?98 Oji Machines in General. 



that we shall succeed in determining, if not the absolute 

 movement of each part of the system, at least in establishing 

 among these different particular movements the relations 

 which are most proper : it is by them, lastly, that we shall 

 give to the moving forces the most convenient situations 

 and directions, the least fatiguing, and the most proper for 

 employing their faculties in the most advantageous manner. 



LVII. This naturally leads us to the following interesting 

 question — Which is the best method of employing any 

 given powers, the natural effect of which is known, on 

 applying them to machines in motion ? In other words. 

 What is the method of making them produce the greatest 

 possible effect ? 



The solution of this problem depends upon particular cir- 

 cumstances ; but we may hereupon make some general ob- 

 servations applicable to all cases. The following are among 

 the most essential. 



The effect produced being the same thing (Lll.) with 

 the momentum of activity exercised by the resisting forces, 

 the general condition i?, that 9 is a maximum : now q never 

 being able to surpass Q, 1st, The quantity O must itself 

 be the greatest possible ; sdly, All this momentum Q must 

 be solely employed in producing the effect proposed. 



In order to make O a maximj/my we must consider 

 that it depends upon four things, viz.: upon the quantity of 

 force exercised by the agent which should produce the effect 

 <7, upon its velocity, upon ils direction, and upon the time 

 during which it acts. Now, 1st, As to what regards the di- 

 rection of the force, it is evident that this power should be 

 in every thing, besides being equal, directed in the same ratio 

 with its velocity, for the momentum of activity which du- 

 ring d t s. power F exercises, the velocity of which is V, and 

 the angle comprehended between F and V, Z, being 

 (XXXII) FV d i cosine z, it is clear that this produce 

 will never be greater than when cosine z will be equal to 

 the total sinus, i. e. when the force and its velocity shall be 

 directed in the same ratio : Sdly, As to what regards the in- 

 tensity of the force exercised, its velocity, and the time du- 

 ring which it is exercised ; we should not determine these 



things 



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