55 
“ On Screw Propulsion/’ Part III., by Robert Rawson, 
Assoc. I.N. A., Hon. Member of the Manchester Literary and 
Philosophical Society, Member of the Mathematiccal Society. 
On the Eesistence of the Element (a) to Angular and 
Translatory Motion. 
19. In the preliminary problem already discussed the 
angular velocity (u) and the velocity (v) of translation along 
the axis AB were assumed, without reference to the cause 
by which these motions were produced and uniformly 
maintained. 
In this problem the only object of investigation was the 
correct estimation of the velocity of the element {a) in its 
normal direction when it was subject to a motion of rotation 
and translation measured by (u) and {y) respectively. 
For the solution of this problem it was not absolutely 
necessary to enquire minutely into the cause by which the 
motions of rotation and translation were produced, or, even 
into the manner by which these motions are related to each 
other during the time the cause of motion ds in full opera- 
tion. 
The application of the ordinary kinetic principles of the 
resolution and decomposition of velocities was quite sufficient 
for the purpose required in the problem, viz. to determine 
the normal velocity of the element (a). 
It is otherwise, however, when the cause of the motion of 
rotation and translation is the subject of consideration. In 
this case the application is required of other laws and 
principles than those which were found adequate and 
necessary in the solution of the preliminary problem. 
