660 Prof. F. Slate on Force- Transformation, 



frame (U) ; with its distinctive notation, and introducing- 

 for (F) a companion to (t? c ) similar to (»„) in (U). 



Some mention has been made already of a " Fresnel 

 coefficient " (k), and of a meaning for it as "inertia-drag/' 

 when associated with the frame (F). There proves to be,, 

 however, a pair of such coefficients (k, «'), symmetrically 

 related to (F, U), like (dr, dr) of equations (12). Some- 

 thing remains to say about this pair, connected with our 

 Newtonian forces (T , T a , IV, IV), including no^v under 

 those symbols values for either the more general (?hj) or 

 the more particular (m ), as the context may indicate. We 

 can quote for observation-frame (F) *: 



i 



J- (31) 



c — I ^ t I c __ -j ( o' c 



cr — u Vo C + u c c c 



K T a > = m l7 (r ) g ; *T = m iy (u)y(v>) *£ . 



Basing frankly on symmetry for the defining ratio (but 

 succeeding members are demonstrable), write then for an 

 observation-frame (U), noting (u' = -r- u) : 



t _ Vo' ~ Ve _ Vc — Vq' _ '? — Vq 2 _ C 2 — V c 2 _ V 'r c 



fC r / 9 , / .i -L a • (O— } 



W it G* + MV« C w — UV C C 



In the special view of relativity, («, */) become equal. Or 

 here visibly through the coincidences that are mentioned 

 below equations (16). But our Newtonian scheme, in 

 the several instances enumerated, gives enlarged reciprocity 

 to frames (F, Uj ; independent phenomena originating (we 

 may say) in either are convertible into terms of the other. 

 The contrast with treating the same phenomena indifferently 

 in all frames of the group is certainly not to Newton's 

 disadvantage. 



Under the definition of («:'), the proofs are direct that 



T tin ' 1 l" ^ ' 



_L° = » l7 K)^+W+«)|,(» w W)). 



y{u) at at K J 



These round out the symmetry because, allowing always 



* From (II.), pp. 38, 43. Eq. (5, 13, 24, 26) there define (T , T a 

 T.',T.O. 



