J. B. 8. Haldank :m7 



VH)ut*t( (»f T r<>m'M|miMl t<» t.h<»m« tl«>injiii(|(Hl for \hv (liHtniici* nii thr hy|»«»- 

 thoiiiH thai thr fm*t«>rH iiru IikniUhI in a Hrmi-ri^itl <'hniiiiMs..iiH i?* n Htmii^ 

 |M)int ill favour of that hy|Nitht«8iN. 



Wo have How the ihiUi for a fairly juuMinit^' rMiimat*' «»! lln- UtUi\ 

 length of the known {xtrtion of a rhronioHonic. r.7. the twx r|)n>np»Miiiir 

 in I>n>sophila Taking soinu of tlu- Ik-mI authonlicaUMl niriLHim iihuu 

 wc have : 



ToUIm 6^H 71-.*. 



This i;ivos a total length of 7\o crntjinnr^^aiis a^MJii.Hi Mtir^Mii ami 

 Hri<i^os' i*stiinatr(<S) of t)(>'2. The HiHcrrjMiiicy is <lnr to th«' fad thiit in 

 some coni|)JinitiveIy lon^ se^nient-s of the chroinoH<uiic (cj/. lMtw««fi tin 

 K>ci of SaMi' and Kudinicntary, a distance of alnnit 1.') c«-ntiiiior^ans) no 

 fjict«.>rs have been located, and such dist;uices tend to !><• un<lerestiiiiat<'«l. 

 It may also bo duo in part to the large probable ern)r involved in usin^' 

 a large number of small distances. 



From eipiation (4) wc may calculate the proportion ot chromosomes 

 giving t cross-overs in the known region. These valius are incoirect, 

 owing to the rigidity of the chromosome, c, being too low, the remainder 

 too high. The theoreticid values arc : 



No cross-over in c„ = e~'''\ or 4f)l / of the chromosonu's 



One „ in c, = 'Tloe""'', or ,*U-4 /^ 



Two cross-overs in c._. = ,^ , <jrl2G"/,^ „ 



•7153g-"15 



Three „ in r, = , or 3() /^ 



rour „ in 04= ^^ , or M) 



and so on. 



The value of c, is Uhi low, the others too high. The nal value of 

 c, -f-Ca4- C5+ ... is the cross-over value of 4<)".S /,,and Morgan(.S) givrs 

 C2 + C4 -I- c« -H ..., the numbi'r of double cross-ovei-s (inchnling "juad- 

 ruples, etc.), as al>out 10 / , .so that q should be about 43 \Vh« 11 



the relation between x and y is ;iceurat<ly known it will Ix- |>os.sible to 

 c«ilculat<i the values of c, with accunicy by integration. 



