246 
Mr T. Tredgold on Steam-Boats. 
“ Man, Nature’s minister and interpreter, acts and understands 
bnly so much of the order of nature as he has observed by the 
assistance of experience and reason his labours are confined 
to directing and modifying the effects of natural causes. These 
causes are often difficult to investigate ; and, therefore, the most 
concise and general modes of reasoning are the best fitted for his 
purpose ; by these methods, the pure sciences have been advan- 
ced to high perfection. I allude to the geometrical and analyti- 
cal methods of reasoning. By signs and characters, the alge- 
braist forms a condensed and faithful picture of the state of the 
problem ; the peculiar merits of this method are comprehensive- 
ness and generality. The geometer effects his object by the re- 
lation of lines and figures, and appeals to the senses for the cer- 
tainty of his conclusions. Each method has its advantages, but 
a mixture of the two modes is superior to either ; because the 
general conclusions of the one may often be proved to the senses 
by the other. 
But to return to the object of this paper, it may easily be con- 
ceived, that the motion of steam-boats, their forms and propor- 
tions, will afford some fine subjects for the application of science, 
and tend to illustrate the remarks we have just ventured, on the 
advantage of the species of knowledge, which is rather founded 
on a just conception of the action of natural causes, than on the 
systematic doctrine of schools. Our object-shall be, to find the 
resistance at different velocities in still water, and the best velo- 
city for the paddles; the disposition and number of the paddles; 
the resistance at different velocities in currents or streams, and 
the velocity for the paddles in such cases. 
In still water, it may be assumed, that the resistance of the 
same vessel is sensibly proportional to the square of the veloci- 
ty ; the difference from this law being too small to produce a 
sensible effect within the range to which the velocity is limited 
in practice. Therefore, if a be the force that will keep the 
boat in uniform motion at the velocity u, the force that will keep 
it in motion at the velocity v 9 will be found by this analogy, 
a 
u 2 : v 2 : : a : — — = the resistance at the velocity v. 
u z 
Now, this force acts with the velocity v ; hence, the mechani- 
