242 STRING ON SMOOTH SV1M \ 



:i the axes; ^> the angle ii 



with the normal to the surface ; ti. 



d*x COBOL' <Ty cosff d*z __co*y 



ice (5) becomes 



T 



-cos< + jFmcos>fr + .K = ............... (6). 



Let u t=0 be the equation to the surface ; thru 



7 cos cos 7 xr 

 ; = pi- = T - = N suppose. 

 du <fa 



dx dy dz 

 c (1) may be written 



and (2) and (3) may be similarly expressed. 



7T 7 

 Eliminate - and 7?^", and we obtain 



+*) (ta-s 



rf'z 



If we put for T its value from (4), th- 



together with u=0, will drtrnninc the curve formed by the 



string. 



I appears from Art. 189 that the resultant of Fm&s and 

 must lie in the osculating plane of the curve at the point 



