PROFESSOR MOSELEY ON THE THEORY OP MACHINES. 287 



with this velocity V, is manifestly the same under whatever circumstances that velo- 

 city may have been acquired ; the effects which a body having a given weight, and 

 moving with a given velocity, is capable of producing (the work which it is capable 

 of yielding) being manifestly independent of the causes from the operation of which 

 that velocity has resulted. Since then the work which a body is capable of yielding, 

 when its velocity has been acquired by the free action of gravity, is represented by 

 that function of its velocity which we call oncrhalf its vis viva, it is represented by 

 the same function when that velocity has been acquired by the action of any other 

 force, or under any other circumstances whatever ; and if the work which it is capa- 

 ble of yielding upon any resistance opposed to its motion be said to be accumulated 

 in it before it encounters that resistance, then under all circumstances is the accumu- 

 lated work of a moving body represented by one-half its vis viva. Giving to the 

 term vis viva this new interpretation, the principle of vis viva, as applied to machines, 

 may be enunciated thus : — " The difference between the aggregate work done upon 

 the machine during any time by those forces which tend to accelerate the motion, 

 and the aggregate work during the same time of those which tend to retard the 

 motion, is equal to the aggregate number of units of work accumulated in the mo- 

 ving parts of the machine during that time if the former aggregate exceed the latter, 

 and lost from them during that time if the former aggregate fall short of the latter." 

 Thus, then, if the aggregate work of the forces which tend to accelerate the motion 

 of a machine exceeds that of the forces which tend to retard it, then is the surplus 

 work (that done upon the driving points, above that expended upon the working 

 points) continually accumulated in the moving elements of the machine, and their 

 motion is thereby continually accelerated. And if the former aggregate be less than 

 the latter, then is the deficiency supplied from the work already accumulated in the 

 moving elements, or it is lost by them, so that their motion is in this case continu- 

 ally retarded. 



2. The moving power divides itself whilst it operates in a machine, first, into that 

 which overcomes the prejudicial resistances of the machine, or those which are op- 

 posed by friction and other causes, uselessly absorbing the work in its transmission. 

 Secondly, into that which accelerates the motion of the various moving parts of the 

 machine, and which accumulates in them so long as the work done by the moving 

 power upon it exceeds that expended upon the various resistances opposed to the 

 motion of the machine. Thirdly, into that which overcomes the useful resistances, 

 or those which are opposed to the motion of the machine at the working point, or 

 points, by the useful work which is done by it. Now the aggregate number of units 

 of useful work yielded by any machine at its working points, is less than the number 

 received upon the machine directly from the moving power, by the number of units 

 expended upon the prejudicial resistances, and by the number of units accumulated 

 in the moving parts of the machine whilst the work is being done. For if S Uj re- 

 present the number of units of work received upon the machine immediately from 



