64 



The Ohio Journal of Science [Vol. XVI, No. 2, 



Infinite Ordinates. The infinite points on a curve are given 

 by the values of t satisfying the equation 



3Xt2+2/ct + l=0 



Except under certain limited conditions to be determined later 

 a curve with infinite ordinates can not be of great statistical 

 value. 



The parabola, k" — 3X=0, obtained by equating the dis- 

 criminant of this quadratic to zero separates the points on the 

 (X, k) plane which correspond to curves of no infinite points 

 from those corresponding to curves of two infinite points. 



Types of Cori/es 



Therefore, all pairs of values of X and k within the parabola, 

 with the exception of the very narrow region also within the 

 first discriminant curve, give uni-modal curves without infinite 

 ordinates. 



Types of Curves. Without entering into detailed proofs we 

 will now investigate the general shape of the curves corre- 

 sponding to values of X and k in each of the distinct regions of 

 the plane of X and k. 



