202 THE PERSISTENCE OF RELATIONS AMONG FORCES. 



To impress the truth here enunciated under its most 

 abstract form, some illustrations will be desirable. 



§ 64. Let two equal bullets be projected with equal 

 forces; then, in equal times, equal distances must be trav- 

 elled by them. The assertion that one of them will describe 

 an assigned space sooner than the other, though their 

 initial momenta were alike and they have been equally 

 resisted (for if they are unequally resisted the antecedents 

 differ) is an assertion that equal quantities of force have not 

 done equal amounts of work; and this cannot be thought 

 without thinking that some force has disappeared into noth- 

 ing or arisen out of nothing. Assume, further, that 

 during its night, one of them has been drawn by the Earth 

 a certain number of inches out of its original line of move- 

 ment ; then the other, which has moved the same distance in 

 the same time, must have fallen just as far towards the 

 Earth. jSTo other result can be imagined without imagining 

 that equal attractions acting for equal times, have pro- 

 duced unequal effects, which involves the inconceivable 

 proposition that some action has been created or anni- 

 hilated. Again, one of the bullets having pene- 

 trated the target to a certain depth, penetration by the 

 other bullet to a smaller depth, unless caused by altered 

 shape of the bullet or greater local density in the target, 

 cannot be mentally represented. Such a modification of 

 the consequents without modification of the antecedents, 

 is thinkable only through the impossible thought that 

 something has become nothing or nothing has become some- 

 thing. 



It is thus not with sequences only, but also with simul- 

 taneous changes and permanent co-existences. Given 

 charges of powder alike in quantity and quality, fired from 

 barrels of the same structure, and propelling bullets of 

 equal weights, sizes, and forms, similarly rammed down; 

 and it is a necessary inference that the concomitant actions 



