OF FLUIDS ON THE MOTION OF PENDULUMS. 



[73] 



61. In the 14th set of experiments, the weight of adhesive air due to the spheres alone 

 has been computed by Baily by subtracting from the whole weight, as given by observation, 

 the weight due to the rods as given by the 13th set of experiments, taking account of the 

 change of weight corresponding to the change in the position of the centre of gyration, the 

 point at which the air is supposed to be attached. According to theory, this process is not 

 legitimate, inasmuch as the weight dragged by a rod in a function of the time of vibration, 

 which is altered when a sphere is attached to the end of the rod. But in the 15th set of 

 experiments the spheres did not materially affect the time of vibration, inasmuch as they were 

 inserted nearly at the centre of oscillation of the rods, and therefore in this case the process 

 is legitimate. Accordingly, I think it is a sufficient comparison between theory and experi- 

 ment in the case of the 15th set, to compare the weights of air due to the spheres alone, as cal- 

 culated by Baily, with the weights calculated according to the theory of this paper with the 

 assumed value of \Zfx. I have exhibited separately the weight corresponding to the correc- 

 tion for confined space, in order to enable the reader to form an estimate of the extent to 

 which the results may be affected by the uncertainty relating to the amount of this correc- 

 tion. 



Weights of air dragged by the spheres alone, as deduced from Baily's results with the 

 spheres at the centre of oscillation of the long rods. 



62. I pass now to Bcssel's experiments described in his memoir entitled Untersuch- 

 ungen iiber die L'dnge des einfachen Sekundenpendels, which is printed among the memoirs of 

 the Academy of Sciences of Berlin for the year 1826. The object of this memoir was to 

 determine the length of the seconds' pendulum by a new method, which consisted in swinging 

 the same sphere with wires of two different lengths, the difference of lengths being measured 

 with extreme precision. In the calculation, the absolute length of the simple pendulum iso- 

 chronous with either the long or the short compound pendulum was regarded as unknown, but 

 the difference of the two as known, and this difference, combined with the observed times of 

 oscillation, is sufficient for the determination of the quantity sought. Nothing more would 

 have been required if the pendulums had been swung in a vacuum ; but inasmuch as they 

 were swung in air, a further correction was necessary to reduce the observations to a vacuum. 

 Since it is necessary to take into account the inertia of the air, as well as its buoyancy, in 

 reducing the observations to a vacuum, Bessel sought to determine by experiment the value of 

 Vol. IX, Part II. 34 



