306 Combination of Linkage Vahies 



tween the three equations. If the points had been plotted from either 

 line (a) or curve (6), 3J would have lain on one side, 32-| on the other, 

 as may be seen from Table I. 



Hence the curve (c) may be taken as a fairly accurate guide to the 

 combination of linkage values, and this remains equally true whether 

 the chromosome theory is adopted or not. For this reason a series of 

 values of 100^ and lOOy {i.e. distances in centimorgans and cross-over 

 values as percentages) calculated from equation (5) are given in Table II. 

 As more results accumulate it should be possible to correct these values, 

 which are rather uncertain for large values of x and y. 



TABLE II. 



100?/ (Cross-over value as percentage) 0-0 5*0 8-0 100 11-0 12-0 13-0 



100 'a; (Distance in centimorgans) ... O'O 5-1 8-2 10-3 11-4 12-5 13-6 



100^ ... 14-0 15-0 160 17-0 18-0 19-0 20*0 21-0 22-0 23-0 24-0 

 100 .X ... 14-7 15-9 17-0 18-1 19-8 20-5 21-7 22-9 24-1 25-3 26-6 



100?/ ... 25-0 26-0 27-0 28-0 29-0 30-0 31-0 32-0 33-0 34-0 35-0 

 100 a; ... 27-9 29-2 30-5 31-9 33-3 34-7 36-2 37-7 39-3 40-9 42-6 



100?/ ... 36-0 37-0 38-0 39-0 40-0 41-0 42-0 43-0 44-0 45*0 46-0 

 100 .T ... 44-3 46-1 48-0 50-0 52-2 54-4 56-9 59-6 62-6 66-0 70-1 



100?/ ... 47-0 480 49-0 49-5 49-7 49*8 49*9 50*0 

 100 a: ... 75-1 81-9 93-0 99-2 109-4 117*7 128-1 oo 



As an example of the use of this table the following problem may be 

 taken : 



'' The factors A and B give a cross-over value of 38*5 °l^, the factors 

 5 and (7 a value of 22-7 7,. What is the value for A and C? " 



Fram the table we find by interpolation that the distance AB m 

 49*0 centimorgans, the distance BG 249. Hence the distance 



AC = AB±BC= 73-9 or 241 centimorgans. 



The cross-over value is therefore 46*8 ^/^ or 22*0 °/^, according as C lies 

 outside AB or between A and B. Morgan's formula would have given 

 61-2 7^ (an impossible value), oi: 15*8 7^; Trow's formula 43*7 7,^, or 

 28-9 7, (by solving the equation m 4- '227 - 2m x '227 = -385). On the 

 reduplication theory the result from AB + BG corresponds to the view 

 that the reduplication between A and G is " secondary " to those between 

 A, B and B, G; the result from AB — BG to the view that the redupli- 

 cation between A and B is secondary to those between A^ G and G, B. 



It should be remarked that the existence of a quantity x which has 

 the property demonstrated above is not a conclusive proof of the chromo- 

 some theory, and indeed such a quantity may occur in certain forms 

 {e.g. Trow's) of the reduplication theory. However the fact that the 



