100 Mr. Baily on the Discordancies in the Methods 



And the lengths of the three pendulums will be respectively, 



upper = gn' = x + ■— 

 middle = g n" = (x — S) + r^jN 

 lower = g7i"' = (x— A) + 



(N \ 2 

 86400 ) '^'^^ 

 give the length of the simple pendulum vibrating seconds : 

 where N must be taken equal to the number of vibrations 

 corresponding to the axis chosen for the multiplicand. 



It is in this manner that I propose at some future time to 

 treat the definitive results which may be obtained by the pen- 

 dulum here alluded to. The numerical operation, however, 

 is so troublesome, the quantities determined by the experi- 

 ments so mixed up with every step of the process, and the in- 

 troduction of a slight error affects so materially the final re- 

 sult, that I have considered it more satisfactory, in the pre- 

 sent viexv of the subject, to deduce the length of the simple 

 pendulum by the same means that I have adopted in the former 

 pendulum : viz. by considering each pair of synchronous knife 

 edges as convertible. That is, by considering the knife edges 

 A and C as convertible, and the knife edges B and D as con- 

 vertible : thus assuming them as two independent convertible 

 pendulums, on the same bar. 



From a mean of 8 measurements at various times, and dif- 

 ferino- very little from each othei-, and from a mean of 8 sets 

 of experiments of about two hours each, on each knife edge, 

 differing also very little from each other (corrected as in the 

 former cases), I find that the distance between A and C is 

 39*3038 inches, and the number of synchronous vibrations 

 86218*3: and that the distance between B and D is 39*3084< 

 inches, and the number of synchronous vibrations 86204'*6. 

 Consequently the length of the simple pendulum will be 



by A. C = (^orT ^^^'^^^^ = 39-1386 



by B. D = (-^<|^yx 39-3084 = 39*1307 



The first of these corresponds very nearly with the value de- 

 duced by Captain Kater : but whence arises the discrepancy 

 between'the two results ; and the discrepancy of both of them 

 from the former result ? The form and construction of this 

 pendulum are precisely similar to the one described in the first 

 part of this communication ; except that it is double the thick- 

 ness: which, on the whole I consider a disadvantage, although 



not 



