,41 6 Journal of Agricultural Research voi. iii. no. s 



ORDINATES EQUALLY DISTRIBUTED 



Up to this point we have considered that the ordinates were distributed 

 at any irregular points on the base line. In the usual case, however, they 

 will, of course, be at equal intervals from one another. When the ordi- 

 nates are given at equal intervals, i. e., when x^ — x^ = x^ — X2= ' " • =^m— 



Xm-v I becomes equal to the number of given ordinates, q=-, and the 



equations for the constants can be put in a somewhat simpler form. 

 For the curve y=a + hx + c logm*; 



c=h[(>{{l+ i)M,-AU)- (P+3;+ i.5)M„] (xviii) 



6=^[2A/,-(/+i)A/„-yjC (xix) 



I ,, '+ I , 

 a=jMo-^-b-]3C (XX) 



where 



/, = 2[(/+i)(^/ + 0jlog.„i-log,„(/ + 0j + -^/= + 6/+3)log,„eJ' 

 y2=|[(' + 2)[log.„^-log,„(/+i)}+/(/+ I) log,„e] 



73 = 7J_('^ + ^ )logio(^ + - ; log,o ; - nogi„e J 



For the curve y=a + bx + cx' + d log,oX.- 



d=u[2oM,~ 30(1+ i)M, + j,M,-j^M„] (xxi) 



c= y [6{A/,- (/+ i)M,}+ iP + 3l+i.5)M„] + ]^ (xxii) 



b=^[2M,-i!+ i)M„]- (/+ i)c-j^ (xxiii) 



a = jMo--j-b-j^.-j,d (xxiv) 



where 



,>I2(p + f/ + 



;X/+i)(/= + 5/ + 



h=j\}(l+ i)(/+;)|log.oj -log,„(/+ j)[ + g'(/^ + 6/+3)log,„ f] 



