60 
The column D should be constant in accordance with 
the above inference. It is nearly so, and the slight deviation 
in the higher speeds may possibly arise from a slight increase 
in the friction of the engine, or, a slight error in the approxi- 
mate estimation of the above causes of resistances. 
Another inference of importance readily follows from 
formula (27) viz. that the best ^ro'peller for one ship is not 
generally the best propeller for another ship. The force of 
this inference is apparent from the circumstance that the 
form and dimensions of the best propeller depend upon the 
values of fx, y', p", n, which are generally different for different 
ships. 
26. Professor Osborne Keynolds, in his interesting com- 
munication to the I. of N. Architects, 1876, has suggested 
the existence, in the wake area of a ship, of a variable velocity 
which increases considerably, when accounted for, the diffi" 
culty of integrating the values of the forces in (19), (20), 
(21) ; and, he applies this variability in the wake velocity 
to the explanation of the propeller’s tendency to cause 
vibrations in the ship. It is not, however, easy to see how 
this effect is produced by the cause assigned, inasmuch as 
the force which tends to twist the axis is a factor of cos.j3, 
a quantity which vanishes in conoidal surfaces, particular 
forms of which are used as propellers in Her Majesty’s navy. 
A problem, however, of some interest and difficulty pre- 
sents itself in formula (27), viz., required the form of pro- 
peller so as to make the coefficient of a minimum for a 
given value of engine power ? 
A somewhat similar problem to the above occupied the 
attention of the early writers on the calculus of variations. 
Newton and others sought the form of the lines of a vessel 
of minimum resistance; but the limited success, even of 
Newton’s solution, to practical shipbuilding does not afford 
much encouragement in a similar attempt, by means of the 
same calculus, to solve the problem of the screw propeller. 
