PROCEEDINGS OF THE POLYTECHNIC ASSOCIATION. 981 



ment, and divide the product by two. The effective space as thus 

 determined, is always proportional to the square of the difference 

 in velocity effected. 



The nature of the difference between the two measures of force 

 is now apparent. One shows the actual condition of a body, as 

 to rest or motion, and is proportional in bodies of equal weight to 

 the time in which a uniformly acting force produces the acquired 

 velocity. The other measui-es the space passed over while the 

 velocity is being acquired. Either measures the change a body is 

 capable of producing on another body wJteii eMimated in units of 

 its own kind. 



Now it happens that the spaces which bodies or atoms traverse, 

 while under the influence of opposing forces, form the most prac- 

 tical mode of determining the magnitude of all the active opera- 

 tions of life. Thus the products of the labor of men and animals, 

 as well as those of machinery of all kinds, consist entirely in results 

 equivalent to the raising of weights. Indeed, considering the 

 atoms of bodies as minute weights, this effect or product of " wovk^^ 

 is universal. While, therefore, the unit of this power of produc- 

 ing ^pace e^'ecYs is a proper oue for units of its own kind, we must, 

 to avoid confusion, distinguish carefully between the power of 

 performing loork and the moving force. 



Thus the compression or extension of a spring is " ivorh j)^^'- 

 formed " upon it, and the spring is capable of performing an equal 

 amount of work in reaction, while regaining its original freedom 

 from tension. So with the expansion of steam or of the gases 

 produced by exploding gunpowder, &c. Their effects are space 

 effects, and should be measured by units of their own kind. Most 

 of the confusion of ideas apparent in the discussions of this subject, 

 arise from attempting to measure a quantity or magnitude of one 

 kind by the unit of another. 



As a general conclusion, we find that a small force in a moving 

 body is capable of doing a great deal of work, if the velocity of 

 the body is very great ; while on' the other hand, a great force in 

 a body so heavy that it has but little velocity, does but compara- 

 tively little work. The converse of this is also true. In giving 

 the same momentum to a light body and a heavy one, more coils 

 of a spring are required for the former than for the latter, and the 

 same amount of work will give more momentum to a heavy body 

 than a lighter one — a principle exemplified in the employment of 

 fly wheels to store up force. 



