J. B. K. IIaldank :]0U 



alone give a priiimry mticm sA(^ : \Ar . \<i(' snr and in zy^nivM nl rum- 

 position A Hi' . abc, A mTioti 



(qrs + tt) A C : (7 + r) .4c : (7 + r) (iT : (r/r/* 4 n ) nr: 



Crros.s-ovrr valin* =■ ' ). 



f/rs \ 'I ^ r h HI 



Ab thin vnluo is less than that of m f /* —2;/*//, it is .still iiiMir cliarly 



im|H>HsibK\ 



Tho supporU*rs of tlir ri'duplimtion throry nmst tlunjnn- explain 

 the deficiency of the tKnibJe eross-over ehisses <»f )^ainet<* (whi<;h fmiu 

 a zygote? of conijMxsition ABC . ahc are Ah(^> and it lie), i )n the ehromo- 

 80me theor)' this is due to the rigidity of the chruinosonus, and until 

 an equally plausible explanation on the redtiplic^ition theory is givi-n, 

 the chn>mosome theory must be considered the more probable of the 

 two, so far Jis the class of evidence dealt with in this jm|H'r is concerne<l. 



It has bt^en shown above that if .1, li and (' are three factors whose 

 loci lie in that onler in the same chromosome, and if //* and n are the 

 cross-over values for A^ B, and B, C n»spectively, then the value for A 

 and C is wH- n —pmn, where p is a number between and 2, increasing 

 on the whole with m-^n, and having the value 1 when m + 71 = alxjut o. 

 The distJinces between loci may now be c^Uculated ;us follows: 



Let X be the distance between the loci of two factoi*s, y their cross- 

 over value, and let the unit of distance be chosen so that when y is 

 sufficiently small .r becomes equal to y. This jissumption is legitimate 

 if we suppose that crossing over is as likely to occur (other things 

 being equal) at one point in the chromosome as another, i.e. that the 

 chromosome is equally flexible and breakable at all points. The unit 

 of distance is thus 100 times Morgan's unit. 



If now we write y—f{x\ the form of this function being indeter- 

 minate, 

 .-. f (x -\- h) — f {x) -\-f(h) —pf{x)/(h), where h is any increment of x. 



. f{x-^h)-f(x)_f(h)-pf(x)f{h) 

 h h 



Now as h is decreased towards 0, - 7— tends to the limit 1. 



h 



dy ^ ^^/{x-hh)-f(x) 

 dx fc-M) h 



= Lt-^^''^"-^^^^^-^^''^ 



A-M) 't 



= 1 — j)f{r), where y> h;is the value assumed when //* ^ //, n ^ <>, 

 = 1 - P!/' 



