OF THE MOTION OF FLUIDS. 203 



Therefore if L be the length of the seconds pendulum in vacuum, 



2s * 



I in air, / = Z« ( 1 — — j 



The correction of the length of the pendulum is thus determined 

 to be double of what it would be if the motion of the air were not 

 considered. It is to be observed that these calculations apply strictly 

 only to the case of a very small ball. The experiments of M. Bessel 



give 1"956 for the coefficient of — . Those of Mr Baily, which were 



made most nearly under the circumstances which the theory supposes, 

 give 1"864. The effects of friction and of the suspending wire, would 

 tend to make the coefficient rather greater than less than 2. I am 

 therefore unable to account for the difference between the experimental 

 and theoretical determinations, which it appears by Mr Baily's experi- 

 ments, is greater as the radius of the ball is greater, excepting perhaps 

 the confined space of the apparatus may have had some effect on the 

 experimental results. 



It would not be difficult to shew from the nature of the analytical 

 expressions, that if the confined space in which the balls vibrate were 

 taken into account in the theory, the same results would be obtained 

 for two balls of different diameters, vibrating in different spaces, if the 

 linear dimensions of the spaces were in the proportion of the diameters, 

 their forms being alike. If this could be verified experimentally, it 

 would shew that the difference of the values of the numerical coefficient 

 which Mr Baily calls n, for balls of different diameters, as well as its 

 deviation from the theoretical value 2, is very probably owing to the 

 confined space of the vacuum apparatus. It would at any rate be de- 

 sirable to ascertain by experiment whether the same ball gives the same 

 value of n, when it oscillates in apparatus of different dimensions. 



Papworth St Everard, 

 March S, 1834. 



* This result I obtained in the London and Edinburgh Philosophical Magazine (September, 

 1833), by assuming the principle of the conservation of vis viva, without employing equa- 

 tion (B). 



