﻿Shaft moving toith Uniform Speed along Us A, vis. 745 



of the physical characteristics of the body, and consequently, 

 as already stated (§2), the fixed observer eliminates from 

 his consideration any distortion due to centrifugal forces by 

 the following condition : — 



Ordinary elastic strains are ignored or, in other words, it 

 is assumed that the elastic constants are infinite. 



He interprets his observations in terms of Euclidean 

 geometry, and so he makes the following geometrical 

 assumptions : — 



(A) Each cross-section of the shaft remains a Euclidean 

 plane, so that its radius alters in the same ratio as 

 its circumference. 



Assumption (A) is the only possible one from the Euclidean 

 standpoint. Its justification lies in the simple form in which 

 the principal contractions appear below. 



Using these deductions and the foregoing assumption, it 

 will be seen below that we can derive expressions for the 

 contractions along the principal axes if we know their posi- 

 tion. At this stage a further assumption must be made, 

 more speculative than the preceding which arises directly 

 from the Euclidean point of view of the fixed observer. 

 According to (A) one of the principal axes of strain lies 

 along the radius, i. e. along the direction of the centripetal 

 acceleration. The other two must then lie in a plane normal 

 to the radius, and we assume that 



(Bj one of these lies along the direction of resultant 

 velocity. 



This last assumption may be justified by analogy with the 

 Wiedemann effect. To a fixed observer a rotating shaft in 

 the form of a thin tube moving along its own axis will be in 

 a state of strain similar to that of a steel tube placed in a 

 coaxial spiral magnetic field. In this instance, if hysteresis 

 be eliminated, as it can be by special experimental methods, 

 one of the principal contractions must be along the resultant 

 magnetic field. The formula for the twist in the tube, 

 deduced on this assumption, has been confirmed by experi- 

 ment. In one case the tube is twisted b}^ a spiral magnetic 

 field, and in the other by its spiral motion. The physical 

 analogy is so close that it seems to the author to justify the 

 fixed observer in applying the same analysis to the twist in 

 each case and in making assumption (Bj about the direction 

 of the principal axis. 



We shall now examine the state of strain in the shaft from 

 the point of view detailed above. In considering the analogy 



