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V. Similarity of Motion in Relation to the Surface Friction of Fluids. 
By T. E. Stanton and J. R. Pannell. 
Communicated by Dr. R T. Glazebrook, F.R.S. 
(From the National Physical Laboratory.) 
Received December 12, 1913,—Read January 29, 1914. 
The laws of the surface friction of fluids have formed the subject of many important 
investigations during the last 100 years, among which may be mentioned the work of 
Poiseuille, Darcy and Osborne Reynolds on the friction of water flowing in pipes, 
that of William Froude on the resistance of thin plates towed in water, and the 
corresponding experiments of Zahm on flat plates in a current of air. Researches in 
this field have also been carried out by Brix, Stockalper, Mallock, Coker, 
Gebers, Brightmore, Grindley and Gibson, and others. 
As a result, the effect on the resistance, of the dimensions of the body over whose 
surface the fluid moves, and of the velocity of flow, are tolerabfy well known for the 
particular fluid and character of motion observed. In the case of the surface friction 
of water in pipes, the researches of Osborne Reynolds have demonstrated the 
existence of similar motions in pipes of different dimensions, but, as far as the authors 
are aware, no systematic series of experiments appears to have been made for the 
purpose of establishing a general relation which would be applicable to all fluids and 
conditions of flow, although the existence of such relationships for different aspects of 
the problem were predicted as a consequence of the laws of motion by Stokes in 
1850,* by Helmholtz in 1873 , t by Osborne Reynolds in 1882,! by Lord Rayleigh§|| 
in 1899 and 1909, and as has been pointed out by Sir George Greenhill, were 
foreshadowed by Newton in Proposition 32, Book II., of the ‘Principia.’ 
The object of the present paper is to furnish evidence confirming the existence, 
* Stokes, ‘ Mathematical and Physical Papers,’ vol. IIP, p. 17. 
t Helmholtz, ‘ Wissenschaftliche Abhandlungen,’ vol. I., p. 158. 
1 ‘Phil. Trans. Roy. Soc.,’ 1883, p. 935. 
§ ‘Phil. Mag.,’ 1899, p. 321. 
|| ‘ Advisory Committee for Aeronautics, Report,’ 1909-10, p. 38. 
VOL. CCXIV.-A 513. Published separately, May 26, 1914. 
