586 ELECTRICAL UNITS. 



605. DERIVED MECHANICAL UNITS. The principal derived 

 units in mechanics are velocity, acceleration, force, work or energy. 



Velocity \v\. Velocity v is the path traversed by a moving body 

 in unit time, or the quotient of a length by a time. Hence, the 

 dimensions of velocity will be expressed by the formula 



Acceleration [y]. Acceleration y, is the ratio of the increase 

 of velocity to the increase of time ; it is therefore the quotient 

 of a velocity by a time, and we have for the dimensions of the 

 unit, 



Force [/]. Force / is the product of a mass by an accele- 

 ration, which gives 



[/] = [LMT-]. 



Work, Energy [W]. Work or energy is the product ot a 

 force by a length ; vis viva, which is a quantity of the same kind, 

 is the product of a mass by the square of a velocity. In both 

 cases we have 



[W] = [L 2 MT- 2 ]. 



The unit of force is that which acting on unit of mass for 

 unit time imparts to it unit acceleration. 



The unit of work is the work produced by unit of force, when 

 its point of application is displaced in its own direction by unit 

 length. 



These two latter units are not those in ordinary use ; the 

 weight is commonly taken as unit of force : for instance a 

 gramme or a kilogramme, and the kilogrammetre as unit of 

 work. This amounts to choosing the unit of force, instead of 

 the unit of mass, as the third fundamental unit. The choice of 

 a weight like that of the kilogramme in the Archives at Paris, 

 as the unit of force, has this inconvenience, that if this body, or 

 any other equivalent, is moved to another part of the globe, its 

 true weight will no longer represent the unit of force, in consequence 



