FACTOR RELATIONS IN QUANTITATIVE INHERITANCE 183 
TABLE XXXIII.—Frequency Distrsutions ror Corotta Lenera ix a Cross 
BETWEEN Varieties OF Nicotiana longiflora Cav. (After East) 
Desisiation 4 ee 2 Class centers in millimeters 
NS: » [ESS ] SV ep PE 
\" jo |s2 34(s7|40|43 46 |40/52|551ss[61 64! 67|z0!73/z6|70l so 85,88 9194 97] 100 
| | | 
_.|13}80/32 | | “| | 
1| 4/28) 16 | Lele 
.| 4]32] 1 | | 
fel |.) 6)22}49la1 
| 2)16/32) 6/1 
BERISCERUE nd sanaeraandaeee ae: | Fy |....|..}..]..]..]...[..]..] 4]10/41/75/40] 3 
(388551830) Uo sees ne 1912] Fo} 61 |..|..|..]..].../..| 1] 5/16/23/18|¢2/37/25/16| 4) 2| 2 
(883)5¢890)2 55.5. sac en onann 1912] F2| 61 |..|..).....|...]..] 2] 4} 2loa/az7isa]3s/aslo7ler! 5] 6) 4 
(383° 1330) 101 eine en 1913] Fs | 72 }..J..)..]..]...{..]..1..}..] 4}20l95/s9/ai|19} 2 
(383 X 330)1-2....0.00.0..... 1913) Fs | 46 |..|.. | 1] 4/26/44/38)22) 7] 4 
(383 X 330)1-3............... 1913] Fs} 50 |..|..|..| 6| 20/53/49 15] 4 
(383 X 330)I-4..0.00.0. 0.2... 1913| Fs | 60 |..|..)..| 2} 3) 9/25/37/70'19110 
(383 X 330)2-1.... ...{1913] Fs | 77 |..]..1..|..1...} a] 0} af a] a] 2/16/33/43/34]20] 6! 1 
(383 X 330)2-3.... ...{1913] Fa] st f..)..]..f..]...{..}..[2.]..] a} 2) g/16}/20lg2}41/17] 3] 3) a 
(383 X 380)2-4....0.0..0.0.0. 1913] Fs| so |..|..!....]...]..}..[..]..} 2} g]1aloa}39/39l3e/ 10] 1 
(383 X 330)2-5.....0.0..0.0.. 11913] Fs | 50 |..]..)..]..] 7/25/55/55/18 | 
(383 X 330)2-6.... .../1913] Fs} 82 )..)..1..]..).../..1..f..1..]..[..] 3] 5!12/20!40!41/30} 9] 2 
(383 X 330)1-2-1.... ..../1914] Fa | 44 |..]..] 8/42] 95/38) 1 
(383 X 330)1-3-1.............|1914) Fs | 43 |..}..| 2/23]122141) 1 | 
(383 X 330)2-6-1............. sTsiet cary fe ald clea eels ed tel ealieelbealleal ze 9 38 75/59] 6) 3) 1 
(383 X 330)2-6-2.... ..../1914) Fa] 87 ]..)..)..f..0f.[f..)..f.f.| 4) 5) 6fat]2a}33lai}29} 8) 5} 1 
(383 X 330)1-3-1-1.. ..../1915} F's | 41 | 3] 6/48/90] 14 | 
(383 X 380)2-6-2-1........... ‘1915 Fs | 90 |..|.. a) ee 2] 3 ery 8 
That the results of experiments in size inheritance may be explained 
by a multiple factor hypothesis is apparent from the explanation which 
follows. For the sake of simplicity we will assume that two races A = 
50 and B = 100 differ by five pairs of genetic factors which display an 
equal effect in size production. The genetic formula for Race A may 
be represented by aabbccddee; and the contrasted Race B by AABBCCDD- 
EE. We assume that the factors display no dominance, that their effect 
is equal and cumulative, and that a dominant factor gives a character 
expression greater by 5 than the corresponding recessive factor. By 
crossing two such races an F; of the genetic constitution AaBbCcDdEHe 
is obtained, which on the above assumptions has a size equal to 75. 
Selfing such a hybrid we would secure, in case these factors displayed 
independent segregation, the following series of phenotypes: 
50 55 60 65 70 75 80 85 90 95 100 
1 10 45 120 210 252 210 120 45 10 1 
These values are merely the coefficients obtained by expanding the 
binomial (a + b).° If these values be plotted, they give an approxima- 
tion to the usual form of normal variability curve as shown by the 
polygon representing expansion of this binomial in Fig. 15, and this 
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