FLUIDS AND THE DETERMINATION OF THE CRITERION. 155 
The fact that these conditions are realized, under certain circumstances, has afforded 
the only means of verifying the truth of the assumptions as to the boundary con- 
ditions, that there shall be no slipping, and as to pm being independent of the 
variations of mean-motion. 
Verification of the Assumptions in the Equation of Viscous Fluid. 
28. As applied to the conditions of PorsruILLE’s experiments and similar experi- 
ments made since, the results obtained from the theory are found to agree throughout 
the entire range so long as w’, v’, w’ are zero, showing that if there were any slipping 
it must have been less than the thousandth part of the mean flow, although the 
tangential force at the boundary was 0°2 gr. per square centimetre, or over 6 lbs. per 
square foot, the mean flow 376 millims. (1°23 feet) per second, and 
du/dr = 215,000, 
the diameter of this tube being 0°014 millim., the length 125 millims., and the 
head 30 inches of mercury. 
Considering that the skin resistance of a steamer going at 25 knots is not 6 Ibs. 
per square foot, it appears that the assumptions as to the boundary conditions and 
the constancy of » have been verified under more exigent circumstances, both as 
regards tangential resistance and rate of variation of tangential stress, than occur in 
anything but exceptional cases. 
Evidence that other Solutions are possible. 
29. The fact that steady mean-motion is almost confined to capillary tubes—and 
that in larger tubes, except when the motion is almost insensibly slow, the mean- 
motion is sinuous and full of eddies, is abundant evidence of the possibility, under 
certain conditions, of solutions other than the singular solutions. 
In such solutions w’, v’, w’ have values, which are maintained, not as a system of 
steady periodic motion, but such as has a steady effect on the mean flow through the 
tube ; and equations (1) are only approximately true. 
The Application of the Equations of the Mean- and Relative-mean-motion. 
30. Since the components of mean-mean-motion in directions y and z are zero, and 
the mean flow is steady, 
On — 0) dU da Nadia — 0% a. 9 =) eee(ee 
MDCCCXCV.—-A. Ke 
