July 9, 1915] 



SCIENCE 



57 



twice as great as another when it will produce 

 twice as much velocity per second when acting 

 on a given body. It follows from this agree- 

 ment that the acceleration produced by an un- 

 balanced force is proportional to the force 

 if the mass^ of the accelerated body is given; 

 and experiment shows to an extreme degree of 

 precision that the acceleration produced by a 

 given force is inversely proportional to the 

 mass of the accelerated body. In this state- 

 ment the mass of the body is understood to be 

 the result obtained by weighing the body on 

 a balance scale. 



The great advantage of the second point of 

 view lies in the fact that the accelerating 

 effect of a force affords a satisfactory basis for 

 precise force measurements; and the only ad- 

 vantage of the first point of view is that the 

 stretch of a spring is easily measured and 

 easily connected with our muscular sense. 



The experimental content of the second 

 point of view as above outlined may be derived 

 from the simple experimental fact that two 

 hricTts fall with the same increasing velocity 

 and therefore with the same acceleration as 

 one hrich. Fig. 1 shows the pull of gravity F 



■massSm 



'•acceleration & 

 Fig. 1. 



fiirce zE 



'.acceleration a 



Fig. 2. 



iacceleration^Q 



Pig. 3. 



on one brick of mass m, and the acceleration 

 produced is a. Fig. 2 shows the pull of grav- 

 ity 2F on two bricks of mass Sm, and the 

 acceleration produced is a. Now suppose we 

 reduce the force on the two bricks to half the 

 value it has in Fig. 2, then according to our 

 agreement* the acceleration produced wUl be 



3 Strictly, if the accelerated iody is given, be- 

 cause experiment only can show that a given 

 ■force will produce the same acceleration in dif- 

 'ferent bodies of the same mass. 



* Our agreement to consider F as half as great 

 when a is half as great does not, in all strictness, 

 apply here. Of course we can, by definition, con- 



halved, as indicated in Fig. 3. Then by com- 

 paring Figs. 1 and 3 we see that the accelera- 

 tion produced by a given force is halved if the 

 mass of the accelerated body is doubled. 



The accelerating effect of an unbalanced 

 force is the starting point of the science of 

 dynamics, and the importance of the above 

 discussion can not be overestimated. It must 

 be remembered, however, that there is an ex- 

 tremely wide variety of effects which forces 

 produce. Thus one may exert a steady pull 

 on a body to overcome friction and keep the 

 tody in motion; one may exert a steady pull 

 on a spring to keep the spring stretched; a 

 ball bat exerts a great force on the ball in 

 setting the hall in motion; steam is condensed 

 into water when it is compressed; ice is partly 

 melted when it is compressed ; and so on. 



Another matter which is always dragged 

 into every discussion of elementary dynamics 

 is the distinction between mass and weight, 

 and although men like Professor Hoskins^ axe 

 never confused thereby, others are confused 

 hopelessly. 



By a certain weight of material we nearly 

 always mean in everyday life an amount of 

 material as measured by a balance scale. Thus 

 we speak of ten pounds of sugar or five tons 

 of coal as weights of these substances. This 

 popular meaning of the word weight is the 

 precise and accepted meaning of the word mass 

 as used by scientific men. Coal dealers and 

 scientific men use the same units of mass, 

 namely, the pound or the kilogram, whereas 

 a diminishing group of engineers would have 

 us measure coal in terms of what John Perry 

 has, in semi-ridicule, called the " slug," the 



sider the pull of the earth on one brick to be half 

 as great as the pull of the earth on two bricks, 

 but experiment only can show that the pull of the 

 earth on one brick would, if applied to two 

 bricks, produce half as much acceleration as the 

 pull of the earth on two bricks! This statement 

 and the statements given in the previous footnotes 

 are intended to convey some idea as to the im- 

 mense amount of experimental fact there is in 

 Newton's second law of motion, however we may 

 attempt to simplify it by agreements as to for- 

 mal definitions. 



5 Science, May 7, 1915, pages 684-685. 



