MOTION IN RELATION TO THE SURFACE FRICTION OF FLUIDS. 
211 
1000 cm. per second, by 8'5 per cent, at 2000 cm. per second, and by 15 per cent, at 
3000 cm. per second. 
This, of course, is an extreme case, since if the intermediate speed observations had 
been taken for the determination of n, a higher value would have been obtained and 
the error in the use of the index law at the highest velocities would have been much 
less. In order to show the manner of variation of n throughout the whole range of 
velocities obtained, the values of n have been determined by the Reynolds method 
at four different stages and are as follows :—• 
Velocity in centimetres per second . . . 58. 258. 900. 2250. 
Value of n from plotting.1'72 1 ‘77 1'82 1'92. 
Similar results showing a gradual increase in the value of n as the velocity increases 
have been obtained by the reduction of the observations for the 0'7125 and 1'255 cm. 
pipes, and it may therefore be taken as fully demonstrated that an index law for 
surface friction cannot be devised which will express the facts with any accuracy, 
except over a comparatively small range in the value of vdjv. It will be obvious that 
this factor must be borne in mind in predicting the skin friction of large bodies 
moving in a fluid from observations on small-scale models moved in the same fluid. 
The Comparison of the Results with those of Previous Experimenters. 
As the method of representing the results of the surface friction experiments 
described in this paper is somewhat novel, it has been considered advisable to reduce 
the observations of some well-known previous experimenters, in a similar manner, and 
to plot them all on the same diagram for the purpose of comparison. Taking only 
experiments on pipes whose roughness was comparable with the ones used by the 
authors, those chosen for reduction are as follows :— 
Experimenter. 
Fluid 
used. 
Nature of surface. 
Diameter of pipes in 
centimetres. 
Darcy 
1 Comptes Rendus de 
Water 
Drawn lead 
2 ■ 7 and 4'1 
l’Academie des 
Sciences,’ vol. 38 
>> 
Bitumen covered 
8-26, 19-6, and 28 -5 
Reynolds 
‘ Phil. Trans. Roy. 
Soc.,’ 1883 
Drawn lead 
0-62 and D27 
Saph and Schoder 
‘Proc. Amer. Soc. Civ. 
Engs.,’ 1903, vol. 51, 
p. 253 
>> 
Drawn brass 
5-31, 3-81, 314, 2-68, 
1-60, 0-82, and 0'27 
Brix 
‘Phil. Mag.,’ vol. 17, 
Air 
Lead 
0-635 
>> 
1909, p. 395 
)> 
Wrought iron 
8-26, 13-2, and 17 -1 
Stockalper 
‘ Revue Uni vers, des 
Mines,’ vol. 7, p. 257 
) J 
Cast and wrought iron 
15 and 20 
2 E 2 
