MUTUAL CHANGES COMMON TO ALL MATTER 67 



according to Newton's First Law of Motion, after the disturb- 

 ing body is removed. 



It is important to understand correctly the manner and 

 degree in which this retardation is brought about. First of 

 all, we learn from direct observation that the retardation is 

 greater in proportion as the mass of the whole system is 

 greater than that of the body under observation. That is, if 

 the mass of the three bodies together is four times greater 

 than the mass of the added body, then the speed acquired 

 by this body in falling for one second will be 8 feet per second, 

 instead of the 32 feet per second which it would gain in falling 

 by itself for the same time. In order to have a clear concep- 

 tion of the cause of this change of speed, it is advisable to 

 regard the arrangement of two perfectly equal masses, con- 

 nected by a non-extensible string which passes over a pulley, 

 as a system in equilibrium and ready to move in a vertical 

 direction, just as if it were released entirely from the stress 

 which exists between the earth and all bodies near it. As 

 a matter of fact, the stress cannot be annihilated, and we have 

 here two such stresses, exactly equal, but made by the string, 

 which is said to be in a state of ' tension/ to counteract each 

 other. (We have a similar counteraction of two stresses when 

 equal masses are placed in the pans of a balance.) Under 

 these circumstances we may regard the system, as it now is, 

 to be just the same as any body placed in such a position in 

 space that it is free from all stresses and, indeed, from all 

 liabilities. This, however, is only true for any disturbance in 

 a vertical direction, but it is only for observing such disturb- 

 ances that it is used. When we come to place the additional 

 mass on one of these equal masses, we make the whole system, 

 i.e. the three bodies, participate in the effect of the stress exist- 

 ing between that additional mass arid the earth. In other 

 words, the change is spread out over three bodies, and the 

 actual rate of motion is diminished in exact proportion to the 

 relative increase in the quantity of matter taking part in 

 the given change. 



By these and similar observations we are led to the general- 

 isation that, in any consideration of the effects of a given 



F2 



