APPENDIX 5 



JD 



principle to the planetary system leads us to an absolute motion in 

 an absolute space. 



It has been asserted that Newton's rotating bucket of water and 

 Foucault's pendulum 1 demonstrate an absolute rotation in an absolute 

 space, but in the words of Professor Mach- : — 



"The universe is not presented to us twice, with resting and again 

 with rotating earth, but only once with its alone determinable relative 

 motions. Accordingly we cannot say what would happen if the earth 

 did not rotate. We can only interpret the case as it is presented to 

 us in different ways. When we interpret it so that we are involved 

 in a contradiction with experience, then we have interpreted it 

 falsely. The fundamental principles of mechanics can indeed be 

 so conceived that even for relative rotations centrifugal forces arise. 



"The experiment of Newton's with the rotating bucket of water 

 only teaches us that the rotation of the water relative to the side of 

 the bucket gives rise to no sensible centrifugal forces, but that these 

 forces do arise from the rotation relative to the mass of the earth and 

 the other heavenly bodies. Nobody can say how the experiment 

 would turn out if the sides of the bucket became thicker and more 

 massive till they were ultimately several miles thick. There is 

 only the one experiment, and we have to bring the same into unison 

 with other facts known to us and not with our arbitrary imaginings." 



Allowing for the difference in terminology between Professor 

 Mach's sentences and our Gnaninat; they show, I think, how far it is 

 safe to go in the idea of absolute direction and absolute motion. In 

 the conceptual model we may define lines, which are conceived as 

 having no relative acceleration of their parts, as " fixed in direction." 

 Take two points O and P in conceptual space ; let the step OP be 

 drawn from O, whether O be in motion or not, and let OP, after draw- 

 ing, be supposed to remain " fixed in direction " ; the tops P of such 

 steps drawn for all instants form ihe path of P relative to O. The 

 statement that, if O and P represent particles of gross matter 

 sufficiently far apart from each other and from other particles, this 

 path will be a straight line, is the principle of inertia. 



The perceptual equivalent for " fixity of direction " in the con- 

 ceptual step was in Galilei's day^ represented with sufficient approxi- 

 mation by direction fixed with regard to the earth ; since Newton we 

 take it to sensibly coincide with direction fixed with regard to the 

 stars. But perceptual absoluteness cannot really be asserted even in 

 the latter case. Should the element of gross " matter," however, be 

 ultimately conceived as a form of ether in motion, the principle of 

 inertia will become a far more easily stated and appreciated axiom of 

 mechanics (p. 289, Tind. footnote). 



1 Maxwell, Matta' and Motion, pp. 8S-92. 



2 Die Mechanik in Hirer Entwiclcelung, p. 216. 



•^ And even now by the writers of elementary text-books who cite bodies 

 projected along the surface of " diy, well-swept ice " as moving in " straight 

 lines " and illustrating Newton's first law of motion ! 



