226 Dynamics. 



the time of passing through Mm will be , and the time through 



M 



24. 



11 i ds 



mm' will be - T -. 

 u -f- du 



From the points M and m 1 as centres, and with the radii 

 , m m') describe the arcs JVn, m t ; then comparing the trian- 

 gles JV m n, JV" w f, with the triangles ./If m r, m m' /, we shall have 



nm = ./Vw X , 

 as 



and 



Whence, 



and 



Therefore the time through MN will be 



m X 



u 

 and the time through Nm' will be, 



w-f- 

 We have, therefore, 



& * a 5 



w + dw 

 an equation which reduces itself to 



^(*JL+ d Ji_jLlL\ = o, or d C^ = 0; 

 d u + dn u % 



