i4 THE POPULAR SCIENCE MONTHLY 



sons are like the mother.^ The explanation is here the same as in the 

 last case. These inbred give the following significant classes : 



The diagram, Fig. 6, shows the imagined relation of the chromo- 

 somes to each other. There are two classes, YWM, GEL, representing 

 "non-crossing-over." There are four classes, YEL, GWM, YWL, 

 GEM, where "single crossing-over" is expected. There are also two 

 classes, YEM, GWL, representing "double crossing-over." 



Other experiments show that the factor for miniature gives a high 

 percentage (about 34) of cross-overs with yellow or with white. We 

 place it at a correspondingly distant point which means that the likeli- 

 hood of a twist occurring between the loci for miniature and that for 

 yellow (or for white) is large. Other experiments show that the factor 

 for yellow body color and that for white eyes rarely cross over. We 

 place them therefore near together. The chance that a twist should 

 occur between Y and W and at the same time another twist between W 

 and M is very small. It is to be anticipated that the double crossing- 

 over would be rare, as it is, in fact. 6 



I have given the argument on which we base our scheme of the 

 linear order of the factors in the chromosomes. I need hardly say that 

 there is no pretension that the distances (calculated in per cent.) corre- 

 spond to real distances, for we know nothing of the actual space occu- 

 pied. But the numbers give the relative positions of the loci in the 

 chromosomes. The procedure justifies itself in one all-important re- 

 spect. By its means we can calculate results before they are tried, and 

 experience shows that the prediction comes true. For example, if we 

 know the location of a factor Y and of another factor W, then when a 

 new factor, M, appears we need only determine its position in regard to 

 Y and we can predict what will happen when a cross is made between 

 M and W. In a word, we can by determining the position of a new 

 factor in regard to any other known factor calculate the results for all 

 other known factors in the same chromosome. When we recall the wide 

 departure, due to linkage, from the accepted Mendelian ratios based on 

 random assortment it is no small gain to be able to calculate the results 

 of all possible combinations by determining two known points. I make 

 this statement even though we may at any time find that linkage is in- 

 fluenced by the environment, or by characteristics peculiar to indi- 

 viduals or to pure strains. Nothing would be more harmful at this 

 stage than that the situation be prejudiced by absolute statements. 



If any one objects to locating these points in chromosomes and pre- 



6 The first and best description of double crossing over is to be found in 

 Sturtevant's paper {Jour. Expt. Zool., 1913). 



