1183 

 in '1) to the natlj, divided by ni { ~ ] . Measured in 'j tlie curvature 



vector — -r is e(|ual to the component of 'j'l (K -|- iiiKi) perpendicular 

 dj dj 



/djy 

 (measured in -j) to the path, divided by in ( — I • Wiien the external 



force is zei'o, (38) becomes : 



dH dx' fdiy d dx' 



= _+_ (40) 



dt^ dl \dtj dl dl ^ ' 



or : 



dH d dx' 



— r= , - _ - (41) 



dt^ dl dl ^ ' 



and talking (35) into account, we find for (39): 



d^jdx' rdj\ \'d dx' dx' dx' ^ 'I 



0= ,;i h = — '^ A . . . (42) 



'^i dj ydtj \dj dj dj dj \ ^ ^ 



Measured in '1 the curvature vector is then equal to zero and 



dx' dx' 3. ' 

 measured in 'j to the component ot -^^ —-'^ A perpendicular to 



aj dj 



the path. 



The change of geodetic curvature is perfectly given by the obtained 

 e(| nations. 



When a vector p is moved geodeticallv once with respect to *1 

 along dx' and another time with respect to "j, the directions of the 

 two tinal positions will show a certain deviation from each other. 

 We might be inclined to suppose this deviation per unit of length 

 to be equal to the ditference l)etween the curvatures measured in 

 the two different ways. The difference between (/p and 'dp is just 

 equal to the difference between two vectors that first coincide with 

 p and are then moved geodetically along dx.' in two different ways. 

 The problem however is not so simple, which is directly evident 

 from \Ue question whether the deviation and the unit of length 

 have to be measured by *1 or by 'j. Measured by "1 the cuivature is: 



j/l dl 

 and measured by 'j : 



d dx'^ 



" 2 M ....... (43) 



d dx'X 



^^)"^- •••••■• <^^) 



and there is no simple relation between the difference of (43) and 

 (44) and the mutual deviation measured in some way of the two 

 possible geodeticallv moving systems of coordinates. 



