58 
element (a); and, if this is considered to vary in proportion 
to the square of the velocity of the rubbing surface it will 
be measured by 
jj," + y^sin^a + 2ruvco^pcoBa^a 
(see Art. 8) where jj," is a constant to be determined by 
experiment. It follows then that 
M = jj.'Z^rttcos.v - {v - V)oos.a} Vcos.v 
+ + 2rtwco^ycoBa + v^sin^aja 
where S has a similar meaning to that which is given in 
the first part of this article. 
24. If, N—nv equations (22) and (23) admit of the fol- 
lowing forms readily obtained. 
(24) 
Where, A2(r^cos^»/cosa)ct = (1 - ^^)E(rcosvcos^a)a 
1 
B2(?'^C0S^j/C0Sa)a = (1 - ?^)^.S(cos^a)a - - 
And, M = i." I c(^y - 2 d(~) + eI 
J 
(25) 
Where, C = 2 { + juVsinV}a 
D = 2{/i(l - :^)rcos^)/cosa - ju'Vcosj/cosa}a 
E = S{ju(l - ^^)^cosvcos^a + ^''sinV } a 
The quantities A, B, C, &c., are partly physical and partly 
geometrical, whose values can be readily calculated by 
integration over the surface of the propeller when jw, fj,", 
and n are given quantities. 
By solving (24) as a quadratic 
w = v{k± - B) (26) 
Substitute this value in (25) and it becomes 
M = «/nC(A± v^A='-B)'‘-2D(A± Va^"B) + E} (27) 
25. If (n) is regarded as a constant quantity for the same 
ship and screw propeller, it follows from (26) that the ratio 
of the sjpeed of the ship to the angular velocity of the 
propeller is constant. 
The data furnished by the trials of the “Iris” (see 
Transactions of the Institution of Naval Architects for 
1879) seem to confirm the truth of this inference. 
The first series gives the following : — 
