[10] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



more than 2 inches in diameter, gave only 1*748. The latter were nearly of the same size 

 as those with which Bessel, by a different method, had obtained k = 0*94.6 or 0*956, which 

 corresponds to n = 1*946 or 1*956. Among the "Additional Experiments" in the latter 

 part of Baily's paper, is a set in which the pendulums consisted of plain cylindrical rods. 

 With these pendulums it was found that n regularly increased, though according to an 

 unknown law, as the diameter of the rod decreased. While a brass tube l^ inch in 

 diameter gave n equal to about 2*3, a thin rod or thick wire only 0*072 inch in diameter 

 gave for n a value as great as 7*530. 



Mathematicians in the meanwhile were not idle, and several memoirs appeared about this 

 time, of which the object was to determine from hydrodynamics the effect of a fluid on the 

 motion of a pendulum. The first of these came from the pen of the celebrated Poisson. 

 It was read before the French Academy on the 22nd of August 1831, and is printed in the 

 11th Volume of the Memoirs. In this paper, Poisson considers the case of a sphere suspended 

 by a fine wire, and oscillating in the air, or in any gas. He employs the ordinary equations 

 of motion of an elastic fluid, simplified by neglecting the terms which involve the square of 

 the velocity ; but in the end, in adapting his solution to practice, he neglects, as insensible, 

 the terms by which alone the action of an elastic differs from that of an incompressible fluid, 

 so that the result thus simplified is equally applicable to fluids of both classes. He finds 

 that when insensible quantities are neglected n = 1*5, so that the mass which we must sup- 

 pose added to that of the pendulum is equal to half the mass of the fluid displaced. This 

 result does not greatly differ from the results obtained experimentally by Bessel in the case 

 of spheres oscillating in water, but differs materially from the result he had obtained for air. 

 It agrees pretty closely with some experiments which had been performed about fifty years 

 before by Dubuat, who had in fact anticipated Bessel in shewing that the time of vibration 

 of a pendulum vibrating in a fluid would be affected by the inertia of the fluid as well as 

 by its density. Dubuat's labours on this subject had been altogether overlooked by those 

 who were engaged in pendulum experiments; probably because such persons were not 

 likely to seek in a treatise on hydraulics for information connected with the subject of their 

 researches. Dubuat had, in fact, rather applied the pendulum to hydrodynamics than hy- 

 drodynamics to the pendulum. 



In the Philosophical Magazine for September 1833, p. 185, is a short paper by Professor 

 Challis, on the subject of the resistance to a ball pendulum. After referring to a former 

 paper, in which he had shewn that no sensible error would be committed in a problem of 

 this nature by neglecting the compressibility of the fluid even if it be elastic, Professor Challis, 

 adopting a particular hypothesis respecting the motion, obtains 2 for the value of the factor 

 » for such a pendulum. This mode of solution, which is adopted in several subsequent 

 papers, has given rise to a controversy between Professor Challis and the Astronomer Royal, 

 who maintains the justice of Poisson's result. 



In a paper read before the Royal Society of Edinburgh on the 16th of December 1833, 

 and printed in the 13th Volume of the Society's Transactions, Green has determined from 

 the common equations of fluid motion the resistance to an ellipsoid performing small oscil- 

 lations without rotation. The result is expressed by a definite integral ; but when two of 



