DEFINITION OF WORK DONE — MACGREGOR. 461 



have a definite magnitude and direction. That the definition 

 may be adapted for use in reasoning based on the Laws of 

 Motion, the axes employed in the definition must be the same 

 as those by reference to which the Laws of Motion hold. Hence 

 the usual definition wnll be freed from its arbitrary character 

 and rendered capable of convenient employment in dynamical 

 reasoning, by the following modification : — Work done is the 

 product of the magnitude of a force into the component displace- 

 ment of its point of application, in its action line, relatively 

 to any dynamical reference system. 



It will be obvious that from this modified definition, the 

 statement which Prof. Newcomb suggests as a definition, may 

 be deduced by the aid of the Third Law of Motion. 



It will also be obvious that in the elementary study of dyna- 

 mics, in which motions of small duration and extent on the 

 earth's surface are considered, and for which lines fixed in the 

 earth are a sufficient reference system, the young student need 

 not be asked to employ so general a definition. For him the 

 ordinary definition will be quite definite, as, in the first stages of 

 study, all displacements, velocities, etc., are specified relatively 

 to lines fixed in the earth at his place of observation, e. g., the 

 North-South line, the East- West line and the vertical. 



The arbitrary character of the ordinary definition being thus 

 removed. Prof. Newcomb's suggested modification loses its raison 

 d'itre. There are moreover three objections which may be urged 

 against it — (1.) It is not a definition merely, but embodies a 

 dynamical hypothesis as well, viz., the Third Law of Motion ; 

 and for the sake of clearness, definitions should be kept quite 

 distinct from hypotheses, (2.) It is not a definition of the 

 work done by a force, as it purports to be, but of the work done 

 by a stress ; and the work done by a force as distinct from the 

 work done by a stress has been found to be a convenient con- 

 ception in dynamical reasoning. (3.) It is applicable only in 

 cases of action at a distance. In all cases of contact action, it 

 would make the work done by a force, zero. In treating of 

 elastic solids and fluids therefore by the contact action method, 

 and in treating cases of apparent action at a distance on the 



