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



occasion gentle currents; and even then would not be very important, because the forces 

 thence arising would not be periodic, and dependent upon the phase of vibration of the 

 pendulum. 



The grand difficulty which besets the observation of the time of vibration of a pendulum 

 oscillating in a liquid consists in the rapidity with which the oscillations subside. The best 

 form of a pendulum to oscillate in a liquid would be a sphere suspended by a fine wire. The 

 vessel containing the liquid and the sphere immersed in it ought to be so large as to render 

 the correction for confined space insensible. But the index of friction of a liquid would pro- 

 bably be better determined by experiments more of the nature of those of Coulomb, or perhaps 

 by the slow discharge of liquids through narrow tubes. 



Among the gases for which • n' ought to be determined experimentally should be 

 mentioned coal-gas, on account of the practical application which it appears possible to make 

 of the result to the laying down of gas-pipes. The calculation of the resistance in a circular 

 pipe is very simple, and is given in Art. 9 of my former paper. According to the equations 

 of condition assumed in the present paper we must put U = 0, U denoting in that article the 

 velocity close to the surface. It appears that the pressure spent in overcoming friction varies 

 as the mean velocity divided by the square of the diameter of the pipe, or as the rate of supply 

 divided by the fourth power of the diameter. This goes on the supposition that the motion is 

 sufficiently slow to allow of our neglecting the pressure which may be spent in producing 

 eddies, in comparison with that spent in overcoming what really constitutes internal friction. 



83. Third object. With respect to experiments for determining the length of the 

 seconds' pendulum, the theory of internal friction rather enables us to calculate for certain 

 forms of pendulum the correction due to the inertia of the air than points out any particular 

 mode of performing the experiments. Even the ordinary theory of hydrodynamics points out 

 the importance of removing all obstacles to the free motion of the air in the neighbourhood 

 of the pendulum if we would calculate from theory the whole correction for reduction to a 

 vacuum. 



Since the theoretical solution has been obtained in the case of a long cylindrical rod, or of 

 such a rod combined with a sphere, we may regard a pendulum formed in this manner, and 

 which is convertible in air, as also convertible in vacuum, for it is of small consequence 

 whether the pendulum be or be not really convertible in vacuum, provided that if it be not we 

 know the correction to be applied in consequence. 



