( 381 ) 



d.v 



= 0, 



SO that tlie curve MA roiiicides with tlie abscissa-axi.s J/^>. Finally 

 with regard to the form of the curve which represents the angle 



\[ f(mcu] as a function of ,t', it appears already from a comparison 



of figures 2 and 3, tiiat this curve JfA, the axis-angle becoming 

 smaller, gradually approaches the straight line that divides into two 

 equal parts the angle between OA and the normal to it in U. 

 Indeed (9) yields 



<iOt a,ua.r = 



\/cos* X cos'^ V — sin^ x sin^ V 



= tq 



•T \ \/cos'^ X — {cos"^ X -\- sbi^ X aln^ V) sin* V 



cos^ X -}- sin^ X sin^ V 

 If T^ l)ecomes smaller, Uji — «,„«.,) increases, and with F=0 



reaches the greatest value ."' , 1, so that then Umax becomes 1^=45°. 



The curves J/'.Ll/ and NBN' then pass into two straight lines which 

 intersect in (>, thus forming right angles, whilst they have shifted 

 45° with regard to direction AB. 



Of great practical importance is the solution of the problem, how 



