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 (iljr .lliilmu Bunkum Hmveratt) 
 
 Magnetic Rotatory Dispersion 
 in Transparent Liquids 
 
 DISSERTATION 
 SUBMITTED TO THE BOARD OF UNIVERSITY STUDIES OF THE JOHNS 
 
 UNIVERSITY IN CONFORMITY WITH THE REQUIREMENTS FOR THE 
 DEGREE OF DOCTOR OF PHILOSOPHY 
 
 June 1921 
 
 ROBERT ALLEN CASTLEMAN, JR. 
 
 Baltimore, Md. 
 1921 
 
MAGNETIC ROTARY DISPERSION IN TRANS- 
 PARENT LIQUIDS 
 
 BY R. A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 ABSTRACT 
 
 Magnetic rotary dispersion of isotropic transparent media. The electron theory 
 as given by H. A. Lorentz is extended, and a formula for the rotation in a range of 
 spectrum in which electrons of only a single type, with critical frequency c/Xi, need 
 be considered, is developed: 
 
 2 
 
 H is field strength, I is length, /* is refractive index, c is velocity of light, and a is a 
 constant which Lorentz puts equal to about \ and Voigt puts equal to zero. To test 
 this theory, substances were chosen whose dispersion was known to conform to the 
 theory of Lorentz, and the magnetic rotations for carbon disulphide, a-monobromnaph- 
 thalene, benzene, nitrobenzene and ethyl iodide for six wave-lengths from 436 to 620 /z/x 
 were determined with a cell 2 cm long in a field of 6480 gauss. The angles could be 
 measured to iV and were found to vary from 4 to 28, increasing rapidly for eacb 
 liquid with decreasing wave-length. Theoretical curves were computed, taking the 
 values of Ci, X x and /u from measurements by others. Below 590 up the experimental 
 curves lie below the theoretical curves, the divergence increasing as the wave-length 
 diminishes until the difference at 423 /x/x is from 4 to 20 per cent. It is suggested 
 that this discrepancy is due to the absorption of the violet end of the spectrum which 
 was neglected in the theory. The results do not decide between the values o and \ for 
 a. The values of e/m for the active electrons may be computed from h t and vary from 
 0.5 to i . 78 X io 7 e.m.u. according to the liquid and to the value of <r assumed. 
 
 i. Introductory. -In 1845 Faraday discovered that isotropic 
 substances when placed in a strong longitudinal magnetic field 
 rotate the plane of polarization of plane-polarized light. The 
 obvious explanation of this, confirmed later by Brace, was the 
 same as that offered by Fresnel for the rotation observed in certain 
 crystals, viz., to consider the plane-polarized beam to be com- 
 posed of two circularly polarized components which travel through 
 the medium with different velocities, one greater and the other 
 less than the velocity of the beam" in the medium when unmag- 
 netized. The variation of the angle of magnetic rotation with 
 the wave-length of the light has been considered theoretically by 
 several writers, and the theoretical relations have been applied to 
 the experimental data available. Such data appear, however, to 
 be rather meager, and it seemed desirable to pursue the subject 
 afresh both theoretically and experimentally. 
 
 45 
 
 461994 
 
46 R. A. CASTLEMAN, JR., AND E. 0. HULBURT 
 
 We do not presume to attempt a historical summary of the 
 researches on the many aspects of this subject. For a summary of 
 the earlier work we make reference to an article by P. Joubin. 1 
 Among the more important theoretical formulae for the magnetic- 
 rotation angle in terms of the wave-length, magnetic field, etc., 
 were those obtained by Joubin, Voigt, 2 and Drude. 3 For a sum- 
 mary of the experimental measurements of the magnetic-rotation 
 angles we -turn to the Landoldt-Bornstein Physical Tables. There 
 the data have been tabulated in many cases as the Verdet Constant, 
 which is defined to be the angle of rotation of plane-polarized 
 light of specified wave-length produced by a medium i cm in 
 length when magnetized by a longitudinal magnetic field of strength 
 i gauss. These measurements were applied by Joubin and Drude 
 to a dispersion theory of isotropic media, although for such a pur- 
 pose the experimental data were hardly sufficiently numerous. With 
 the exception of a few transparent liquids and solids the Verdet 
 Constant was found either for unresolved light or for a single wave- 
 length of monochromatic light. In the cases of those substances 
 whose Verdet constant has been determined for a number of wave- 
 lengths throughout the spectrum, one could introduce the values 
 into a suitable dispersion formula to test a dispersion theory. 
 Unfortunately, however, the refractive indices of most of these 
 substances do not conform to any of the simpler dispersion for- 
 mulae whose constants have a physical interpretation, and so these 
 data are, from this standpoint, uninteresting. 
 
 In the present work transparent liquids were chosen whose 
 dispersion conformed approximately to the electronic dispersion 
 theory of H. A. Lorentz. 4 The angles of magnetic rotation of 
 plane-polarized light for a series of wave-lengths of light in the 
 visible spectrum were measured. A formula of Lorentz giving 
 .the relation between the refractive index and the strength of the 
 magnetic field was modified to express the magnetic-rotation angle 
 in terms of the wave-length, the field strength, and other quantities. 
 The formula was found to agree approximately with experiment in 
 
 1 Theses, Faculte des Sciences, Paris, 1888. 
 
 * Magneto- und Elektrooptik, 1908. 
 
 3 Lehrbuch der Optik , 1906. * Theory of Electrons, 1909. 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 47 
 
 those regions of the spectrum wherein the assumptions upon which 
 it was based were valid. 
 
 2. Theoretical. Suppose plane-polarized light of wave-length 
 X in vacua traverses a length / of a medium of refractive index ju 
 for the wave-length in question with a velocity v. If the medium 
 is placed in a magnetic field of strength H y such that the lines of 
 magnetic force are parallel to the direction of propagation of the 
 light, the medium becomes doubly refracting. The two circularly 
 polarized components, which compose the plane-polarized beam, 
 now pass through the medium with velocities v s and v 2 , and the 
 medium has the corresponding refractive indices ^ and yL 2 , 
 respectively. 
 
 Eddy, Morley, and Miller, 1 followed by Mills, 2 have shown by 
 an interferometer method that 
 
 or 
 
 Mi Ma M 
 
 This was determined by measurements on carbon disulphide. The 
 accuracy of the work was none too great, because the experiment 
 was a difficult one; but, within the error of observation, the fore- 
 going relation was true. It may be noticed that from general con- 
 siderations one would not expect (i) to be exactly true, and further 
 that one would expect the difference between (i) and the exact 
 truth to be small. However, we now assume that (i) is true for 
 all the substances and throughout the wave-length range used in 
 this investigation. 
 
 Let 6 be the observed angle in radians of the rotation of the 
 plane of polarization produced by the magnetized medium. It is 
 easily shown 3 that 
 
 \8 . . 
 
 M2-Mi = ^, (3) 
 
 where X is the wave-length of the light in vacuo. 
 
 1 Physical Review, 7, 283, 1898. 
 
 3 Ibid., i8 ; 65, 1904. 3 Drude, loc. cit., p. 396. 
 
48 R. A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 \f) 
 Solving (2) and (3) for ^ and ^2, and considering small 
 
 compared with /*, we obtain 
 
 , 
 
 27T/ 
 
 Let us turn to a consideration of the dispersion theory in this 
 connection. We restrict the discussion to isotropic, transparent 
 media in which the temperature remains constant. We use the 
 electron theory of dispersion as given by H. A. Lorentz (loc. cit.). 
 Let and E x be the X components of the displacement of the 
 electron from its equilibrium position and the electric force, 
 respectively, 77, f , E y and E 2 are the 7 and Z components of these 
 quantities; they are all expressed in c.g.s. electromagnetic units. 
 The components of the " restoring force" with which the medium 
 acts upon the electron are /, /ry, and /f . The charge on the 
 electron in c.g.s. electromagnetic units is e, its mass is m. N is the 
 number of such electrons per unit volume, a- is a constant which 
 Lorentz has shown to be approximately one-third for isotropic 
 media. The external magnetic field is denoted by H in c.g.s. 
 electromagnetic units. We shall suppose H to have the direction 
 of the axis of Z, which is also the direction of the propagation of 
 the light. The magnetic permeability of the medium is taken as 
 unity. 
 
 We find for the equations of motion of the dispersion electron 
 of a single type 
 
 (5) 
 
 -ft. 
 
 Let e be the base of natural logarithms, and let all dependent 
 
 .2 ire f. 
 
 variables of (5) contain the time only in the factor e'~*~ where - 
 
 A 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 49 
 
 is the frequency, X the wave-length of the vibration in vacuo, and 
 c the velocity of light in vacuo. The solution of (5) gives the 
 refractive index fj. as determined by the relation 
 
 H, 
 
 (6) 
 
 where 
 
 The subscript s 1 is used to denote the 5th type of electron. is 
 
 X 5 
 
 the frequency of the natural undamped vibration of this electron. 
 When the plus sign in equation (6) is used, n is the ju 2 of (4), and 
 when the minus sign is used ju is the ^ of (4). 
 
 Equation (6) describes fj, in terms of the constants of a single 
 type of dispersion electron. There may be other types of disper- 
 sion electrons in the medium with constants peculiar to the type, 
 so that in the more general case the right-hand member of (6) 
 becomes a summation of similar terms, one term for each type. 
 For this case the complete dispersion formula is 
 
 (7) 
 
 We assume we are dealing with a region of the spectrum in 
 whicji the change of the refractive index with wave-length is 
 determined by the electrons of a single type, so that in the sum- 
 mation of (7) all the terms except one may be replaced by a quantity 
 q l which is independent of X and H. Then (7) becomes 
 
 . (8) 
 
 Li , 
 
50 R. A. CASTLEMAN, JR., AND E. 0. HULBURT 
 
 where 
 
 (9) 
 
 2-Kcm 
 
 A special case occurs when H is zero. For this (8) becomes 
 equivalent to the well-known dispersion formula of Lorentz : 
 
 do) 
 
 I I 
 
 Introducing (4) into (8) gives: 
 
 L : =?i+T * u - (i: 
 
 It was expedient to transform this relation to one more amen- 
 able to arithmetical computation. This was readily done because 
 
 \Q TT 
 
 - and h t were smaller than the other quantities appearing 
 
 27T/ A 
 
 with them in the denominators by a different order of magnitude. 
 Equation (n) becomes to a close approximation 
 
 6 is in radians. 
 
 We notice that if we use either the two plus signs of (11) or 
 the two minus signs, we arrive at the same equation for (12). 
 This shows that equation (8) is in close agreement with (4) . We 
 notice also that, other quantities remaining constant, 6 is propor- 
 tional to / and H in turn. This agrees with the experimental 
 measurements of Rodger and Watson 1 and Dubois. 2 
 
 1 Phil. Trans. Roy. Soc., A 186, 621, 1896. This paper contains further references. 
 
 2 Wied. Ann., 35, 137, 1888. 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 51 
 If <T is given the value f , equation (12) becomes 
 
 When a is placed equal to o, equation (12) becomes 
 
 irCAHl MX* ,* 
 
 ' (I4) 
 
 Formula (14) agrees with one given by Voigt 1 when his quantities 
 are expressed in c.g.s. electromagnetic units. 
 
 To compare the experimental measurements with the theory 
 the following procedure was used. Values of the refractive index 
 of the liquid under investigation for wave-lengths in the visible 
 spectrum were taken from data published by others. Three 
 values of M and the corresponding three values of X were sub- 
 stituted in equation (10), and the three constants q lj C ly and X x 
 were computed. Using these three constants, a fourth value of X 
 was substituted in (10) and the value of M calculated. If this 
 value of n agreed approximately with the observed value, the sub- 
 stance was considered to conform to the Lorentz dispersion equation 
 (10) for the region of the spectrum in question. The values of 6 
 for a number of wave-lengths in the visible spectrum were meas- 
 ured for a known length / of the liquid subjected to a known 
 magnetic field H. The constant hi was then determined by 
 substituting in equation (13) the values of H, I, C x , X,, and the 
 values of X, 6, and M for a specified wave-length. 6 was then 
 computed by means of (13) for the other wave-lengths, and the com- 
 puted value was compared with the observed value. 
 
 3. Experimental arrangements. The arrangement of the appa- 
 ratus is shown in plan in Figure i. A gas-filled lamp with a spiral 
 tungsten filament and a mercury- vapor lamp served as sources of 
 light. The mercury- vapor lamp was used for observations at 
 wave-lengths 435.9 MM and 546. i MM; the tungsten lamp was used 
 for observations from the green to the red end of the spectrum. 
 
 1 Loc. cit., p. 130. 
 
R. A. CASTLEMAN, JR., AND E. 0. HULBURT 
 
 The source of light, shown by A, Figure i, was focused on the 
 slit Sj of the spectrograph by a lens / x , 3 cm in diameter and of 
 focal length 22 cm. 
 
 The spectrograph consisted of the Littrow mounting of a plane 
 grating. The grating had a ruled area 6 cm by 7 . 5 cm and was 
 ruled 15,000 lines to the inch. The cone of light from slit s^ was 
 reflected by a right-angle glass prism through the large lens / 2 , 
 10 cm in diameter and with a focal length of 75 cm. The spectrum 
 was brought to a focus at slit s 2 . The grating was mounted on a 
 turntable which could be rotated from the outside of the case 
 containing the spectrograph. so that various wave-lengths of light 
 could be made to pass through the second slit. The grating 
 possessed a bright first order, and this first-order spectrum was 
 
 FIG. i 
 
 used throughout the present work. The dispersion was such that 
 with slit s 2 o.25mm wide a beam of light containing a wave- 
 length range of 5 A, or 0.5 /zju, passed through. Both slit s x and 
 slit s 2 were always o. 25 mm in width. 
 
 The monochromatic beam of light emerging from slit s 2 , after 
 being rendered parallel by a lens / 3 , 2.5 cm in diameter and of 
 focal length 12.5 cm, passed through the polarizing nicol n^ and 
 through the pierced pole pieces of a Ruhmkorff magnet between 
 which the cell C containing the liquid under investigation was 
 placed. The light then traversed the analyzing nicol prism n 2 
 and finally entered the telescope T. . The lenses / x , / 2 , and l z were 
 achromatic doublets. 
 
 The cell which contained the liquid was made of glass. A 
 short length, about 2 cm, of glass tubing of internal diameter i cm, 
 to which had been sealed a small side tube, was ground until the 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 53 
 
 ends were plane-parallel to within 0.003 cm - Glass plates with 
 optically plane surfaces were cemented to this. Rubber cement, a 
 mixture of lead oxide and glycerine, and LePage's liquid glue, were 
 found useful as cements in various cases. The cell was filled 
 through the side tube. The length of the column of liquid was 
 found by subtracting the thickness of the end plates from the 
 external length of the cell. The liquids used were obtained from 
 the Chemical Laboratory and were of a high degree of purity. 
 
 The pole pieces of the Ruhmkorff magnet were elliptical in 
 shape to give a uniform magnetic field; they were adjusted to be 
 2 . 5 cm apart. To calibrate the magnet, the angle of rotation 6 
 for sodium light was observed for a known length of carbon disul- 
 phide for a current of 26.0 amperes through the magnet. From 
 6 and from the value of the Verdet constant of carbon disulphide 
 for sodium light, which has been carefully determined by Rodger 
 and Watson (loc. cit.), the average strength of the magnetic field 
 between the pole pieces was calculated, and was found to be 
 6480 gauss. This field strength was used for all the rotation 
 measurements of this paper. It was found by tests that the rota- 
 tion angle 6 had the same absolute value for the magnetic field 
 direct and reversed. This indicated that hysteresis effects in the 
 magnet were negligible. 
 
 The mounting of the analyzing nicol carried a circular scale 
 which measured the rotation angles to one-tenth of a degree of arc. 
 It was found that the analyzer could be set for extinction for all 
 the wave-lengths with a precision of two-tenths of a degree. The 
 values of the rotation angle were in all cases the means of at least 
 four measurements, two taken with the field direct and two with 
 the field reversed. It was considered that the mean angle was 
 correct to one-tenth of a degree of arc. 
 
 4. Errors and corrections. No correction was made for the 
 error due to scattered light. There were two ways in which 
 scattered light might introduce systematic error into the rotation 
 measurement, the first arising from light scattered by the grating, 
 and the second from multiple reflections by the surfaces at the 
 ends of the cell which held the liquid. To determine the effect of 
 the light scattered by the grating, the beam issuing from slit s 2 was 
 examined with a transmission grating. When the tungsten lamp 
 
54 R- A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 was used as the source of light, it was found that the beam con- 
 tained light of foreign wave-lengths of rather feeble intensity; in 
 the case of the mercury lamp this foreign light appeared still 
 weaker. Upon looking into the telescope and setting the analyzer 
 for extinction it was found that the image of slit Si did not fade 
 out against an absolutely black background. Very faint light was 
 seen in the field, due no doubt to the light scattered by the grat- 
 ing and to imperfections throughout the optical system. The 
 settings for extinction could, however, be made with precision, 
 and it was deemed that the extraneous light introduced no appreci- 
 able systematic errors. Any error due to multiple reflections from 
 the surfaces of the ends of the glass cell was avoided by rotating 
 the cell slightly until these surfaces were not perpendicular to the 
 beam of light. The error which this caused in the determination 
 of / was negligible. 
 
 TABLE I 
 
 x e 
 
 436 HfJL 1.7 
 
 503 i-3 
 
 546 0.9 
 
 579 0-85 
 
 589 0.85 
 
 620 0.8 
 
 It had been feared that errors due to temperature would be 
 troublesome, but it was found that these fears were needless. To 
 carry out a complete series of measurements of the rotation angle 
 for five wave-lengths in the visible spectrum required about an 
 hour. During this time the magnet heated up, and the tempera- 
 ture of the liquid in the cell increased. The increase was never 
 more than 3 C. In the case of carbon disulphide the temperature 
 coefficient of the Verdet constant for sodium light has been deter- 
 mined. 1 A three-degree change in temperature changed the Verdet 
 constant by about 0.5 per cent. In the present case it was 
 considered that errors due to temperature changes were for the 
 most part less than 0.5 per cent, and that it was unnecessary to 
 arrange a more accurate control of the temperature of the liquid 
 in the cell. 
 
 1 Rodger and Watson, loc. cit. 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 55 
 
 The rotation angle 6 due to the liquid alone was obtained from 
 the observed rotation angle produced by the liquid in the cell by 
 subtracting from this observed angle the angle of rotation pro- 
 duced by the empty cell for the wave-length in question. Table I 
 shows for the two glass plates- on the ends of the cell. The 
 thickness of the two plates together was o. 315 cm, the field strength 
 was 6480 gauss. The magnetic-rotation angles plotted in the 
 figure have in all cases been corrected for the effect of the glass 
 ends of the cell. 
 
 5. Carbon disulphide. The data for this substance and the 
 results of the calculations are given in Table II and Figure 2. We 
 shall discuss these in some detail, and shall avoid a repetition of 
 the discussion for the other substances. The observed values of 
 6, shown by circles in Figure 2, have been plotted as ordinates 
 against wave-lengths as abscissae; a smooth line, curve i, has 
 been drawn through them. The strength of the magnetic field, 
 the length of the layer of liquid, and the temperature at the begin- 
 ning and the end of the experiment are shown in the first two lines 
 of Table II. 
 
 Verdet 1 has recorded relative values of 6 for carbon disulphide 
 for a number of wave-lengths in the visible spectrum. The mag- 
 netic field used was not mentioned. For the sake of comparison 
 the values given by Verdet have been reduced to agree with 
 curve i for \ $89 . 3 pp and are shown by crosses in Figure 2. 
 Joubin (loc. cit.} also carried out measurements on carbon disul- 
 phide. Neither the magnetic field, nor the length of the liquid, 
 nor the temperature were recorded. By a coincidence his value 
 for 6 at X 589.3 MI was the same as that of curve i, namely io?3. 
 His values have been plotted as dots in Figure 2. We think that 
 the measurements of curve i were correct, for they were repeated 
 with precision a few weeks later. 
 
 In order to introduce these experimental results into the dis- 
 persion formula (10) we assume that the absorption of carbon 
 disulphide is inappreciable for the visible wave-lengths in question. 
 Such an assumption is manifestly not accurate, because this sub- 
 stance absorbs the blue end of the spectrum to a certain extent. 
 
 1 Verdet, Oeuvres completes. 
 
R. A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 We take the values of the refractive index found at 2o?o C. by 
 Flatow. These and the corresponding wave-lengths are shown in 
 
 the third and fourth lines of Table II. 
 Substituting these values into for- 
 mula (10), the values of the constants 
 Ci, q ly A! were computed and are 
 tabulated in the fifth line of Table II. 
 The agreement between (10) and ob- 
 servations was tested by using the 
 foregoing values of the constants and 
 computing ju for X 394 juju to be i . 7043. 
 The observed value was i . 70226, and 
 
 20 
 
 10 
 
 Carbon disulphide 
 
 MZO 
 
 500/xyui 
 
 FIG. 2 
 
 TABLE II 
 
 CARBON BISULPHIDE 
 
 600 
 
 #=648ogauss 7=2.272 cm 
 
 / Temp. 2i?2 to 22?oC. 
 
 \44i.6ji/i 508.6 589.3 
 
 fj, i. 67180 1.64586 1.62806 at 20?o C. 
 
 Observed by Flatow, Ann: d. Phys.< 12, 85, 1903. 
 
 d=io.38iXio 8 
 
 57272 
 
 Xi=204. 
 
 X 394 nn 
 
 observed ju= i .70226 
 calculated JJL = i . 7043 
 
 -s forX 589. 3 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 57 
 
 the agreement was considered sufficiently close. These numbers 
 are given in lines 7 and 8 of Table II. The dispersion of carbon 
 disulphide and a-monobromnapthalene has been more fully dis- 
 cussed in a former paper. 1 
 
 The constant hi was then determined by substituting in equation 
 (12) the values of H, /, C t , and Xj given in Table II, and the values 
 of X, 6, and ^ for the wave-length 589 . 3 /z/i. This gave 3 . 95 X io~ 5 
 for hi, as shown in the last line of Table II, when all the quantities 
 were expressed in c.g.s. and c.g.s. electromagnetic units. 
 
 The constants of (13) were now completely known, and (13) 
 was then used to compute the values of for the range of the 
 spectrum under investigation. The computed curve is shown by 
 the dotted line, curve 2, of Figure 2. It is seen that the agreement 
 between the observed and calculated values of 6 was fairly close 
 for the longer wave-lengths, but that for the shorter wave-lengths 
 the theoretical value was greater than the observed value, the 
 difference between the two values increasing as the wave-length 
 decreases. This difference between theory and experiment may 
 be attributed, in part at least, to the neglect of the effect of absorp- 
 tion in the theory. The discrepancy was in the right direction to 
 be attributed to this effect, for the introduction into the theoretical 
 formula of terms denoting absorption will produce a decrease in the 
 computed values of 6 for the shorter wave-lengths. 
 
 In his treatise on optics Drude 2 has derived two theoretical 
 expressions for the magnetic rotatory dispersion of isotropic media, 
 one based on the "molecular stream" hypothesis, and the other on 
 the "Hall effect" hypothesis. When written in a form to show the 
 connection between 6 and X, neglecting absorption, the two formulae 
 were, respectively, 
 
 and 
 
 1 A str -o ^physical Journal, 46, i, 1917. 
 
 2 Loc. cit., p. 406. 
 
58 R. A. CASTLEMAN, JR., AND E. 0. HULBURT 
 
 a ly a 2 , a 3 , and a 4 were quantities which involved the masses, the 
 charges, and the numbers of the "bound" and "free" electrons, 
 the strength of the magnetic field, the length of the medium, etc. 
 The refractive index wave-length relation in this connection was 
 
 (17) 
 
 Drude applied these equations to Verdet's magnetic-rotation meas- 
 urements on carbon disulphide and creosote in the following man- 
 ner. Using the value of X x obtained from (17) and two known 
 values each of 6 and X, the remaining two constants of (15) or (16) 
 were determined. The 0-X curve from either formula, which thus 
 traversed two of the observed points, was found to pass closely to 
 the remaining observed points. We do not believe, however, that 
 the agreement found in this way between theory and experiment 
 possesses great significance. One would not expect a theory which 
 neglected absorption to portray the observations with great 
 exactness. 
 
 Joubin (loc. cit.) has also derived a formula for the dispersion 
 of magnetic rotation of somewhat the same type as (15). He 
 applied this to the observations of rotations of carbon disulphide 
 and creosote, which were measured for the purpose, in much the 
 same manner as done by Drude. 
 
 6. a-monobromnaphthalene. This substance was investigated 
 in a manner similar to that described in the case of carbon disul- 
 phide. Table III shows a portion of the data and the results of 
 the calculations. This table has been compiled exactly as was 
 Table II for carbon disulphide, and therefore requires no further 
 explanation. The observed values of 6 have been plotted as 
 circles in Figure 3, and a smooth line, curve i, has been drawn 
 through them. The computed values of 6 from equation (13), 
 using the constants of Table III, are shown by the dotted line, 
 curve 2, of Figure 3. The differences between the observed and 
 theoretical values are similar to those noted for carbon disulphide. 
 
 7. Benzene. The values of 6 for this substance were deter- 
 mined throughout the visible spectrum. These are shown by 
 circles in Figure 4, through which a smooth line, curve i, has been 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 59 
 
 passed. The Verdet constant of benzene was found by Jahn 1 to 
 
 be 0.0297 minutes of arc for sodium 
 
 30[_ light. From the data of Figure 4 and 
 
 Table IV we obtain 0.0291 minutes 
 of arc for the same wave-length. 
 Jahn's value is not far different from 
 this. 
 
 The computed values of 6 from 
 equation (13) are shown by the dotted 
 line, curve 2, of Figure 4. It is seen 
 that the differences between 
 the observed and theoreti- 
 
 20L \\ cal values are of the same 
 
 character as those of the 
 previous cases. 
 
 I2 C 
 
 CX-TTI on obrom naphthalene 
 
 H20 
 
 SOOjuym 
 
 FIG. 3 
 
 600 
 
 TABLE III 
 
 tt-MONOBROMNAPHTHALENE 
 
 = 6480 gauss 
 
 Temp. 
 
 to 2o?y C. 
 
 =2.272 cm 
 
 X 434 MM 486 589 
 
 M i. 70433 1.68245 1.65876 at i9?4 C. 
 
 Observed by Briihl, Ber. Chem. Ges., 22, 388, 1897. 
 
 . 398X108 
 
 ^=0.70889 
 
 X 656 ju/j 
 
 observed /x= i .64995 
 calculated /x= i .6500 
 
 7^=5.02X10-5 forX 589.3 
 
 1 Wied. Ann., 43, 280, 1891. 
 
6o 
 
 R. A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 8. Nitrobenzene. The results of the work on this substance are 
 shown in Table V and Figure 5. The observed values of 6 were 
 
 plotted as circles in Figure 5, and a 
 
 col \ smooth line, curve i, has been drawn 
 
 \ through them. The computed values 
 
 \ of 6 from equation (13) are shown 
 
 by the dotted line, curve 2. 
 
 Discrepancies of the same char- 
 acter exist between the observed and 
 theoretical values of 6 as were noticed 
 in the preceding cases, but perhaps 
 greater in magnitude. 
 
 10' 
 
 6 
 
 Banzene 
 
 M20 
 
 600 
 
 FIG. 4 
 
 TABLE IV 
 BENZENE 
 
 77=6480 gauss 
 
 Temp. 22?9 to 24^6 C. 
 
 /=2.28o cm 
 
 X 434 nfj, 486 589 
 
 ju i*. 52380 1.51323 1.50111 
 
 Landoldt-Bornstein Tables. 
 
 at 2o?o C. 
 
 0.49898 
 
 173.8 AM 
 
 X 656 fJLfJL 
 
 observed ju= i .49646 
 calculated ju= i .4964 
 
 -5 for X 589.3 /z/z 
 
\ 
 
 MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 61 
 
 9. Ethyl iodide. The circles of Figure 6 show the observations 
 on this substance; a smooth line, curve i, has been drawn through 
 
 the observed points. Other data are 
 given in Table VI. Perkin 1 had de- 
 termined the Verdet constant of 
 ethyl iodide to be 0.0296 minutes of 
 arc for sodium light. From the pres- 
 ent data we find 0.0300 for this wave- 
 length. The two values are not 
 \ greatly at variance. The computed 
 
 x 2 values of 6 from equation (12) are 
 V shown by the dotted line, curve 2, 
 
 1 
 
 10 
 
 Nitrobenzene 
 
 H20 
 
 500/x/x 
 
 FIG. 5 
 
 TABLE V 
 
 NITROBENZENE 
 
 600 
 
 H = 6480 gauss /= 2. 272 cm 
 
 Temp. 2i?4 to 22^6 C. 
 
 \4S6.2fjLfji 589.3 656.3 
 
 AIL 57165 I.553I9 1-54641 
 
 Landoldt Bornstein Tables. 
 
 at 2o?o C. 
 
 6.o66Xio 8 ' 
 
 =o. 62924 
 
 X 434 . i 
 
 observed jj,= i . 5895 
 calculated M =1.5888 
 
 /Z!=2.56Xio~5 for X 589.3 
 
 Smithsonian Physical Tables, 1920. 
 
62 
 
 R. A. CASTLEMAN, JR., AND E. O. HULBURT 
 
 Figure 6. It is seen that the discrepancies between the observed 
 
 and theoretical values are similar to 
 those of the preceding cases. 
 
 10. Discussion of results. It has 
 been demonstrated that the formula 
 (13), which has been developed from 
 the electron theory of Lorentz, served 
 to express with a certain exactitude 
 the dispersion of the magnetic rota- 
 tion of certain liquids throughout 
 the visible spectrum. For the longer 
 
 10 
 
 Ethyl iodide 
 
 420 
 
 500/jiM 
 
 600 
 
 FIG. 6 
 
 TABLE VI 
 ETHYL IODIDE 
 
 gauss 
 
 Temp. 
 
 to 
 
 C. 
 
 /=2.220 CHI 
 
 X486.2JU/I 589.3 656.3 
 
 n i. 52356 1.51203 1.50738 
 
 Observed by Lorentz, Wied. Ann., n, 70, 1880. 
 
 at 2o?o C. 
 
 <7i=o. 50762 
 
 X 434 . i 
 
 observed /* = i . 5343 7 * 
 calculated JJL= i . 5336 
 
 7^=5. 90X10-5 for X 589.3^ 
 
 *Haagen, Pogg. Ann., 131, 117, 1866. 
 
MAGNETIC DISPERSION IN TRANSPARENT LIQUIDS 63 
 
 wave-lengths of the visible spectrum the agreement between theory 
 and experiment is quite close. For the shorter wave-lengths dis- 
 crepancies occur which increase as the wave-length decreases. 
 The liquids investigated above possess strong absorption in the 
 ultra-violet and appreciable absorption in the blue end of the 
 spectrum. We may therefore reasonably attribute the discrepancy 
 between theory and experiment in large part to the neglect of 
 absorption. If absorption is taken into account in our equations, 
 Xi is increased, and in general the modification which the constants 
 of the equations undergo is such as to bring the theoretical values 
 of into closer agreement with the observed ones. The absorp- 
 tion of these substances for light has, however, not been meas- 
 ured accurately, and it seems unprofitable at this time to consider 
 its effect numerically, 
 
 ii. The values of e/m. From the known value of h l} the ratio 
 of the charge to the mass of the electron may be calculated by 
 
 TABLE VII 
 
 A, e/m 
 
 Carbon disulphide ............ 3.95X10"$ 0.74X10? 
 
 a monobromnaphthalene. . . . -5.02 0.95 
 
 Benzene .................... 5 .34 i .01 
 
 Nitrobenzene ................ 2.56 0.49 
 
 Ethyl iodide ................. 5 . 90 1.12 
 
 means of formula (9). This has been done and the results are 
 shown in Table VII; e/m is expressed in c.g.s. electromagnetic 
 units. 
 
 Becquerel 1 , Voigt, 2 and Siertsema 3 have derived formulae for 
 the dispersion of the magnetic rotation, by means of which e/m 
 can be found as soon as the Verdet constant and the dispersion 
 dfji/dK of a substance for the same wave-length X are known. These 
 three formulae reduce to the same one, namely 
 
 m 
 
 X IE ' d\ ' 
 
 1 Comptes rendus, 125, 679, 1899. 
 
 a Wied. Ann., 67, 351, 1899. 3 Comm. Lab. Leiden, No. 82, 1902. 
 
64 R. A. CASTLEMAN, JR., AN> E. O. HULBURT 
 
 Using (18), Siertsema computed e/m for air, carbon dioxide, hydro- 
 gen, water, carbon disulphide, and quartz. The numbers varied 
 from o . 75 X io 7 to i . 77 X io 7 . 
 
 12. The effect of a upon the calculations. The value of the 
 quantity cr has no very critical effect upon the variation of 6 with 
 wave-length. The calculated curves of the diagrams have been 
 obtained by the use of J for cr in formula (12). If a is put equal 
 to o in (12), we arrive at Voigt's formula (14), and if this is used 
 to calculate the change of 6 with X we find values of 6 which are a 
 trifle less than those obtained from (13). They are about i per 
 cent less at X 434 juju, but are practically the same for wave-lengths 
 greater than 500 /zju. If cr is given values greater than f , the com- 
 puted values of are found to be somewhat greater than the 
 values given by (13), and therefore in greater discordance with the 
 observed values. For example, in the case of carbon disulphide, 
 if c7 = f, 0is 25?! at434ju/z. 
 
 The values of e/m change to some extent when cr is given 
 different values. This is shown for carbon disulphide in Table 
 VIII. We conclude that, as far as the present data are concerned, 
 
 TABLE VIII 
 
 <r e/m 
 
 1.78X107 
 
 1 0-74 
 
 I 0.30 
 
 I 0.25 
 
 it makes little difference whether cr is o or J. If, however, a is 
 increased above J, the discrepancies between the theory and the 
 observations become greater. 
 
 In conclusion the authors take pleasure in expressing their 
 thanks to Dr. J. S. Ames for valuable and constructive criticism. 
 
 JOHNS HOPKINS UNIVERSITY 
 February 1921 
 
VITA 
 
 Robert Allen Castleman, Jr., son of Robert Allen and Fannie (Funsten) 
 Castleman, was bora at The Hague, Westmoreland Co., Virginia, on 
 January 4, 1892. He graduated at the Baltimore City College in 1909, 
 and then attended undergraduate courses at the Johns Hopkins Univer- 
 sity during the three years, 1910-13. He taught at the Episcopal High 
 School, Alexandria, Virginia, from 1913-15, and took his A.B. degree 
 at George Washington University in 1915. During the year 1915-16 he 
 was assistant in physics at Tulane University, taking graduate courses 
 in physics and mathematics. He returned to Johns Hopkins University 
 in 1916 as a graduate student in physics and electrical engineering, 
 taking his M.A. degree at that institution in 1917. From 1917-20 he 
 was at the Bureau of Standards, holding positions of laboratory assistant 
 and assistant physicist. At the same time he continued his studies 
 under the direction of Professor Ames. He returned to Johns Hopkins 
 in 1920, taking work in physics, mathematics, and applied mathematics. 
 He has had lectures under Professors Ames, Wood, Pfund, Bliss, 
 Whitehead, Cohen, and Murnaghan. 
 
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