278 Dr. T. H. Havelock. A\yore, i, 
assumptions, we obtain an expression for the amplitude of the transverse 
waves thus originated, and for the resistance R, in which the velocity enters 
in the form e-#”; this function is seen to have the general character of the 
experimental curves. Adding on a similar term for the waves diverging 
from bow and stern, and, finally, in the manner of W. Froude, an oscillating 
factor for the interference of these bow and stern waves, we find a formula 
for the wave-making resistance of the type 
R = ae" 4 B {1—y cos (m/v?)} e-™. 
In this expression there are six adjustable constants ; we proceed to reduce 
the number of these after transforming into units which utilise Froude’s law 
of comparison. We use the quantity c, defined as 
(speed in knots)/,/(length of ship in feet), 
and we express the resistance in lbs. per ton displacement of the ship. An 
inspection of experimental curves, and other considerations suggest that the 
quantities 7, m, 1 may be treated as universal constants ; with this assumption, 
a three-constant formula is obtained, viz., 
R= ae~7558% 4 B {1 —v cos (10°2/c?)} 6-29, (3) 
where the constants «, 8, y depend upon the form of the ship. 
We then treat (3) as a semi-empirical formula of which the form has been 
suggested by the preceding theoretical considerations; several experimental 
model curves are examined, and numerical calculations are given which show 
that these can be expressed very well by a formula of the above type. 
Since the constant « is found to be small compared with 8, it is not 
allowable to press too closely the theoretical interpretation of the first term, 
especially as the experimental curves include certain small elements in 
addition to wave-making resistance. If we limit the comparison to values 
of ¢ from about 0°9 upwards, it is possible to fit the curves with an 
alternative formula of the type 
R = B {1—y cos (10°2/c?)} ee, 
and some examples of this are given. 
The effect of finite depth of water is considered, and a modification of the 
formula is obtained to express this effect as far as possible. Starting from 
an experimental curve for deep water, curves are drawn, from the formula, 
for the transverse wave resistance of the same model with different depths ; 
although certain simplifications have to be made, the curves show the 
character of the effect, and allow an estimate of the stage at which it becomes 
appreciable. 
In the last section the question of other types of pressure distribution is 
36 
