60 To what Order of Lever does the Oar belong ? 



7 3 2 1 

 On the common theory -> ~> o> 9* 



On the true theory 7, 3, 2, 1. 



Thus the effect of outrigging, so as to place the rowlock at 

 one fourth the length of the oar instead of one eighth, would, 

 on the common view, only be to increase the power by one 

 sixth ; on the other view, it more than doubles it. 



Again, if we suppose the oar to remain with the rowlock at 

 one fourth of its length, while the hands are successively at 

 the handle, one eighth from the handle, at the rowlock, and 

 one eighth and one fourth outside, the successive proportions 

 of power to resistance are : — 



On the common theory -^ -=3 1, -> -> 



On the true theory 3, 6, 0, — 6, —3 



(the minus sign representing the reversal of the effect) . It 

 cannot be said that this difference is practically unimportant, 

 except in the sense that practical men will be led by expe- 

 rience, and not by a theory so manifestly erroneous as the 

 former. It would be enough for such men to be told that, 

 according to this theory, it is easier to move a boat by rowing 

 than by dragging. 



Now let us look at the case of a canoe. Here we may sup- 

 pose that the middle of the paddle remains at the same distance 

 from the canoer's body. Practically it is as if the paddle were 

 attached at its middle point to a rigid rod resting against his 

 body. If we are to apply to this case the same sort of reason- 

 ing which writers on Mechanics use in the former case, we 

 must treat this middle point as the point of application of the 

 resistance. Then we have the result that, as one hand moves 

 forward and the other backward, they counteract one another. 

 This is, I think, a reductio ad absurdum. There is no alter- 

 native but to treat the middle point as the virtual fulcrum. 

 The actual fulcrum is of course in the body of the canoer, but 

 this does not affect the question. 



There are two analogous cases which seem worth consider- 

 ing. First, that of a paddle-steamer. Here there is an 

 instantaneous lever of which the point that is actually at rest 

 is the lowest float in the water ; and following the received 

 theory of the oar, or rather on the same principle, we should 

 regard this as the fulcrum, the resistance acting at the shaft 

 or axis of the wheel. It would follow that when the 



