322 Researches in the Theory and Calculus of Operations. 



of the (n— n-hl) th or first degree by an equal opposing 

 force, terminating in equilibrium or annihilation. A single 

 impulsion is a force of the first degree. A periodical suc- 

 cession of equal impulses is given by a force of the second 

 degree, and such is the rank of force employed to produce 

 either frictional or voltaic electricity. The heat arising from 

 a uniform rate of combustion is a force of the second de- 

 gree, requiring to be uniformly supplied with fuel by a 

 force of the, third degree, and causing the production of a 

 uniform phenomenal effect by its reduction to the rank of 

 first degree (the generation of steam, which terminates in 

 uniform motion) ; but if the heat accumulates from confine- 

 ment, or from augmented combustion, it becomes itself a 

 force of the third degree, and its effect increases in higher 

 terms than linear or simple ratio (law of Mariotte). 



In the production of motion, if a series of balls be each 

 struck by one impulsion, the resulting motions are all uni- 

 form ; but when an equal series of impulsions are applied 

 to one same ball, the resulting motion is accelerated, as 

 the velocity has accumulated. Suppose a series of atwood 

 machines arranged at the edge of a shelf placed at a given 

 height above the earth's level, along which are laid as 

 many balls ready to be turned off. On reaching the till of 

 the machine, each ball will thence move uniformly during 

 the rest of its descent. But without such machine, a single 

 ball would receive from the gravitating force as many suc- 

 cessive equal impulsions as were given to the whole series 

 in the former case, and the movement is accelerated, the 

 accumulated velocity in the latter being equal to the sum 

 of the velocities in the former case. A uniform movement 

 may therefore be always regarded as the result of a single 

 application of a force of the second degree. 



In the conversion of water into steam, a number of suc- 

 cessive impulses of heat are consumed in transforming the 

 atomic forces from the liquid to the gaseous form (fig. 44), 



