By William Fulton

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30–35). Mitchell (Mitchell 1993) has questioned this interpretation of Mach’s ideas of space. I shall return to the question of matter in Chapters 4, 11 and 12. See references in (Jouguet 1909, notes 7 and 48). 24 Principles of mechanics before Hertz colliding with each other two by two, communicate opposite equal velocities to each other. (Dugas 1988, p. 437. The quote is from 1851) A similar deﬁnition of equal mass was put forward by Mach: ‘All those bodies are bodies of equal mass, which mutually acting on each other, produce in each other equal and opposite accelerations’ (Mach 1883, p.

If we accept additivity of mass as an experimental fact (this is not mentioned by Mach) this observation will explain why usual weighing tells us inertial mass. Mach pointed out that the constants m1 and m2 that enter into Newton’s law of gravitation F = G(m1 m2 /r 2 ) are other constants (the gravitational masses). Only experience teaches us that they are proportional to the inertial masses. Force. The deﬁnition of the concept of force and its relation to Newton’s three laws of motion and the parallelogram of forces remained a major problem in the foundation of mechanics and although remarkable clariﬁcations were arrived at during the nineteenth century, Hertz did not consider the matter to be settled.

In a review of the second edition of T and T’ (Thomson and Tait 1879) Maxwell highlighted the use of this method in physics. Having stated that Newton’s laws are sufﬁcient to deal with mechanical problems such as the motion of the solar system where we believe we can observe all that we have to account for he continued: But when we have reason to believe that the phenomena which fall under our observation form but a very small part of what is really going on in the system, the question is not – what phenomena will result from the hypothesis that the system is of a certain speciﬁc kind?