254: REPORT—1874. 
and if h=H, we have, for the complete current, 
M= sve ; 
and this must equal Ft, as given in equation (1) ; 
or, since ¢=1", 
Fy= sve, 
or, since salt water weighs 64 lbs. per cubic foot, so that o=64, and g=32:2, 
we may write the equation with sufficient exactness 
Von 
a ae 
3F 
or, as the extreme breadth of the current, H= ve" 
If we apply this to the 50-ft. varnished surface, having a speed of 600 ft. 
per minute, or 10 ft. per second, which had the definite resistance of 
12-5 lbs., we have 
H='375 ft., or about 43 inches ; 
and this was not far from the truth, though, as it is not easy to obtain an 
exact measurement, the agreement must not be represented as more than 
approximate. 
But if the surface had been 500 feet instead of only 50 feet in length, and if 
we could assume the same resistance per square foot to be retained through- 
out the length, the current would be 3°75 feet broad, and the velocity, to a 
sensible distance from the surface, would be not far short of that of the 
surface; and we should have to encounter the paradox that under these 
circumstances the surface when enveloped in a favouring current more than 
3 feet in breadth, and having, for a breadth of many inches, scarcely less 
speed than the surface itself, would be experiencing the same resistance as 
when entering undisturbed water. 
If we suppose the law of distribution of velocity through the current to be 
different from that assumed in the above investigation, so as to allow particles 
having much less velocity to be near the surface, the breadth to be assigned 
to the current must be on the whole much greater, and the method by which 
the velocity could be thus distributed would be difficult to conceive. 
However, we do in fact see that the current is greatly disturbed by eddies ; 
and these, no doubt, furnish a machinery by which the distribution of velo- 
city is modified—the modification being of such sort that relatively undis- 
turbed particles are being perpetually fed inwards towards the surface from 
the outer margin of the current; and it is by this agency alone that the 
resistance throughout the length of surface is so little reduced as these ex-- 
‘periments prove: though, on the other hand, it seems to me certain that 
unlimited elongation of surface must nevertheless be accompanied by an all 
but unlimited reduction of resistance. At least it appears impossible to con- 
ceive a system of eddies such as to bring undisturbed particles across a current 
of unlimited width into close proximity with the surface, and in such quick suc- 
cession, as a sustained scale of resistance would imply. 
Practically, however, although these experiments do not directly deal with 
surfaces of greater length than 50 feet, they afford data sufficient to enable us 
to predict with tolerable certainty the resistance of surfaces of such lengths as 
