4«8 



NJ4TUME 



[June 17, 1926 



(li) 



where the square bracket has the usual significance 

 of concentration. 



Now in Deacon's process, which is represented by 

 the chemical equation 



4HC1 + 0, = 2H,0 + 2CU, 



we should have 



[C1,]_[HC1F 



[CV] LHCi'p • • • 



Taking Hl^^ as 3, }:^\^\ is 9, provided that the 

 [HCIJ lL\^\ 



temperature and concentration of the oxygen are 

 selected so that the concentration of the chlorine is 

 small at equilibrium. 



But the ratio of the atoms of the two varieties of 

 chlorine is given by 



[ci,i+Mcicrj 



■ [CV]+i[ClGl']' 

 and this, by equations (i.) and (ii.), is equal to — 7-^ 



which differs appreciably from 3. 



Deacon's process is selected merely for the purpose 

 of illustration. 



If the isotopic varieties of chlorine are insepara'ble 

 by the method above indicated, it is clear that 



whence 



[ ci,]+Mcicrj _ [Hci] ^ [cy i 

 [ci3']+i[cici'] [Hcr] LcVJV' 



2[ci,Mcv]i=[cici'j. . 



(iii.) 



(iv.) 



Now consider two solids composed entirely of Clj 

 and CL' molecules respectively. The vapour pressures 

 of the two solids will be very nearly (if not exactly) 

 the same — say p — at the same temperature U 



Evaporate a ^ram-molecule of both the solids. 



Reduce the pressure of the CL isotope to /),, and that 



of the CI/ isotope to p^, and then introduce both 



unsaturated vapours into a van't Hoff's equilibrium 



.box. The total work done in these operation is 



..R/log^Ji. 



AP2 ■ 



Now remove 2 grarri-tnolecules of the ClCl' 

 variety (which from equation (iv.) will obviously be 

 at the pressure 2Vp\p2) from the equilibrium box. 

 Increase the pressure to p, and finally condense at 

 this pressure to the solid form. The work done 

 during this series of operations will be 



R/log, 





Therefore the total work performed in effecting the 

 change represented by the equation 



CI2 (solid) + CV (solid) = 2CICI (solid) 



is Rflog4=A. 



But it is difficult to understand how the free energy 

 A could differ appreciably from zero if the molecular 

 heats of the three varieties of chlorine are nearly the 

 same^-as they are generally supposed to be — and if 

 the entropy of the reactants CU and CI/ is equal to 

 that of the resuhanti 2CICK at the absolute zero tem- 

 perature, as Nernst postulates in his heat theorem. 



An attempt is being made in the Jesus College 

 Laboratory to separate the isotopes of chlorine by a 

 method similar to that given 'above. A negative result 

 would be difficult to reconcile with Nernst 's theorem 



A p. 

 that -~^ = o tx. the absolute zero.' 

 at 



Jesus' College, Oxford. 



NO. 2642, VOL. 105] 



,D. L. Chapman. 



(0 



(2) 



(3) 



A Note on Telephotography. 



Having examined a number of formulae for the 

 circle of illumination in telephotography, and found 

 them all to be inapplicable in certain cases, 1 

 propose the following, which seem reasonable and 

 are applicable in all cases. These formulae are par- 

 ticularly vital, in the line along which telephotography 

 is at present developing. 



Let Ck = Full circle of illumination. 

 Ce = Circle of equal „ 

 CM=Mean circle of ,, 

 M = Magnification. 

 fi = Focus of positive lens. 

 fi = )) negative „ 

 b = Diameter of positive lens, 

 t" = „ negative ,, 



Then 



c -M!L/£±MiiMM 

 c - M'/i" 



" M(/i-/,)+/2 • • • 



The last formula (3) is not only the simplest, but it 

 is also the accurate value for the circle when the aper- 

 ture (b) of the positive lens is small. It is the mean 

 between the full (i) circle and the evenly illuminated 

 (2) circle. The first (i) is the most usually used. It 

 gives the diagonal of the largest plate that can be 

 employed. The second (2) gives the circle that is 

 equally illuminated. If it is possible to make the 

 aperture (b) of the positive lens equal to the dia- 

 meter (c) of the negative lens, this formula becomes 

 the simplest. 



Ck = Mc. 



I have received an opinion on the above from a 

 distinguished authority upon geometric optics. He is 

 of the opinion that it is necessary to add that certain 

 assumptions have been made in deciding these for- 

 mulae. These assumptions are (o) that the lenses are 

 thin, (/3) that the aberrations may be neglected, and 

 (y) that the focal lengths of both lenses, /, and f^, are 

 definite quantities. 



(a) Photographic positive lenses are usually not 

 thin. Negative telephoto lenses, except some high- 

 power lenses, are always thin. With a thick lens the 

 "equivalent planes" for the two sides (the "object 

 space" and the "image space ") are different. As all 

 measurements in the above formulae are made from 

 the back of the positive lens and the front of the 

 negative lens, no confusion can arise between the 

 equivalent planes. 



(P) The aberrations of a photographic lens are 

 negligible. 



(7) The positions of the equivalent planes of the 

 negative lens move over a small space with a change 

 of ■ magnification. This quantity is negligible in 

 deciding the circle of illumination, which does not 

 need to be known exactly. 



The position of the equivalent plane of the whole 

 ■""^r'^es •^reatly with a change of distance of object. 

 This can be completely corrected bv substituting the 

 "back conjugate focus" of the positive lens for the 

 distance, in place of the "principal " focus (/,) in the 

 above formulae. In telephotography, the object is 

 usua'lly "at infinity," and this correction is hot 

 necessary.. ■ 



In a short note it is not possible to do more than 



indicate the conditions in which these formulae mav 



be I'spd. Consult Lan-Davis on "Telephotography" 



and. Beck and Andrews's "A Simple Treatise on 



I Photographic Lenses " (Appendix) for "equivalent 



• planes." ' . A. B. 



