REPOUT ON HYDROSTATICS AND HYDRODYNAMICS. 149 



The theory has been also put to the test of expermient by 

 M. Bidone, who succeeded in overcoming in great measure an 

 obstacle in the way of making the experiments according to the 

 conditions supposed in the theory, arising from the adhesion of 

 the water to the immersed body*. His observations confirm 

 the existence and laws of motion of the accelerated waves. 



V. Scarcely anything worth mentioning has been effected 

 by theory in regard to the resistance of fluids to bodies moving 

 in them. The defect of every attempt hitherto made has 

 arisen from its proceeding upon some hypothesis respecting 

 the law of the resistance ; for instance, that it varies as the ve- 

 locity, or as the square of the velocity: whereas the law, which 

 cannot be known a priori, ought to be a result of the calcula- 

 tion, which should embrace not only the motion of the body, 

 but that of every particle of the fluid which moves simulta- 

 neously with it. The only problem that has been attempted 

 to be solved on this principle, is one of very considerable in- 

 terest, relating to the correction to be applied to the pendulum 

 to effect the reduction to a vacuum. The memoir of M. Pois- 

 son, " On the Simultaneous Motions of a Pendulum and of the 

 surrounding Air," was read before the Royal Academy of Paris 

 in August 1831, and is inserted in vol. xi. of iheiv 3femoires. 

 He takes the case of a spherical ball suspended by a very slen- 

 der thread, the effect of which is neglected in the calculations ; 

 the ball is supposed to perform oscillations of very small ampli- 

 tude, so that the air in contact with its surface is sensibly the 

 same during the motion. A simpler problem of resistance can- 

 not be conceived. M. Poisson considers the effect which the 

 friction of the particles of air against the surface of the ball 

 may have on its motion, and comes to the conclusion that the 

 time of the oscillations is not affected by it, but only their ex- 

 tent. The most important result of the theoretical calculation 

 is, that the correction which has been usually applied for the 

 reduction to a vacuum, and calculated without considering the 

 motion of the air, must be increased by one half. This he finds 

 to agree sufficiently with some experiments of Captain Sabine. 

 He also adduces forty-four experiments of Dubuat, made fifty 

 years ago, upon oscillations in water, and three upon oscilla- 

 tions in air. These give nearly the same numerical result, and 

 agreeing nearly with the value 1^. The experiments, however, 

 of M. Bessel give results which coincide with Dubuat's for os- 

 cillations in water, but determine the correction in air for re- 

 duction to a vacuum to be very nearly double that hitherto 



• See vol. XXV. of the Memoirs of the Royal Academy of Turin. 



