PRINCIPLES OF MECHANICS. 537 



velocity, or of the weight into the square of the velocity ; — still the 

 examples taken were cases of action in machines and the like ter- 

 restrial objects. But Newton's discoveries identified celestial with 

 terrestrial mechanics; and from that time the mechanical problems 

 of the heavens became more important and attractive to mathemati- 

 cians than the problems about earthly machines. And thus the gen- 

 eralizations of the problems, principles, and methods of the mathe- 

 matical science of Mechanics from this period are principally those 

 which have reference to the motions of the heavenly bodies : such 

 as the Problem of Three Bodies, the Principles of the Conservation 

 of Areas, and of the Immovable Plane, the Method of Variation of 

 Parameters, and the like (Chap. vi. Sect. 7 and 14). And the same 

 is the case in the more recent progress of that subject, in the hands 

 of Gauss, Bessel, Hansen, and others. 



But yet the science of Mechanics as applied to terrestrial machines 

 — Industrial Mechanics, as it has been termed — has made some steps 

 which it may be worth while to notice, even in a general history of 

 science. For the most part, all the most general laws of mechanical 

 action being already finally established, in the way which we have 

 had to narrate, the determination of the results and conditions of any 

 combination of materials and movements becomes really a mathemat- 

 ical deduction from known principles. But such deductions may be 

 made much more easy and much more luminous by the establishment 

 of general terms and general propositions suited to their special con- 

 ditions. Among these I may mention a new abstract term, introduced 

 because a general mechanical principle can be expressed by means of 

 it, which has lately been much employed by the mathematical engi- 

 neers of France, MM. Poncelet, Navier, Morin, &c. The abstract term 

 is Travail, which has been translated Laboring Force ; and the prin- 

 ciple which gives it its value, and makes it useful in the solution of 

 problems, is this ; — that the work done (in overcoming resistance or 

 producing any other effect) is equal to the Laboring Force, by what- 

 ever contrivances the force be applied. This is not a new principle, 

 being in fact mathematically equivalent to the conservation of Vis 

 Viva ; but it has been employed by the mathematicians of whom I 

 have spoken with a fertility and simplicity which make it the mark 

 of a new school of The Mechanics of Engineering. 



The Laboring Force expended and the work done have been de- 

 scribed by various terms, as Theoretical Effect and Practical Effect, 

 and the like. The usual term among English engineers for the work 



