ON THE MOTIONS OF CONNECTED BODIES. 87 



strikes them, if the two portions were separated without tlie loss of any force. 

 But unless some art has been previously employed in producing a partial se- 

 paration, it will fre(juently be found, that the stick has strength enough to 

 break the glasses before it gives way. 



The subject of preponderance, or of the action of "weights or forces coun- 

 teracted by other forces, and incumbered with foreign matter to be put in 

 motion, requires for its discussion a previous knowledge of the simple opera- 

 tion of forces, of the conditions of equilibrium, and of the estimation of rota- 

 tory power. The consideration of the effects of preponderance enables us to 

 determine, in some circumstances, the best possible proportions of the powers 

 of machines, for producing the required effects in the most advantage- 

 ous manner. For, in order that motion may be produced, it is not sufficient 

 that there be an equilibrium, in procuring which a part only of the power is 

 expended, but there must be an excess of force above that which would be 

 necessary for the equilibrium; and it is often of consequence to know what 

 portion of the power must be employed in each way, in order that the great- 

 est effect, may be produced in a given time. We are sometimes told, that 

 what we gain in power, we lose in time. In one sense indeed the remark is 

 true; thus one man can do no more by a powerful machine in ten hours, 

 than ten men can do by a weaker machine in one hour; but in other senses 

 the assertion is often erroneous; for by increasing the mechanical advantage 

 to a given degree, we may in some cases considerably increase the perform- 

 ance of a machine, without adding to the force. 



According to the nature of the force employed, and to the construction 

 of the machine, a different calculation may be required for finding the best 

 proportions of the forces to be employed ; but a few simple instances will 

 serve to show the nature of the determination. Thus, in order that a smaller 

 weight may raise a greater to a given vertical height, in the shortest time 

 possible, by means of an inclined plane, the length of the plane must be to 

 its height, as twice the greater weight to the smaller, so that the acting force 

 may be twice as great as that which is simply required for the equilibrium. 

 This may be shown experimentally, by causing three equal weights, sup- 

 ported on wheels, to ascend at the same time as many inclined planes of the 

 same height, but of different lengths, by means of the descent of three other 



