n SMOOTH SCEPACE. 241 



Xm we roust pat Am + R cot a, and 



uilar flul i ana Zm ; therefore 



iV^ + JTm + flcosa- ...(1), 



(2), 

 (3). 



Multiply (1) by 5* (*) ty j; **& () by gj, and add; 

 then, since 



because a tangent to the surface at any point is perpendicular 

 normal at that point, we have, as in Art. 188, 



Again, multiply (1) by cos a, (2) by cos , and (3) by cosy, 

 and add ; then 



+ m [X cos a + Ycosff + Zcos 7) + R - ... (5). 



\f bo tit /i&r, r*t, Zmf, and ^ 



the angle makes with the normal to the surface 



:) ; then 



cos a + Y cos ft + Zco*7Fco^. 



radius of absolute curvature of the curve formed 

 M string at the point (x, y, :) ; a', /?, 7' the angles its 



T. s. 



