Philosophical Magazine Series 6 ISSN: 1941-5982 (Print) 1941-5990 (Online) Journal homepage: http://www.tandfonline.com/loi/tphm17 LXVII. Pleochroic halos J. Joly F.R.S. & Arnold L. Fletcher B.A.I. To cite this article: J. Joly F.R.S. & Arnold L. Fletcher B.A.I. (1910) LXVII. Pleochroic halos , Philosophical Magazine Series 6, 19:112, 630-648, DOI: 10.1080/14786440408636842 To link to this article: http://dx.doi.org/10.1080/14786440408636842 Published online: 21 Apr 2009. Submit your article to this journal Article views: 4 View related articles Citing articles: 2 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=6phm20 Download by: [University of Arizona] Date: 06 June 2016, At: 16:15 ~30 Prof. J. Joly aJ~d Mr. A. L. Fletcher : the reflected snnlight arc separ~lted, there is not a largo p.rtion of unpolarized light in the latter, a serious objection to a radiation pressure theory of t)le tails al,pears at once. When a comet has a dense bright nucleus, a certain small proportion of fis intrins;c light must show evidence of polarization, due to scatterhag by the tail, of light emanatin V t~om the nucleus. But this effec~ would probably be t,o small to be observed in any case. Radiation from the nucleus may also, in some cases, give a radiation pressure assisting: that of the sun, although the gravitational actioll of the nucleus can never be important. All observations r~lating to polarization would be liable to be affected by the presence of fluorescence, and in view of the results (~btained by Wood *, deductions from them demand as much caution as those fi'om the observed brightness. LXVII. _Pleochrolc tildes. HT/ J. JoLv, F.R.S., and ARI~'OLD L. FLETCHER, B.A.I.t [Plates VIII. & JX.] INCE the date of an earlier paper on the subject of S Pleochroic Halos:~ the examination of many halos of special interest has elicited points of sufficient importance to justify fuller con.~ideration o[ the subject. In the paper referred to it was shown from the measure- ment o[ halos in a Greisen that the radial dimension of the corona, or outer halo, when compared with that of the darker central area was such as to support the conclusion that the corona represents a shell of less complete ionization (or other effect) due to the a rays of radium C only ; while the more intensely darkened centre was ascribable to the influence of all those rays which range no further than those of RaA. It was also found that calculation of these radii, according to Bragg's law connecting the ionization range Downloaded by [University of Arizona] at 16:15 06 June 2016 with the square root of the molecular weight, gave distances closely corresponding with those observed. The mica in which these halos occurred was subsequently found to be a lithia-bearing variety--the somewhat variable species classed as zinnwaldite. But, as will be seen further on, this emen- dation introduces no contradiction to the views originally expressed. In a letter to 'Nature' of February 10th the fact of the existence, in some cases, of an accentuated outer border to the corona, in accordance with the increased effect ~ Phil. Mag. July 1908, p. ] 84. CommunieA,tedby the Authors. ** Joly, Phil. M~g. February 1910, Pleocl~'oic Halos. 6;41 of the :z ray towards the end of its hinge, "~s shown in tile Bragg curves, was confirmed; and the identification of thorium halos recorded. As the number of measurements multiplied it appeared as if the calculated or theoretic values tended to range a very little above those determined by observation. The source of this has been found to lie in tl~e mode in which Bragg's law was being applied. The method of applying this law had in- vited the comparison of the average square root of the atomic weight of the mineral containing the halo with that of air. Now Bragg and Kleeman's figures and results do not bring air quite harmoniously into llne with the solid substances examined (Phil. Mag. Sept. 1905), and it seemed a more correct procedure to calculate the range in the mineral by comparison with the square root of the atomic weight of a substance more generally in agreement with the law and similar to the mineral in 1;hysicai-state. Choosing aluminium tbr the purpose, the table given further on for the ranges in some important halo-bearing minerals, has been calculated both for the ~t rays of RaC and RaA and for ThC and ThX. The calculation is most readily made as follows. Bragg and Kleeman found that if the products of range and density in a number of different substances are compared with the corresponding products in ~he case of air, the several quotients obtained stand in the same relation one with another as the square roots of the atomic weights of the several sub- stances. The quotient for aluminium has the value 1"23. If we assume the range in air to be one centimetre, then the A x 1"23 corresponding range in aluminium is ~'= ~, where A and $ are the densities of air and aluminium. Also we have ~r?.r a t Sr =a; ~here ~:, r' are the density and range in any particular mineral; a' is the average square root of the Downloaded by [University of Arizona] at 16:15 06 June 2016 atomic weight of the mineral, and a tim square root of the atomic weight of almninium. Substituting the expression for r and taking the density of air as 0"0012; and writing ! 5 15 for a ; we have d=0"000287~p ; which gives the range in the mineral corresponding to one centimetre in air. Thus for certain biotites a ~ is found to be 4"5 and ~ 2"8, hence ~=0"000461. Then for the rays of RaC, having a range in air of 7"06 cm., we find the range in this biotite to be 0"0326 mm. The quantity a: may be determined either from 632 Prof. J. Joly a~zd Mr. A. L. Fletcher : a molecular formula or fl'om a chemical analysis. In the first case we multiply the square root of each atomic weight by the number of such atoms present; sum the values so found ; and finally divide by the number of atoms entering into the formula. In the second case we deal with each molecule separately, adding the square roots of the component atomic weights and dividing' by the number of atoms in the molecule. The number obtained is the average square root of the atomic weights entering into the molecule. It is to be multiplied by the percentage quantity of the molecule present, as given in the analysis. The numbers obtained are to be added and their sum divided by 100. The following are the ranges in air of the a rays of the uranium, actinium, and fhorimn families of elelnents :-- I. II. IIl'. Iv. em. cm. Olli, OlD, Uranium ... 3'5 2"8 t~adioactinium. 4"8 Thorium 3"5 Ionium 2"8 2"1 Act X 6"55 Radiothorinm 3"9 Radium 3"54 2'84 :Emanation. 5"8 Th X 5"7 Emanation... 4"23 3"60 Act B 5'50 Emanation. 5'5 l~aA 4"83 4'05 Th ]3 5"0 RaC 7"06 6"35 Th C 8"6 RaF 386 3"16 Column I. gives the lhniting ionization ranges in air at 760 ram. pressure, and Col. II. the approximate distances in air at which the ionization effect is a maximum in the case of the uranium family. The values in Col. lI. are deduced partly by scaling directly from the Bragg and Kleeman curves, partly by assuming that a deduction of 7 mm. from the limiting range ~ives the approximate position of most Downloaded by [University of Arizona] at 16:15 06 June 2016 intense ionization. Thesevalnes we shall require later. The distances in Cole. III. and IV. are the limiting ionization ranges in air in the case of the actinium and thorium families *. In a pleochroie halo we may have either the uranium derivatives acting or those of thorium ; or, again, a mixture of both. In the first case the radius of the halo is limited * See Bragg and Kleeman, loc. cir. and Phil. Mag. June 1906 ; Allen, Phys. Rev. xxvii. 1908 ; Le Radium, Jan. ]910, p. 2 ; Levln, Phys. Zeit. 1906, p. 521 ; Ku~era and )Ia~ek, Pt, ys. Zeit. 1906, p. 339 ; Hahn, Phil. Mat. Sept. 1906. Pleoch roic Halos. 633 by the ionization range of ttaC in the particular mineral in which the halo is formed. In the second the radius is limited by the range of ThC. In the third it will again be limited by the range of ThC. It might, in general, be difficult to distinguish the last two cases from once another ; but if the halo is not over exposed we would expect in the Ra-Th halo a corona with inner and outer radii corresponding to the radii of RaC and ThC. Thus if formed in biotite the radius of the pupil would be about 0"033 mm. and of the corona or iris 0"040. There is no difficulty in distinguishing uranium from thorium halos, however blackened up they may be. In biotite the outer radius era good uranium halo is never very different fl'om 0'033 mm.