APPENDIX 



NOTE I 



On the Principle of Inertia and " Absolute Rotation " (p. 286) 



Consider a very thin straight piece of material string AB, which in 

 the conceptual limit may approach a straight line. Let C and D be 

 two adjacent physical points of this line which in conception may 

 approach to geometrical points. Now suppose the fact observed to 

 be that AB remains straight and disconnected from other " matter," 

 but that we are ignorant whether it is really in motion or not. Let 

 us now suppose the string separated between C and D, say by 



A CD B 



a pair of scissors, without immediately altering the motion, if there be 

 such. One of two things may now occur— either the pieces AC, DB 

 continue to appear as parts of one unbroken piece of string AB, or 

 else AC and DB begin to separate between C and D. Now the only 

 thing of which we have destroyed the possibility is clearly a 

 mechanical relation— a tension (p. 308) between the material points 

 C and D. Hence, if the parts begin to separate after the application 

 of the scissors, C and D must have had a tension between them, or 

 have exerted mutual accelerations before the cutting in twain (p. 304). 

 That is to say, D must initially have had an acceleration relative to C 

 in the direction AB. Or we may assert, that in the limit two parts 

 of a material line will tend after division to separate or not to 

 separate according as its parts have a relative acceleration in the 

 direction of its length. Now if we suppose the string or material 

 line incapable of stretching, it is clear that D cannot initially have a 

 velocity relative to C in the direction AB. Hence it follows that the 

 acceleration of D relative to C must be of the nature of normal accelera- 

 tion (p. 225), or the line AB must be spinning as a luJiole round 

 some axis. On the other hand, if the parts AC and DB remain after 

 being cut in twain in the same straight line, then no material particle 

 C of AB has any acceleration relative to another particle D in the 

 direction AB. In this case the line AB may have motion of transla- 

 tion as a whole, but has no spin. 



