302 Combifiatiofi of Linkage Values 



of the three observed vahies is based on a count of less than 500 in- 

 dividuals (in which case the probable error of the cross-over value 

 ma}^ exceed 1*5 °/^, as pointed out by the author (6) elsewhere) a query 

 is placed in the last column. 



It will be seen that the observed values, when m-\-n exceeds *5, 

 lie almost wholly between m + n — mn and- m-^n — 2mn, as demanded 

 by the theory above. The three discordant values out of 19 are no 

 more than would be expected in view of the probable errors of the 

 observations due both to small numbers and differential mortality. 

 When m + n is less than *5 the results are somewhat more irregular, 

 as the calculated values from the three formulae are not very different, 

 but the majority of observations lie between m + n and m + n — mn, as 

 demanded by the theory. 



This table also enables us to test the formulae given by Trow (2), 

 based on the reduplication theory. If reduplication takes place so that 

 A and B when coupled give the gametic series 



qAB : lAb : laB : qab I cross-over value m = 1 , 



whilst B and G give the series 



r BG :lBc:lbG:rbc{ cross-over value n = ) , 



V r + lj' 



then A and G should give the series 



(qr + l)BG:(q-\-r)Bc:(q + r)bG:(qr^l)bc 



I cross-over value = ) . 



\ qr + q + r -[- 1/ 



11 2 



This latter value = H - ; — — = m + ^ — 2mn. Hence 



q + l r+1 (g-hl)(r-f-l) 



on this hypothesis the observed cross-over values for A and G should 



cluster round m + n — 2mn, and approximately equal numbers should be 



greater or less than it. In other words, as many values should fall in 



class B as in classes a, /3, and 7 together. 



The expectation is therefore 18 (S), 18 (a, 3, and 7); the actual 

 numbers are 3*5 (S), 32'5 (a, y8, and 7), reckoning the single value 7S 

 as half in each class. Hence the above form of Trow's theory is 

 untenable. 



On a more complicated form of the same theory, which Sturtevant(7) 

 has shown to be impossible on other grounds, A and G when coupled 



