A. II. Thow 291 



CO. 



1. 24^6 2:iAc 22Ad 21/le 2()A/ \<)Aff lAy 



2. 2SAc 22Ad 2lAe -lOAf \'.)Ar, lAy 



3. 2-IAd 21Ae 20Af I'JAtj lAij 



4. 21^6 20Af WAg ^A>J 



5. 20 Af WAg I Ay 



fi. 19 Ag I.ly 



24. lAy 



The whole series of cross-overs in this case will he 



24.1^ 4G.lc CMAd HiAe lOOAf 114.1,7 



12(L4// l:}(i/li ]UAj 1.50.4/,- 154.4^ 15G.4/« 



15QAn 154^0 1504/> 144/l(y imAr I'lGAs 



lUAt 1004m HiAv ()GAw 464a; 24.1y 



The luiniber of N. C. O.'s is readily deteriiiiiied from the table 



on p. 292. The ratios (isj— W !-> ) are thus determinable in any case 



of double crossing over, and can be compareil with the corresponding 

 ratios for a single crossing over. (See Table on p. 2!)3.) 



Thus, with twenty-six factors, A to Z, a number approximating to 

 those already located in the first chromosome, it is not difficult to 

 calculate the corresponding series of ratios and the percentages by 

 this method. The table on p. 293 gives the result of such a calculation 

 arranged to shew the relationships of single and double crossing-over. 



My mathematical colleague, Prof. Pinkerton, has suggested to me the following 



formulae, as a ready meaus of calculatiug the values of the ratio, „— ^^ — ' , ,, ,, . 

 ■' ° C. O. + N. C. O. 



Let there be n pairs of allelomorphs, An, Bh, Cc, etc., numbered from 1 to r and 

 on to II, thus: 



1 2 r n 



A n Bl 



a h in 



The following formulae enable one to calculate the number of C. O.'s Am, etc., with 

 little ditSculty. 



One crossing : r - 1. 



Two crossings : (r - 1) (n - r). 



Three crossings : (i- - 1) r H , — tt-^ • 



' ' 1x2 1x2x3 



