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



was to be expected beforehand that the results of calculation would fall short of those of 

 observation, inasmuch as only two arcs were registered in each experiment, so that no data 

 were afforded for eliminating the effect of that part of the resistance which did not vary as the 

 first power of the velocity. 



78. I have now finished the comparison between theory and experiment, but before con- 

 cluding this Section I will make a few general remarks. 



When a new theory is started, it is proper to enquire how far the theory does violence to 

 the notions previously entertained on the subject. The present theory can hardly be called 

 new, because the partial differential equations of motion were given nearly thirty years ago by 

 Navier, and have since been obtained, on different principles, by other mathematicians ; but 

 the application of the theory to actual experiment, except in some doubtful cases relating to 

 the discharge of liquids through capillary tubes, and the determination of the numerical value 

 of the constant xi', are, I believe, altogether new. Let us then, in the first instance, examine 

 the magnitude of the tangential pressure which we are obliged by theory to suppose capable 

 of existing in air or water. 



For the sake of clear ideas, conceive a mass of air or water to be moving in horizontal 

 layers, in such a manner that each layer moves uniformly in a given horizontal direction, 

 while the velocity increases, in going upwards, at the rate of one inch per second for each inch 

 of ascent. Then the sliding in the direction of a horizontal plane is equal to unity, and there- 

 fore the tangential pressure referred to a unit of surface is equal to xi or /x'p. The absolute 

 magnitude of this unit sliding evidently depends only on the arbitrary unit of time, which is 

 here supposed to be a second. In the case supposed, it will be easily seen that the particles 

 situated at one instant in a vertical line are situated at the expiration of one second in 

 a straight line inclined at an angle of 45° to the horizon. Equating the tangential pressure 

 xi'p to the normal pressure due to a height h of the fluid, we get h = g' 1 xi, g being the force 

 of gravity. Putting now g = 386, xt'= (0J16) 2 for air, xi = (0.0564) 2 for water, we get 

 h = 0.00003486 inch for air, and h = 0.000008241 inch for water, or about the one thirty-thou- 

 sandth part of an inch for air, and less than the one hundred-thousandth part of an inch for 

 water. If we enquire what must be the side of a square in order that the total tangential 

 pressure on a horizontal surface equal to that square may amount to one grain, supposing the 

 density of air to be to that of water as 1 to 836, and the weight of a cubic inch of water to be 

 252.6 grains, we get 25 feet 8 inches for air, and 1 foot 10 inches for water. It is plain that 

 the effect of such small forces may well be insignificant in most cases. 



79. In a former paper I investigated the effect of internal friction on the propagation of 

 sound, taking the simple case of an indefinite succession of plane waves*. It appeared that 

 the effect consisted partly in a gradual subsidence of the motion, and partly in a diminution of 

 the velocity of propagation, both effects being greater for short waves than for long. The 

 second effect, as I there remarked, would be contrary to the result of an experiment of 



• Camb. Phil. Trans. Vol. VIII. p. 302. 



