q/' the Pendulum made by Capt. Kater, M. Biot, S)C. 17 



bable hypothesis that observation and experiment will war- 

 rant. In such circumstances, however, we cannot with pro- 

 priety attempt to ascertain accurately on mathematical prin- 

 ciples the exact form of the meridian, or whether they are all 

 similar to one another: — this, depending on a great variety 

 of very nice observations, must be the work of time. I can 

 only add that the subject will not be lost sight of ; and as ma- 

 terials increase, efforts shall be repeatedly made to arrive at 

 the truth. 



As the method of ascertaining the length of the pendulum 

 proposed by Capt. Kater is now, from its simplicity and ac- 

 curacy, much used, it appeared to me that a hvi formulae, of 

 easy application to the necessary reductions, would not be un- 

 acceptable. 



On the small Corrections of Pejidulums, on account of the tnmide 

 Variations they may he supposed to undergo from Change of 

 Temjyerature, Latitude, Sfc. 



If N = 86400 be the number of oscillations of the pendu- 

 lum L in a mean solar day ; and n, not differing much from 

 N, the number of oscillations of a given pendulum /, nearly 

 equal in length to L ; we can easily find approximations to 

 these quantities for small differences' 



From the common treatises on mechanics we have the 



time t — —, consequently - = ^/ - , and / = -^^. Now 



" "■ n L, n- 



suppose the pendulum L to be mcreased by the small quan- 

 tity A L to find A N, the number of seconds N will be di- 

 minished, or those the pendulum will lose in a day. 



In this case let L + A L = ^^^^, = L+ ^^ nearl}', 

 henceAL=-^=-^^ (1) 



and AN =-^ = 1-^ (2) 



It may be observed, that the same formulae can be applied 

 when N is increased, and consecjuently L diminished. 



Again : let 8L be the variation of L for one degree of the 

 thermonu'tcr to compute the change of L or N, then on this 

 account A L= «g A L x L (3) 



and A -N = -J-^— - = ^ = i N?i6L (4-) 



n here being the number of degrees of difference of tempe- 

 rature. * 



Acc()rding to the mean of a number of experiments upon va- 

 rious kinds of brass, its lineal variation from the freezing to the 



Vol ry5. No. :i2]. Jan. ]Horu C 'boiling 



