Measure of Forces applied to Machines. 269 



is to act, forms a product less than the constant number 23134000, 

 or exceeding it but a little, the power may be considered as suf- 

 ficient for the proposed effect, it being supposed to act as in the 

 two preceding examples. But if the velocity with which the 

 weight is to be moved, is considerable compared with g , it will 

 be necessary to subtract from the constant number 23184092, 

 the quantity of motion m v due to the velocity with which the 

 body is to be moved ; and if the weight multiplied by g /, the ve- 

 locity which a falling body would acquire in the time during 

 which the machine is to be worked, forms a product smaller than 

 the remainder above found, the power may be deemed sufficient. 



388. In what we have now said, we have taken no account 

 of friction. When the motion of the machine has become uni- 

 form, (which is the state in which machines ought to be consider- 

 ed) the effect of friction may be regarded as constant, and it 

 may be compared to a new mass required to be moved together 

 with the proposed mass. Thus, in the case above considered, 

 the friction being supposed equivalent to the weight of a known 



part of the mass m, this resistance will require in the power 



a quantity of motion equal to mg /, and thus, 



c 



mv -\ -- mg t -{- mgt, 

 c 



or 



/ 



will be the measure of the moving force. 



If then, in the experiment above referred to (the axle being 

 supposed to have a radius much less than that of the cylinder), 

 we suppose the friction to have been T V of the weight, mv being 

 neglected, as it may be in this case, we must augment the number 

 23184000 by its twelfth part; then the force of a man in similar 

 circumstances may be represented by the number 25116000. 

 We see, therefore, that to be able to estimate with sufficient ac- 

 curacy the force of a man, we must previously ascertain the ra- 

 tio of the force of friction to that of the weight, in the experiment 

 employed, with the view of determining this force. Then if k 



