THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 109 



their common centre of^gravity cannot possibly rise."* Here 

 we have an appeal to a principle, used again with great effect 

 in Huygens' famous solution of the problem of the " compound 

 pendulum,"! which, in the hands of the Bernouillis, developed 

 into the Principle of Vis Viva& which Helmholtz made his 

 starting point in his epoch-making work on the " Conservation 

 of Energy." The same instinctive perception that a body or 

 a system cannot, under the influence of its own weight, move in 

 such a way that the centre of gravity is raised a conviction 

 which is recognised as identical with the denial of the possi- 

 bility of the perpetuum mobile^ was shown by Machl" to 

 underlie the Principle of Virtual Work (or Velocities) which 

 Lagrange made the basis of his Mtcanique Analytique, and hence 

 of the method of " generalized co-ordinates " which plays so 

 important a part in modern mathematical physics.** 



50. 



Helmholtz starts with the Newtonian concept that the 

 task of physical science is to reduce the phenomena of Nature 

 to unchanging, attracting, and repelling forces acting between 

 mass-points; the magnitude of the forces depending merely 

 upon the distances between the points. He showsff that in 

 such a system of mass-points and forces the vis viva will be 



* Tractatus, p. 382. 



t Horologium oscillatorium, 1673. The solution is described by Mach> 

 op. cit., pp. 174-9. 



| Huygens had, in the Regulas of 1669, already formulated for 

 collisions of perfectly elastic bodies the rule : " Summa- productorum a 

 mole cujuslibet corpori duri, ducta in quadratum suae celeritatis eadem 

 semper est ante et post occursum eorum " (Eeg. 6, Phil. Trans., No. 46, 

 p. 928). 



Helmholtz, Ueber die Erhaltung der Kraft, 1847. 



|| Cf. Helmholtz, op. cit., p. 8 ; also Mach, Popular Scientific Lectures^ 

 Eng. trans., 1894, p. 147. 



TT " On the Conservation of Energy " in Popular Lectures, 1894. 

 ** See Routh, Rigid Dynamics, i, Ch. VIII. 

 tt Op. cit., pp. 10-12. 



