J. H. K. ilALPANK 293 



Henct* tho on»M8-<>v«T vuluo in Wili'M] /. A' - 7r>f» and i\H 



....... . "•* ■-*^- 'l'l>'i^ rnith«r 7 imr S 



AUHV 



an* iinpritlvihlf vuIih's for .r, thr prohaMlit y «»t an « rmi us ^nat us nr 



gn*aU»r than 511 lK»in^ only about 27 / , us may !»<• s».ii fVom a tal.I.- oi 



values of "'■■ I f'^df. 



\V«» shall now considn- the zyL^otic scrirs ol)tain«<l in F. \t\ mating' 

 iuter se thv h\ zyijotrs i-onsid^nd alK»v«'. Tln' rx|M'('t«M| |no|>..i tions an- 



- + P' t n ^ ~ P' 1 / ' ~ P' If P' I 

 / An : / Ah: / (i/i :'. ah, 



4 4+4 



when' AH.viv. rrpn'st'nt t.ln' visible characters of the zygotes, ('misider 

 a gn)Uj» of » such zyi;<)ti's. Put t = j)"^, and h't /„ Iw an aj)j)ro\iiiiaie 

 value of t, while T=f„ + S is the value which is most probable from the 

 given oKservation. Also let ^,, f.,, t^, f^ be the four values of / (al(ulat«'<l 

 from the four classes observed. 



Then ti= - 2, 



^=l- 



4(^16) 



f.= I 



^{(tli) 



t,= 



4(a6) 



.'. t, + t, = L + t,. 

 Hence for any value of 8 the probability of the observed proportions 



2 + f , 1 - ^ 1 - f, U ; 



— T— AB : — T— Ab : —7 aJi : , (ib 



4 4 4 4 



being obtained in a group of « zygotes is proportional to 



Exp. 



j-'1 f"!"'-M'"'' 



2 + ^„ + S 



4 



ia + S 



4 



or 



" [(to - ^ + ^)- (^a - t; + 3 )■- 4 (/„ - f. 4 3 )-' ( fa - /. + 3 )• 





1 - ta fa I 



since h may be neglected in comi)arison with /„ or 1 -/„. th«»ugh not 

 with ta — ti, etc. 



