8 MeadOWCROFT, Treatment of Geodesic Torsion. 



Then 



HN HN PQ dR R' 

 tan X ~ ^ = 



JJ'iV FQ ' B'N ds' ' R'-R 



{R'-R) 



Now by Meunier's theorem 



cosx=-|- 



^pT ^/^A* R"- I - r■^ 



Again 



tan X = - 



R-^-p\ 



P 

 the result may be expressed in the form 



or 



(Hi) 



An expression for the torsion may be derived from 

 Lancret's theorem by means of Meunier's theorem in 

 much the same way. 



We have 



. , Rdp - pdR 

 • •• -sinx'^X = — ^ — 



. • . (R^ - f^fdr) = ^dR - dp 

 R 



. dR^R dp^R^j^.._ ^,^i^ j^y Lancret's theorem . . (iv), 

 ds p ds p<T 



which gives a when o has been found.. 



These formuK-e, as might have been expected, would 

 in general give p and a as very complicated functions 

 of X, y, z. 



