98 Mr. Baily 07i the Discordancies in the Methods 



the convertible pendulum, I was naturally led to conclude that 

 I had inadvertently committed some error, which had escaped 

 my repeated examination. But my suspicions were removed 

 by the result of some experiments on a pendulum of another 

 kind ; and which has presented anomalies still more remark- 

 able. 



It has been shown by M. Prony, in his Lemons de Mechanique 

 Analytique, vol. ii. page 340, that we may determine the length 

 of the simple pendulum, by knowing the distance between, and 

 the number of vibrations made by, three knife edges placed 

 parallel to each other, and in the same vertical plane : since 

 these elements ai'e sufficient to enable us to determine not only 

 the distance of either knife edge from the centre of gravity of 

 the pendulum, but also the accelerative foixe of gi'avity, and 

 consequently the momentum of inertia. I therefore caused a 

 pendulum to be constructed on this j)rinciple ; but, 

 with the addition of another knife edge: thus obtain- 

 ingjbur axes of suspension, instead of three. By which 

 means, I could at any time get four combinations of 

 three axes, and thus obtain a mean result much nearer 

 the truth. I likewise caused the axes to be so placed that 



they should be convertible in pairs : that is, the knife b 



edges A and C are so placed that the vibrations on 

 them are synchronous, and the axes convertible: and 

 the same with respect to the knife edges B and D. 

 In a pendulum of this kind, therefore, we may deter- 

 mine the length of the simple pendulum, vibrating 

 seconds, either by the knife edges A — C, or the knife 

 edges B — D, according to Captain Kater's plan ; or 

 from any combination of three of the knife edges, ac- 

 cording to the method of M. Prony ; which, as it has 

 not yet appeared in any English work, I shall here 

 briefly describe, although at present I shall not make 

 any practical use of it. 



In the construction of Pi'ony's pendulum it is not 

 essential that the knife edges should be placed at dif- 

 ferent ends of the bar; unless it be intended that they 

 should be convertible. But it will be much more convenient 

 that they should be so situated : and that they should also be 

 so placed that each pair may be, as nearly as possible, equally 

 distant from the centre of gravity. On this principle, there- 

 fore, it follows that two of the three axes, chosen for the solu- 

 tion of the problem, will be on one side of the centre of gra- 

 vity ; and the other, on the opposite side. Let the distance 

 (in inches) between the extreme axes be denoted by A : and let 

 the distance between the middle axis and that axis which is on 



the 



