( 380 ) 



and O' A., 

 MA is: 



Fig. 4. 

 give the size of V. Tiie general equation ot the curves 



, smVt<jV 



8171 2y max = — — , 



cos X cot X 



y'miix = 2 ^^ «<'* 



from wliich 



ünVtgV 



dx 



smVtgVy 

 cos X cot xj 



f sinVtfjV\ 



\cos X cot x) 



\-^2Ufx 



sin F «(/ F (1 + 'Itg^x) cot x 

 2 \/cos^ X cot^ X — sin^ ^'tg^ ^ 

 sin^ V 1 + sm^ x 



cos X 



2 cos X y'cos'^ X cos^ V — sin^ x siïi* V 



So for X =: the direction of tlie tangent is given by : 



dy max 



(10) 



-j- sin* V 

 ~d^ ~ i—)2cosV' 



For '^ = 1- V by 



dy' 



dx 



=. X 



as the term under the root-mark becomes =: 0. So the tangents in 

 .4 on the curves form right angles with the dii-ection MO. 



It further follows from the formula (10) that the rise of the curve 

 for the same value of .v grows smaller as the value of T^diminishes, 

 as is also shown by tig. 4. If V becomes = 0, as in the hexagonal 

 and tetragonal system, then we also have 



