PART II. 



COMPARISON OF THEORY AND EXPERIMENT. 



Section I. 

 Discussion of the Experiments of Baity, Bessel, Coulomb, and Dubuat. 



54. The experiments discussed in this Section will be taken in the order which is most 

 convenient for discussion, which happens to be almost exactly the reverse of the chronological 

 order. I commence with the experiments of the late Mr Baily, which are described in the 

 Philosophical Transactions for 1832, in a memoir entitled "On the Correction of a Pendulum 

 for the Reduction to a Vacuum : together with Remarks on some anomalies observed in Pendu- 

 lum experiments." 



The object of these experiments was, to determine by actual observation the correction to 

 the time of vibration due to the presence of the air in the case of a great number of pendu- 

 lums of various forms. This was effected by placing each pendulum in succession in a vacuum 

 apparatus, by which means the pendulum, without being dismounted, could be swung alter- 

 nately under the full atmospheric pressure, and in air so highly rarefied as nearly to approach 

 to a vacuum. The paper, as originally presented to the Royal Society, contained the results 

 obtained with 41 pendulums, the same body being counted as a different pendulum when 

 swung in a different manner. Out of these, 14 are of such forms as to admit of comparison 

 with theory. An addition to the paper contains the results obtained with 45 pendulums more, 

 of which 24 admit of comparison with theory. The details of these additional experiments 

 are omitted, the results only being given. 



Baily has exhibited the results obtained with the several pendulums in each of two ways, 

 first, by the value of the factor n by which the correction for buoyancy must be multiplied 

 in order to amount to the whole effect of the air as given by observation, and, secondly, by 

 the weight of air which must be conceived to be attached to the centre of gyration of the 

 pendulum, adding to its inertia without adding to its weight, in order that the increased 

 inertia, combined with the buoyancy of the air, may account for the whole effect observed. 

 I shall uniformly write n for Baily's n, in order to distinguish it from the n of Part I. of the 

 present paper, which has a totally different meaning. In the case of a pendulum oscillating 

 in air, it will be sufficient, unless the pendulum be composed of extremely light materials, to 

 add together the effects of buoyancy and inertia. Hence if the pendulum consist of a sphere 

 attached to a fine wire of which the effect is neglected, or else of a uniform cylindrical rod, we 

 may suppose It = 1 + k, where k is the factor so denoted in Part I. ; so that if M' be the mass 

 of air displaced, kM' will be the mass which we must suppose collected at the centre of the 

 sphere, or distributed uniformly along the axis of the cylinder, in order to express the effect 

 of the inertia of the air. The second mode of exhibiting the effect of the air was suggested 

 by Mr Airy, and is better adapted than the former for investigating the effect of the several 



