108 THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 



" observations and experiments " from which he drew the con- 

 viction that the product of mass and velocity was the 

 determining circumstance in dynamical transactions. Hence 

 we have found it advisable to devise a hypothetical series of 

 experiences by the consideration of which this conviction might 

 be reached. It is otherwise with the conviction ihat the " vis 

 viva," the product of the mass into the square of the velocity, 

 is the determining circumstance. 



49. 



In 1669 Huygens acquainted the world, by means of the 

 Philosophical Transactions "of our own Eoyal Society, with 

 his laws of motion of colliding elastic bodies. In 1703 a 

 posthumous Tractatus de motu corporum ex percussione was pub- 

 lished,* in which these laws appeared systematically deduced 

 upon the basis of certain assumptions, which as a rule are of the 

 kind called by Mach " instinctive perceptions," and are clearly 

 set forth. 



Of this character, for example, is the assumption that the 

 velocities, relative to an observer, with which two colliding 

 bodies separate, will not be changed if the two bodies and 

 the observer have an additional common velocity imposed upon 

 them as they would have, for instance, if the experiment were 

 performed upon a uniformly moving boat.f But when Huygens 

 reaches the case of elastic bodies of unequal mass, and 

 endeavours to prove the proposition^ that if such bodies collide 

 with velocities inversely proportional to their masses, they will 

 separate with the same velocities, he finds himself able to do so 

 only by showing that a contrary supposition is forbidden by an 

 axiom of complete certainty in mechanics. " which states that 

 in a movement of bodies which is caused by their own weights, 



* Translated as No. 138 of Ostwald's Klassiker der exakten Wissen- 

 tchoften. I have used this translation, 

 t Tractatus, p. 370. 

 t No. VIII. Pp. 381-6. 



