No. 646] THE SYSTEMATIC LOCATION OF GENES 409 



of the sex chromosome of Drosophila willistoni. We have 

 here 7 intervals to determine, and fifteen crossover per- 

 centages are given [1]. Table II shows the data, and 

 the series of weighting quantities derived from them. 



Reduced-Rough.. 



Scut^Peach 



Scute-Beaded 



Scute-Rough . . . . 

 Scute-Deformed.. 



Peach-Beaded.'.'.' 

 Peach-Rough. .. . 

 Beaded-Rough.. . 



Rough-Triple 



Rough-Deformed 

 Rough-Rimmed . . 

 Triple-Rimmed . . 

 Deformed-Rimme 



744.90 

 2,117.78 



68875 



From this table we write down the normal equations 



313,423p^+ 10,136(^2 -f + = 3,507.72 



10,136p + 183,380)0 + 158,509^ -|- I38,766p -|- 31,674p, -f 31,674p^ 



' ' ^ * + 21,379p^ = 11,103.93 



10,136» + 158,5090 + 182,663p + 152,416p + 31,674p^ -f 31,674p^ 



4- 21,3'79p^ = 11,521.58 

 10,136p -f- 138,766p -f 152,416p + 171,703p -f- 31,674p^ -f- 31,674p^ 



+ 21,379p. = 11,525.74 

 31,674 (p^ + P3 + P,) 4- 341,778p^ + 177,345p^ -f- 145,451p^ =z 6,996.42 

 31,674 (pI + pi + p*) -f 177,345p'^ + 238,152p^ + 206,258p^ = 6,790.46 

 21,379 (p^ + P3 + P^) + 145,451p. + 206,258p^ + 217,460p'. = 5,580.36 



Using a calculating machine, the work so far is rapid 

 and mechanical; the solution of the normal equations 

 may in this case be much simplified by obser^dng the uni- 

 formity of some of the sets of coefficients, a type of uni- 

 formity which is probably characteristic of crossover 

 data. Thus by considering {pz + Ps + Pi) as a single 

 quantity, pi is immediately expressible in terms of it, and 

 by solving the last three equations we may do the same 

 for ps, Pa and p^; substituting finally in equations (2, 3, 



