6o 



MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



dx dy dz 



ds ds ds 



d 2 x d?y d 2 z 



7s~ 2 Js 2 ds 2 



d?x dfy dh 



? ~ds* dT 3 



2.681 The direction cosines of the tangent to a space curve in the form (c) are: 



I, m, n = 



i, y', *' 



'i + y' 2 + z' 2 

 where accents denote differentials with respect to x: 



~dx~ } dx 



2.682 The principal radius of curvature of a space curve in the form (c) is: 



(j + y* + ,^8 } I 



(y'z" - z'y") 2 + y" 2 + z" 2 

 2.683 The radius of torsion of a space curve in the form (c) Js: 



(i + y' 2 + z' 2 )* 



2.690 The relation between the direction cosines of the tangent, principal 

 normal and binormal to a space curve is: 



I m n =i. 

 V m' n 

 I" m" n 



2.691 The tangent, principal normal and binormal all being mutually perpen- 

 dicular the relations of 2.00 hold among their direction cosines. 



