xlviii ■ Tables for Statisticians and Bionietricians [XXVIII 



it is not needful to euter separate products, the sums being reached which are 

 placed at the foot. Next from Table XXVIII we read off 



S{x) = 0, 8(0^) = 2 (Silo"-)), 8(0^) = 0, S(.i-*) = 2(8(15% 



8 (a,^) = 0, 8 (of) = 2(8 (lo")). 

 These give us : 



8 (.<-•=) = 24S0, 8 (of) = 356,624, 8 (.r«) = 6096,5840. 

 We have now all the numerical data for a solution. Let the retiuired cubic be 



y = Co + CiX + c^afi + CsO^. 

 Then we must make u = 8 (y — Co — c^x — c.,af — c^af)- a miuimuni. The resulting 

 equations are 



8(y) = Co-S ( 1 ) + c, 8 (x) +0,8 (*•-) + c^8 (x'), 

 8 (xy) ==c„8 (x) +c,8 (sfi) + c^S (a?) + 0^8 (x*), 

 8 (x'y) = CoS (xi") + c,8 (a^) + c,8 (x>) + c,8 (x'), 

 S(a^y) = Co8 (x>) + c,S (*-*) + c,8 (*•=) + c,8 (x'). 

 (i) (ii) (iii) (iv) (v) (vi) (vii) 



y 



.r 



- 7-0 



' -15 



- 6-8 



-14 



- 6-6 



-13 



- 6-5 



-12 



- 6-5 



-11 



- 6-5 



-10 



- 6-25 



- 6-0 



- 6-0 



- 5-2 



- 5-0 



- 4-5 



- 4-0 



- 3-0 



- 2-0 

 



1-0 

 1-5 

 2-0 

 2-5 

 4-0 

 4-5 

 6-5 

 7-5 

 9-5 

 9-5 



lOo 

 ir.'i 

 ir.T 

 1 1 -5 

 11-5 



- 9 



- 8 



- 7 



- 6 



- 5 

 ■ 4 



- 3 



- 2 



- 1 

 

 1 

 2 

 3 

 4 

 5 

 6 

 7 

 8 

 9 



10 

 11 

 12 

 13 

 14 

 15 



S (x) = 2Z-Hb — 



225 



196 



169 



144 



121 



100 



• 81 



64 



49 



36 



25 



16 



9 



4 



1 







1 



4 



9 



16 



25 



36 



49 



64 



81 



100 



121 



144 



169 



196 



225 



xy 



x-y 



-3375 



-2744 

 -2197 

 -1728 

 -1331 

 -1000 



- 729 



- 512 



- 343 



- 216 



- 125 



- 64 



- 27 



8 



1 







1 



8 



27 



64 



125 



216 



343 



512 



729 



1000 



1331 



1728 



2197 



2744 



3375 



— S(Ay)=1833-45 5(xV) = 4560-35 ' 5 (.i.-V) = 248,807-85 



