

 these was carefully determined in parts of a standard scale, 

 which was the property of the late Sir George Shuckburgh. The 

 pendulum was furnished with three weights, the largest fixed, 

 and the two others moveable. 



The moveable weights were shifted, until the number of vibra- 

 tions in 24 hours, on either knife edge, was equal, when it is 

 evident that the one knife edge being considered as the point of 

 suspension, the other must be in the centre of oscillation, and 

 the distance between the knife edges will be equal to the length 

 of a simple pendulum vibrating in the same time. 



It appears from a table, given by the author, of 12 sets of expe- 

 riments, for ascertaining the number of vibrations made by the 

 pendulum in 24 hours, each set consisting of four experiments, 

 from which the length of the second's pendulum is deduced, that 

 seven of these sets are within one ten thousandth of an inch of 

 the mean result, two within two ten thousandths ; and of the 

 remaining sets, the greatest difference is less than three ten 

 thousandths of an inch. 



The conclusion deduced by Capt. Kater from his experiments 

 is, that the length of the pendulum vibrating seconds, in vacuo, 



