HELMHOLTZ IN BERLIN 



equations solved geometrical problems, and demon- 

 strated geometrical propositions. Descartes's error in 

 theoretical physics was in conceiving matter as moved 

 only by impulsion and pressure, and not by internal 

 forces ; but he recognised that the quantity of matter 

 and motion in the universe remained unchanged. He 

 also defined the quantity of motion as being equal 

 to the product of mass and speed (in v). The next 

 great name in this arena of thought is Leibnitz, who, 

 about the same time as Newton was engaged on 

 establishing the differential calculus or calculus of 

 fluxions. He argued that it was rather the quantity 

 of vis that remained unchanged in the universe, and 

 he defined this quantity as the product of the mass 

 and the square of the speed (m <y 2 ). The two views 

 led to a schism among thinkers, some supporting 

 Descartes, among those Euler, while others were on 

 the side of Leibnitz. Kant admitted the Leibnitzian 

 view with a limitation. It is, however, wholly a 

 question of definition and of nomenclature. If we 

 mean by a force, a cause proportionate to the quantity 

 of motion of a body, the Cartesian principle applies ; 

 but if we mean by force, the power of a body to 

 overcome a continuous and uniform resistance, the 

 formula of Leibnitz holds good, namely, that the 

 work performed by the force is equal to the pro- 

 duct of half the mass into the difference of the 

 squares of the speeds at the commencement and at 

 the end of the motion. Both principles were recog- 

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