286 C. LEVINTHAL 



to the frequency of recombination obtained in the crosses a X c and b X c, 

 and d is likewise located by means of the crosses a X d and b X d. So far the 

 mapping can be done for any arbitrary set of numbers obtained from the 

 crosses; but the one additional cross, c X d, determines the consistency of 

 the mapping on a one-dimensional structure. If the independent crosses with 

 a and b locate c and d near to each other, then one must observe a low recom- 

 bination frequency in the cross c X d i£ a one-dimensional mapping is to 

 suffice to represent the data. 



The ordering of mutations can also be done in a way which is mathe- 

 matically independent of the determination of distances— by makmg use of 

 a cross of two particles which differ with respect to three mutations. In such 

 a cross, there wiU be particles in the progeny which receive one genetic marker 

 from one parent and two from the other. The character that lies between the 

 other two will occur least frequently in the progeny associated with the two 

 markers from the other parent. If any number of different mutations are 

 studied, they can, of course, be ordered along a line by a succession of three- 

 factor crosses. Although these two methods of ordering mutations along a 

 Hne are independent of each other in a formal sense, all the models which 

 have been suggested to explain one also explain the other. It must, however, 

 be kept in mind in what follows that although the genetic map is defined by 

 a set of real operations, the map itself is an abstract way of representing the 

 results of certain experiments and, except by inference, has no physical 

 reality. 



B. Techniques of Phage Crosses 



A phage cross is carried out by infecting a single bacterium with two or 

 more different types of virus particles. When the phages are mixed with 

 bacteria in a hquid suspension, the rate at which they attach is determined 

 only by the bacterial concentration and the composition of the medium. If 

 care is taken to use bacteria which are equally sensitive to each of the 

 infecting phage types, one can obtain cells in which two or three genetically 

 different types grow. The number of each of the phage types which take part 

 in the infection is determined by the proportions of the various types added 

 to the absorption tube. In preparing these mixedly infected cells, it is fre- 

 quently necessary to use some method of arresting the development of the 

 system so that the first phage particle to attach does not prevent late 

 arrivers from participating in the growth process. The way in which the first 

 phage particle to infect a cell can exclude others which arrive a few minutes 

 later is not clear, but the phenomenon can be eliminated by agents which 

 temporarily stop cell metaboUsm. After a sufficient amount of phage has 

 adsorbed, the unadsorbed parental particles must be eliminated, either by 

 differential centrifugation or by antiphage serum; the infected cells are then 



