Gravitation and Light 325 



Forty years a.oo there was a phase of strong remonstrance in 

 this country against the famihar uncritical use of the phrase 

 centrifugal force. The implication was that the term force should 

 be restricted to intrinsic unchanging forces of nature, which are 

 determined physically by the mutual configuration of the system 

 of bodies between which they act: these forces are then held 

 responsible for the accelerative effects specified by the Newtonian 

 second law of motion. In this sense, centrifugal force so-called 

 would not be a force of nature, but would be the reaction postulated 

 in the scheme of the Newtonian third law to balance an imposed 

 centripetal acceleration. 



This formative principle, the Newtonian third law, of balance 

 everywhere between appHed forces and reactions against palpable 

 changes of motion, as amplified in the Scholium an]iexed to it — 

 which so widely reached forward towards modern theory as 

 Thomson and Tait especially have remarked — would then assert 

 that the forces of nature that act on the framework of a material 

 body and the forces of reaction that are thereby induced in it, 

 form together a system of forces that preserve statical equilibrium 

 in relation to the constraints of that framework, as tested by the 

 principle, also Newtonian in its origin, of virtual work. This 

 became in time the Principle of d'Alembert (1742), who did not 

 invent it, but exhibited its power and developed its method by 

 applying it to a great dynamical problem of unrestricted form, 

 that of the precession of the equinoxes. As a preliminary to its 

 solution he had to develop in general terms the equations of static 

 equilibrium of a system of forces considered as applied to a single 

 rigid body such as the Earth, that is, to create a formal science of 

 Statics: and it may be said to be the mode of development rather 

 than the principle itself that constitutes his essential contribution 

 to general dynamical theory. Cf. the historical introductions in 

 Lagrange's Mecanique Analytique. 



2. The principle of the relativity of force has recently become 

 prominent again, and pushes along further on the same lines; it 

 now even puts the question — Are there intrinsic forces of nature 

 at all? May not all force, including universal gravitation, be ex- 

 pressible as reaction against acceleration of motion, just after the 

 manner of the obviously unreal centrifugal? On such a view, 

 wherever there is a force of gravitation in evidence, its presence 

 must be replaced by an acceleration common to all of the material 

 bodies at each place and relative to our frame of measurement, 

 of amount equal and opposite to the intensity of the force. That 

 would be the end of the matter, if any frame of reference could 

 be found to satisfy this condition. There being then no forces left, 

 the Principle of Least Action would make orbits simply the shortest 

 paths in the frame. Newtonian uniform space and time certainly 



