( 500 ) 



of four dimensions dOd0 1 and the extension dódó x , which we may 

 imagine as a rectangle in the region of the dd^, when we project them 

 as two mutually normal coordinates in a plane. 



Everj point in the rectangle represents therefore a number of 

 combinations of velocities with equal J and 6 l . The sides of the 

 rectangle with equations d=c and 6 l =.c l , correspond in the region 

 of the ó'ó\ with the right lines wó' -\- m l (2ó\ — d) =(pi -f- wij c 

 and m^'j -J- m ('2d' — d\) = (m -|~ ? ' ? i) c ls so that from the combina- 

 lions represented by points within the rectangle after the impact 

 others follow represented by points within an oblique parallelogram. 



The formula --—-(= 1 expresses that the two figures have the 



same area. Now the extension after impact is equal to this paralel- 



v 



d$ 



dl 



■J 



a 



j 



