THEORY OP ^IDES* 
22 ) 
perhaps -OOC 1 , d being four times the depth j but instead of 
having f as a measure of the height corresponding to the 
resistance, we may determine the equivalent inclination by find- 
ing j- ) which will be — ° 2cv 5 and this we are to compare with 
the greatest force tending to produce the horizontal motion, or 
1,5708< ? But since V ^7W0q av*+2cv . 1*5708? 
6216X5280 ' 6216 X 5280* d * 6216X5280 
ar+2c 1*5708 , . .... 
— - — — * — - — > and the greatest resistance will be to the 
d 4147200 
greatest propelling force as ( av+2c ) to d , or as 
35^ + 126 to the depth in inches, that is, as + 10§feetto 
the depth. Hence it appears that if this calculation were 
sufficient to determine the magnitude of the resistance, that part 
of it which varies as the square of the velocity would be small 
in comparison with the part which varies as the velocity, not 
only for a tide of one foot, but even for one of ten feet in 
height ; and that both parts would become almost insensible in 
a sea of considerable depth. In fact, however, the observations 
have been made under circumstances so widely different, that 
no valid conclusions can be formed from them with respect to 
depths so great and velocities so small, even if we could dis- 
regard the irregularities of the bottom of the sea, which, by 
the eddies and other deviations depending on them, must create 
a much greater resistance than the calculation indicates ; and 
this resistance, from the nature of the centrifugal forces con-* 
cerned in it, is much more likely to vary as the square of the 
velocity than as the velocity simply. If we employed Dubuat’s 
original formula » = (t+ 1 .^ --3.) 
we might infer that the resistance or adhesion would annihilate 
the velocity when *3 HL V (6 + 1-6)) became equal to 
2 97, l being the cosecant of the inclination, or here 
sotbai:, if -3 (v r 6— HL,/(6+l'6)) = 136.9 : con- 
sequently nothing can be inferred from the calculation, except 
that Dubuaf’s formula is totally inapplicable to the case ; perhaps, 
however, the extravagant resistance, which is indicated by it, 
jpay be admitted a's a conjectural argument, to shew that the 
resistance, 
