GENERAL PRINCIPLES 39 



weight has to traverse the whole depth of the well. The work 

 done is the product 'Of the two factors ; force and displacement. 

 In the same way, it is not enough to press a file heavily on a piece 

 of metal, as it is in displacing the file under a certain pressure 

 that it will produce work the really useful effect. All indus- 

 trial machinery illustrates the work done by forces. It is not 

 however, necessarily correct to estimate the energy expended by 

 the quantity of work accomplished, because the former depends 

 in addition to the force and displacement, on various factors. 

 Thus, if two labourers are each digging over 100 square metres, 

 the one who has the hardest ground and the worst tools will do 

 more work in the mechanical sense, although the result is the 

 same. 



Before Poncelet (1826) and Coriolis (1829), the word force was 

 used in the sense of work, that incorrect use has disappeared 

 to-day. The great natural philosophers of the XVI Ith and 

 XVIIIth Centuries (Huygbens, Bernoulli, De La Hire, Lavoisier, 

 Carnot) and even Helmholtz, as late as 1848, did not use the 

 term force except as the expression of the product of a weight 

 by a distance. 



29. Work of a Deformable System. A system subjected to 

 external forces and deformable by their action is at the same 

 time constrained by internal forces, each of its points is therefore 

 displaced internally and externally, producing external work 

 and internal work. Let A and B be two points of the system, 

 the action of the one equalling the reaction of the other. This 

 will be a force F (fig. 66). If the deformation of the body 

 separates A from B by a very small quantity dr, the work done 

 will be + (Fxdr). If, on the contrary, it draws them together, 

 the work done will be negative and equal to (F X dr) . 



f , *_ F 



Fir.. (J6. 



The total internal work will be the sum, positive or negative, 

 of the elements of work dr. It is designated by T r -. In a perfect 

 undeformable solid, T, O 2> the work of the internal forces 

 being zero, and the work of the external forces T* only being 

 considered. 



The internal work is of a molecular order ; thus the molecules 

 of a gas, set in motion in every direction by a variation of tem- 

 perature, produce work T-, which is not necessarily zero. Obviously 

 internal agitation exists in the muscles which sustain an effort 

 of some duration, a static effort, and those molecular vibrations 

 constitute work , certain learned scholars have created, to ex- 

 press this, the term static work (Heidenhain, Haughton, 



