Interferometer Study 
 
 OF 
 
 Radiations in a Magnetic Field 
 
 JOHN CUTLER SHEDD 
 
 A Thesis Submitted for the Degree of Doctor of Philosophy 
 University of Wisconsin 
 1899 
 
 [Reprinted from the Physical Review, Vol. IX., Nos. 1 and 2, 1899.] 
 
Press of 
 
 The New Era Printing Company 
 Lancaster, Pa. 
 
<avas^ 
 
 PREFATORY NOTE. 
 
 The historic interest in the class of experiments to which the fol- 
 lowing research belongs, consists in the importance of establishing 
 the electromagnetic theory of light upon an experimental basis. 
 
 The first link in this connecting chain is furnished by Faraday’s 
 discovery of the magnetic rotation of the plane of polarization. A 
 second link is furnished by the experimentally determined ratio of 
 electromagnetic to electrostatic units as expressed by the equation 
 
 V = i / ■ s/ Km 
 
 where V — velocity of light in a non-conducting medium; 
 
 K— dialectric inductive constant of the medium ; 
 m = magnetic inductive constant of the medium. 
 
 A third link is furnished in Hertz’ epoch-making experiments on 
 electrical waves. The influence ©f a magnetic field of force upon a 
 source of light placed within it, is a fourth link, and marks one of 
 the most important advances that has been made since the electro- 
 magnetic theory was first set forth. 
 
 A further importance is to be attached to such experiments in 
 that much light will be thrown upon the motions of the ultimate 
 particles of matter, and possibly upon the ultimate structure of 
 matter itself. 
 
 
TABLE OF CONTENTS. 
 
 Page 
 
 Prefatory Note. 
 
 Part One. Historical Survey. 
 
 History,... i 
 
 Lorentz’s Theory, 3 
 
 Methods, 5 
 
 Experimental Results, 7 
 
 Modified Theories, 10 
 
 Summary, 14 
 
 Part Two. Experimental Work. 
 
 Introductory Note, 15 
 
 Outline of Work, 15 
 
 Section I. Preliminary Survey, 16 
 
 Summary, 19 
 
 Section It. The Interferometer Method, 20 
 
 Adjusting the Interferometer, 22 
 
 Visibility Curves, 23 
 
 Polarization, 26 
 
 Summary, 27 
 
 Measurement of Change of Wave-length, 28 
 
 Section III. Comparison of Magnetic Shift at Different Tem- 
 peratures, 32 
 
 Summary, 37 
 
 Section IV. Measurements of Magnetic Shift, 38 
 
 Ratio of Ionic Charge to Ionic Mass, 43 
 
 Polarization, 43 
 
 Summary, 45 
 
 Recapitulation, 45 
 
 APPENDIX. 
 
 I. Extract from Life of Faraday, 47 
 
 II. Extract from M. Ch. Fievez, 47 
 
 III. Extract from Perot and Fabry, 48 
 
 BIBLIOGRAPHY. 
 
 I. The Interferometer, 50 
 
 II. Radiations in a Magnetic Field, 50 
 
AN INTERFEROMETER STUDY OF RADIATIONS IN 
 A MAGNETIC FIELD. I. 
 
 John C Shedd. 
 
 Part One. Historical Survey. 
 
 I N 1845 Faraday discovered the rotation of the plane of polar. 
 
 ization due to a magnetic field of force. This, perhaps, sug- 
 gested the further experiment as to the effect of a magnetic field 
 upon a source of radiation placed within it. 1 
 
 In the light of what is now known Faraday’s repeated failure to 
 obtain positive results from this last experiment may be ascribed to 
 the low dispersive power possessed by his apparatus, and to the com- 
 paratively low temperature of the gas flame used as a source of 
 radiation. 
 
 In 1865 Maxwell propounded the electromagnetic theory of 
 light, which not only correlated all hitherto observed phenomena, 
 but also furnished a scientific basis for future research. 
 
 In 1875 Professor Tait 2 presented a paper “ On a Possible In- 
 fluence of Magnetism on the Absorption of Light” which, while 
 not realized by him experimentally is of interest in this connection. 
 He says in part : 
 
 “ The explanation of Faraday’s rotation of the plane of polariza- 
 tion of light by a transparent diamagnetic requires, as shown by 
 
 1 Appendix I. 
 
 2 Proc. Roy. Sec. Edinburgh. Sessions 1875-76, p. 16S. 
 
2 
 
 JOHN C. SHEDD . 
 
 [Vol. IX. 
 
 Thomson, 1 molecular rotation of the luminiferous medium. The 
 plane polarized ray is broken up, while in the medium, into its 
 circularly polarized components, one of which rotates with the 
 ether so as to have its period accelerated, the other against it in a 
 retarded period. Now, suppose the medium to absorb one definite 
 wave-length only, then — if the absorption is not interfered with by 
 the magnetic action — the portion absorbed in one ray will be of a 
 shorter, in the other, of a longer period than if there had been no 
 magnetic force ; and thus, what was originally a single dark absorp- 
 tion line might become a double line, the components being less 
 dark than the single one.” 
 
 The line of reasoning here presented, if applied to a source of 
 radiation (instead of absorption) placed in a magnetic field would 
 give an analogous solution of two bright lines of less intensity than 
 the original line. 
 
 The first experimental results in this field of work were ob- 
 tained by M. Fievez 2 in 188^—86. His observations consisted in a 
 broadening of the spectral line, and increased brilliancy of illumina- 
 tion. No observations are recorded as to the state of polarization. 
 
 The phenomena of reversal and increased brightness of the lines, 
 while undoubtedly precipitated by the action of the magnetic field, 
 were probably due, primarily, to changes of temperature and den- 
 sity. The broadening of the line, however, was undoubtedly a 
 genuine magnetic effect, and as Preston 3 remarks, had Fievez been 
 acquainted with the theory of the subject the whole question would 
 have been settled in 1885. 
 
 Fievez does not seem to have been familiar with what Faraday 
 had done as regards the state of polarization, nor to have taken any 
 special precautions against spontaneous reversals : yet, while his 
 work may, in the light of recent investigations, appear meager, it 
 deserves an important place in the history of the subject, and must 
 sooner or later have led to the very results reached by Zeeman. 
 
 A paper entitled “ Causes of Double Lines and Close Satellites 
 
 1 Reprint Thomson’s Papers on Electrostatics and Magnetism. Second Edition, p. 
 423, Footnote. 
 
 2 Appendix II. 
 
 ’Phil. Mag. (5), 45 , 1898, P- 338 - 
 
No. i.] 
 
 INTERFER OME TER S TUD V 
 
 3 
 
 in the Spectra of Gases,” by G. J. Stoney, 1 though not considering 
 the special case of magnetic forces, has, nevertheless, a theoretical 
 bearing upon the subject.. 
 
 Of still greater importance are the writings of Lorentz, 2 pub- 
 lished in 1892 and 1895, inasmuch as they were a guide to Zeeman 
 in his experiments. 
 
 In March, 1897, Dr. P. Zeeman 3 communicated to the Philosoph- 
 ical Magazine the results of a research that has proved wonderfully 
 fruitful in his own hands and also in the hands of others. Zeeman 
 was familiar with Faraday’s experiments, but did not* know of 
 Fievez’s work. He was influenced, as a matter of course, by Max- 
 well’s electromagnetic theory of light, and in particular was guided 
 by Lorentz’ s exposition of it. His first experiments were identical 
 with those of Faraday, excepting that he had a Rowland grating 
 of 14,000 lines to the inch, and hence had a much greater disper- 
 sion. With this arrangement of the apparatus, a broadening of the 
 spectral line was observed, similar to that seen by Fievez. Guided, 
 however, by Lorentz’s theory, Zeeman tested the state of polari- 
 zation of the broadened line, and found that, when viewed parallel 
 to the lines of force, the edges of the line were circularly polarized 
 as predicted by Lorentz’s theory. 
 
 Lorentz' s Theory . — In this theory it is assumed that light vibra- 
 tions are the vibrations of electrically charged ions of definite mass. 
 Thus suppose such an ion having a charge e and mass m, to vibrate 
 with simple harmonic motion about its center of equilibrium. Such 
 an ion moving in a magnetic field would then experience mechan- 
 ical forces, which would cause a change of period of vibration. The 
 amount of this change of period would depend upon the ratio ejm, 
 and the measurement of the change of period would give a knowl- 
 edge of this ratio. 
 
 The equations giving the modified period are derived as follows , 4 
 
 In Fig. 1 let the origin be at o and the axis of Z be parallel to 
 
 1 Sci. Trans. Roy. Dublin Soc., Vol. IV., p. 563, 1891. 
 
 2 Lorentz, “ La Theorie electromagnetique de Maxwell.” Leyden, 1892. “ Versuch 
 
 einer Theorie der electrichen und optischen Erscherungen in bewegten Korpern.” Ley- 
 den, 1895. 
 
 3 Phil. Mag. (5), 43, p. 226. Same art. Astro. Phys. Jr., 5, p. 332, 1897. 
 
 4 See Zeeman, Phil. Mag. (5), 43, p. 226. 
 
4 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Fig. 1. 
 
 the lines of force, the axes of X and Y being perpendicular to this 
 direction. Then if H be the strength of field, the equations of mo- 
 tion relative to the X and Y axes are 
 
 in 
 
 in 
 
 d 2 x 
 
 d 2 y 
 
 ~d? 
 
 dx 
 
 = -K 2 v- eH 
 
 dt 
 
 (0 
 
 The term K is the coefficient of elasticity of the ion, the second 
 term gives the mechanical force due to the magnetic field. 
 
 The solution of these equations yields for the period of vibration 
 the following values : 
 
 If H= o, T = — —r (2) 
 
 If H be not zero, and we regard all forces in the X Y plane as 
 symmetrcial with respect to the axis of Z, then 
 
 T 
 
 in «/ in 
 
 K 
 
 eH \ 
 2 K %/ in ' 
 
 (3) 
 
 The meaning of equations (2) and (3) is as follows : 
 
 If we analyze along the three coordinate axes, the motion of 
 the moving ion, which by virtue of this vibration is emitting light, 
 we shall have three component vibrations of equal period. We 
 may next compound the two components which lie in the X Y 
 plane into circular motion, and since we do not know the sense of 
 rotation, we may conceive it to be in both directions simultaneously. 1 
 
 If the source of light be viewed in a direction parallel to the 
 magnetic field, the component whose motion is parallel to the axes 
 of ^ is not effective, and the ray is, therefore, composed of circularly 
 
 1 The sense of rotation will depend upon the sign of the charge e upon the iron. 
 
No. i.] 
 
 INTERFEROMETER STUDY. 
 
 5 
 
 polarized components, whose periods of rotation are the same, and 
 for zero magnetic field have the value given by equation (2). If 
 the magnetic field be equal to H t then the periods become changed, 
 and are given by equation (3). The periods being changed by 
 equal and opposite amounts, the original spectral line becomes two 
 lines of equal intensity, symmetrically situated with respect to the 
 original unmagnetized line ; the components being circularly polar- 
 ized in opposite senses. 
 
 Viewed in a direction normal to the magnetic field, the component 
 parallel to the axis of Z, and, therefore, parallel to the axis of the 
 magnetic whirl, is not affected by it, is unaltered in period and ap- 
 pears as a plane polarized ray. The two circular components, being 
 now viewed parallel to the X Y plane, also appear as plane polar- 
 ized rays, the plane of polarization being normal to that of the Z 
 component. 
 
 Thus viewed, the spectral line is broken up into three component 
 lines, and if the magnetic field is of sufficient intensity there will be 
 seen three distinct lines, the two outlying ones having their vibra- 
 tions in a plane normal to the magnetic field, and the central one 
 in a plane parallel to it. If the magnetic field is not powerful 
 enough to separate the three components they will overlap, and the 
 line appears merely broadened. The components may, however, 
 be isolated by means of a nicol prism. 
 
 In his earlier work 1 Zeeman obtained only a broadened line, but 
 by means of the nicol he was able to test the state of polariza- 
 tion ; and, later, 2 he succeeded in obtaining both the doublet par- 
 allel to the magnetic field, and the triplet normal to the field, as 
 predicted by Lorentz’s theory. 
 
 Methods . — In the further progress of the work two radically dif- 
 ferent methods have been developed. 
 
 The first is that followed by Zeeman and many other investiga- 
 tors. It consists in photographing the spectral lines, and in meas- 
 uring the separation of the “ magnetized” components by means of 
 the micrometer dividing engine. The chief merit of this method is 
 that a permanent record is secured in the photograph. It is also 
 
 1 Phil. Mag. (5), 43, p. 226. 
 
 2 Phil. Mag. (5), 44, pp. 55 and 255 ; 45, p. 197. 
 
6 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 an advantage that the phenomenon is observed directly. The limi- 
 tations of the method are : First , the fact that the quantity to be 
 measured is minute, and the micrometer method of direct measure- 
 ment is of necessity limited in range ; Second , it frequently happens 
 that the components, whose distances apart are to be measured, are 
 so nebulous as to make it exceedingly difficult to make exact mi- 
 crometer settings. Third , the time of exposure necessary is some- 
 times so long as to make the method prohibitory. 
 
 The second method is due to Professor A. A. Michelson, and 
 may be called the Interferometer Method. It has been used suc- 
 cessfully with magnetic fields far too weak to give any sensible effect 
 by the direct method, and has been shown to have a delicacy and 
 sensitiveness far in excess of any photograph. The method, as 
 used by Professor Michelson, consists in obtaining the visibility 
 curves of the spectral line, both when unmagnetized, and also with 
 fields of different intensity. These visibility curves are then ana- 
 lyzed , 1 and the distribution of light at the source of illumination ob- 
 tained. This gives directly the various “ magnetic” components 
 of the line : By means of a nicol prism the two planes of polariza- 
 tion may be separately examined. 
 
 The advantages of this method are — briefly — First , the visibility 
 curve enables the separation of lines not hitherto resolved by any 
 other method. Second , the eye is the instrument of investigation, 
 and hence there is no need of long exposure as in the case of taking 
 photographs. Third , any change of polarization — or other effect — 
 taking place during the period of observation may be detected, while 
 the photographic process is necessarily an integrating method. 
 
 The disadvantages are : First , the method is an indirect one, i. e., 
 the observations are made not on the lines themselves but on in- 
 terference fringes produced by them. Second , the accurate estimate 
 of a visibility curve is by no means an easy matter, and the rare 
 success attained by Professor Michelson has been equalled by 
 no one else, and can only be approached by practice and great, 
 patience. Third , the record of the instrument is not automatic, as 
 in the photograph, and is subject to the personal error of the ob- 
 server. Fourth , the reflection from the half silvered surface of the in- 
 
 1 Ph.il. Mag. (5), 34, p. 280, 1892. Astro. Phys. Jr., 7, p. 129, 1898. 
 
No. i.] 
 
 IJVTEKFER OME TER S TUD V 
 
 7 
 
 terferometer affects the two beams polarized in perpendicular planes , 
 to a different degree, so that when both beams are simultaneously 
 observed they have not their normal ratio of brightness, with the re- 
 sult that the fringes are correspondingly deceptive. 
 
 In the hands of an experienced observer the interferometer is un- 
 doubtedly the most powerful instrument of attack that is available 
 at present, unless, indeed, Professor Michelson has presented in the 
 Eschelon Plate Spectroscope, an instrument of equally great value. 
 Under circumstances less favored than those enjoyed by Profes- 
 sor Michelson, it is difficult to see how the Interferometer Method 
 as he uses it, can be successfully used. There are, however, modi- 
 fications rendering this instrument more available, which have been 
 used by the present writer. 
 
 Experimental Results . — The agreement between theory and ex- 
 periment presented by Zeeman’s early experiments was truly re- 
 markable, and the apparent simplicity of the phenomenon seemed 
 equally worthy of notice. This apparent simplicity, however, was 
 soon found not to be true of all spectral lines, and more complex 
 forms were found. Exceptions were also found to the state of 
 polarization as first described by Zeeman. 
 
 The first observer to note a departure from the normal form was 
 M. Cornu. 1 His apparatus was similar to that of Zeeman except- 
 ing that he used a double image prism, and was thus able to ob- 
 serve both planes of polarization simultaneously. For a magnetic 
 field strength of 1 3,000 C. G. S. units he observed that the sodium 
 line, D l when viewed normal to the magnetic field was a quadruple, 
 the inner components being polarized perpendicular to the mag- 
 netic field and the outer ones parallel to this direction. The line, 
 D 2 he found to be a hazy triple with each member perhaps doubled. 
 
 M. Cornu was soon followed by others. Preston 2 succeeded in 
 photographing as many as five different types, and Michelson 3 
 with the interferometer showed three well marked groups of lines. 
 
 As regards polarization Becquerel and Deslandres 4 have found 
 
 1 Astro. Phys. Jr., 6, p. 378, 1897; 7, p. 163, 1898. 
 
 2 Phil. Mag. (5), 45, p. 330, 1898; 47, p. 165, 1899. 
 
 3 Phil. Mag. (5), 44, p. 109, 1897, same Art. Astro. Phys Jr., 6, p. 48, 1897 ; Phil. 
 Mag. ( 5 ), 45, p. 348, 1898, same Art. Astro. Phys. Jr., 7, p. 131, 1898. 
 
 4 C. R., April 4, 1898. 
 
8 
 
 JOHN C. SHEDD. 
 
 [VOL. IX. 
 
 that one of the iron lines when viewed perpendicularly to the mag- 
 netic field becomes a triple, in which the usual state of polarization 
 is reversed. The same phenomenon has also been observed at the 
 Johns Hopkins 1 University. 
 
 The classification of lines as given by Preston is shown in Fig. 
 2, who thus describes them. 
 
 Fig. 2. 
 
 In i we have the normal triplet. In 2 we have the weak middled ‘quartet’ in 
 ■which nearly all the light is concentrated in the two side lines. Next we have in 3 the 
 doublet in which the central line has completely disappeared. Next in 4 we have the 
 double doublet, or two pairs of fine lines, and finally in 5 the sextet or three pairs of 
 equally spaced sharp lines.” 
 
 Preston 2 cites the following as examples of the above types 
 
 Type 1, Cd, 4678 ; Mg, 5167 ; Zn, 4680 and the vast majority 
 of other lines. Type 2, Mg, 5183 ; Cd, 5086; Zn, 4810. Type 
 4, Mg, 5173 ; Cd, 4800; Zn, 4722. In his latest work 3 Preston 
 seems to restrict his classification to three types, viz. : “Diffuse 
 triplets,” “quartets” and “pure triplets.” It may be that types 3 
 and 4 are modified forms of the same type, as also 2 and 5. This 
 would leave but three types. 
 
 The types found by Michelson 4 are shown in Fig. 3. The up- 
 per curves are taken by the interferometer and the lower by the 
 Echelon plate spectroscope. The spectral lines are viewed normal 
 to the magnetic field in both figures 2 and 3. 
 
 1 Astro. Phys. Jr., 8, p. 48, 1898. 
 
 2 Phil. Mag. (5), 45, p. 330. 
 
 P Phil. Mag. (5), 47, p. 178. See also Nat., Vol. 59, p. 226, where seven types are 
 given. 
 
 4 Astro. Phys. Jr., 7, p. 136, 1898. Nat., March 9, 1899. 
 
No i.] 
 
 INTERF'EROME TER S TED V. 
 
 9 
 
 L 
 
 i 
 
 
 JL- 
 
 1 
 
 
 ^aI\a/\aA/\/\ - 
 
 
 B 
 
 
 .4 .3.2 .1 B.l.2.3.4 
 
 B ' 
 
 
 TYPE 
 
 1 
 
 TYPE II 
 
 type nr 
 
 
 
 PLANES OF POLARIZATION-! a 
 ( B 
 
 _J A 
 
 = EQUITORIAL 
 = AXIAL 
 
 
 
 A 
 
 B 
 
 
 
 qrEEN _ 
 
 JIM 
 
 A 
 
 A « 
 
 
 blue — 
 
 A 
 
 All 
 
 B 
 
 
 
 
 A 
 
 B 
 
 II 
 
 
 
 _JL 
 
 A/V . 
 
 
 
 
 B 
 
 Fig. 3 . 
 
 X 
 
 The following are 
 
 : some 
 
 examples : 
 
 
 
 Type I. 
 
 
 Type II. 
 
 Type III. 
 
 Hg 
 
 yellow line. 
 
 Hg 
 
 violet line. 
 
 Hg green line. 
 
 Cd 
 
 red line. 
 
 Cd 
 
 blue line. 
 
 Cd green line. 
 
 Zn 
 
 red line. 
 
 Zn 
 
 blue line. 
 
 Mg green line (5 183) 
 
 Au 
 
 green line. 
 
 Na 
 
 yellow line. 
 
 
 Ag 
 
 yellow line. 
 
 Au 
 
 yellow line. 
 
 
 Ag 
 
 green line. 
 
 
 
 
 Michelson adds a fourth type in which a broad or complex line is 
 simplified or narrowed in the magnetic field. Examples of this are 
 Cu yellow line and Mn green line (5340). This effect is true of 
 the central member of the triplet in the case of these two lines. 
 
 If now a comparison be made between such lines as have been 
 observed by several persons the following rather meager data are 
 found. 
 
IO 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Table I. 
 
 Lines. 
 
 Type. 
 
 Field Strength. 
 
 Observer. 
 
 Zn. 4810. 
 
 I Diffuse triplets. 
 
 
 Preston. 
 
 6 6 6 6 
 
 Type II 
 
 10,000. 
 
 Mich el son. 
 
 Cd. 5086. 
 
 Diffuse triplets. 
 
 
 Preston 
 
 “ “ 
 
 Type III. 
 
 10,000. 
 
 Michelson. 
 
 “ 4800. 
 
 Quartets. 
 
 
 Preston. 
 
 66 66 
 
 Type II. 
 
 10,000. 
 
 Michelson. 
 
 Na. Dj^ 
 
 Type II. 
 
 10,000. 
 
 Michelson. 
 
 “ “ 
 
 Quartet. 
 
 13,000. 
 
 Cornu. 
 
 “ D 2 
 
 Type II. 
 
 10,000. 
 
 Michelson. 
 
 6 6 66 
 
 Sextet. 
 
 13,000. 
 
 Cornu. 
 
 The results of such a comparison are of little value, unless the 
 conditions as regards the source of radiation and the magnetic field 
 strength are known to be the same. Two things are, however, ap- 
 parent. 
 
 I. The phenomenon is by no means as simple as was at first sup- 
 posed by Zeeman. 
 
 II. The superiority of the Interferometer Method as regards re- 
 solving power is shown. 
 
 Modified Theories . — Having found that the extremely simple de- 
 ductions from Lorentz’s theory, as made by Zeeman, do not com- 
 prehend the observed phenomena, it becomes necessary, either to 
 present a new hypothesis or suitably to modify the old one. This 
 modification has been made by Lorentz , * 1 II. Larmor 2 and others, while 
 Preston 3 has pointed out that the paper of Dr. Stoney , 4 already 
 cited, anticipates the desired theory. 
 
 Dr. Stoney considers the effect of perturbing forces upon an ion,, 
 moving in an elliptical orbit under the action of a central force, 
 which is proportional to the distance. If the perturbing force be 
 such as to cause the orbit to rotate in its own plane, then the spec- 
 tral line becomes a doublet. Thus if the ion be moving with an. 
 
 1 Proc. Roy. Acad. Sci. Amsterdam, June 25, 1898. Also Astro. Phys. Jr., 9, p. 37. 
 Wied. Ann., Bd. LXIII., p. 278, 1897. 
 
 2 Phil. Mag. (5), 44, p. 503. 
 
 3 Phil. Mag. (5), 47, p. 171. 
 
 4 Trans. Roy. Soc. Dublin, Vol. IV., p. 563. See also Preston, Phil. Mag. (5), 47 r - 
 p. 171. 
 
No. i.] 
 
 INTER FER OR/E TER S TUB V 
 
 I I 
 
 angular velocity J 2 then U = 2 t:N where N is the frequency of the 
 rotation. If now an angular velocity of to be impressed upon the 
 system as a whole, and in the same plane as U, then the resultant 
 angular velocity is the algebraic sum of the two. The resultant 
 frequency will also be the algebraic sum ; and since is to be 
 regarded in both senses, the resultant motion will have a double 
 frequency of N 4- n and N — n. 
 
 Viewed dynamically the equations show what forces are neces- 
 sary to produce the above changes. If the ion rotate with an 
 angular velocity il, and the orbit itself rotate about an axis passing 
 through the center of force, and having a direction (Imii) with an 
 angular velocity to, then the component velocities referred to the 
 rotating orbit are 
 
 _ dx 
 
 U ~ dt ~ 
 
 _ d l__ 
 V ~ dt~ 
 
 dz 
 
 W= ~di == 
 
 1 
 
 — tony -f- tomz 
 
 — tolz -f tonx I 
 
 — to nix- f- toly 
 
 (4) 
 
 The component accelerations are 
 du 
 
 I 
 
 = — tonv -f tomw 
 
 — — tolw + tonu [ 
 
 dt 
 dv 
 dt 
 dw 
 
 — 77 = — to mu 4- tolv 
 at j 
 
 (5) 
 
 Expanding equation (5) from equation (4) the acceleration along 
 the axis of X is 
 
 du d 2 x 
 dt ~ dt ' L 
 
 dy 
 
 dz 
 
 ton - 7 - + tom —r~ — ton 
 dt dt 
 
 ly) 
 
 -j- tom | 
 
 dz_ 
 
 dt 
 
 tomx -f to 
 
 which, by adding the term tol (to lx — to lx) and remembering that 
 / 2 -f //z 2 + n 2 — 1, reduces to 
 
JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 I 2 
 
 (Px 
 
 ~dt 2 
 
 = - 2W | 
 
 dy 
 
 n 
 
 dt 
 
 dk 
 
 m -rr 
 
 dt 
 
 j — co 2 x -f co 2 1 (lx -J- my -j- ns). 
 
 Two similar expressions give the acceleration along the Y and Z 
 axes. 
 
 The total acceleration experienced by the ion is then 
 
 d 2 x 
 
 dP 
 
 -f to 2 x -f co 2 1 (lx -j- my -f- ns) 
 
 ** + " (* w - ” ii ) 
 
 Z= - iPz- d JL = etc. 
 
 dt 
 
 ( 6 ) 
 
 In the case of a magnetic field of force, if the axes of Z be taken 
 parallel to the magnetic field then (/, m , ii) become equal to (o,o, i) 
 and equations (6) reduce to 
 
 X = — Q 2 x -|- oj 2 x -f 2 co 
 
 dt 
 
 F= — Q 2 y + (u 2 y — 2(0 ~ 
 
 Z= - !Pz 
 
 ( 7 ) 
 
 Now the central force producing the original rotation is I 2 2 x. The 
 
 dy 
 
 perturbing forces are then represented by the terms co 2 x + 2 co -rr 
 
 and 
 
 to 2 y 
 
 dx . . . . . dy 
 
 2 to — • Examining these it is seen that 2 to ^ 
 
 and — 2 to 
 
 dx 
 
 dt 
 
 are the X and Y components of a force 2 tov acting perpendicularly 
 to v, the linear velocity of the ion. If then a charged ion move in a 
 magnetic field with a velocity v, 2 tov is the force it would experience 
 due to the magnetic field. The terms to 2 x and to 2 y represent cen- 
 trifugal forces due to the impressed velocity to, and in the first 
 approximation may be neglected. Finally, if K— 2 to, the above 
 equations become identical with those of Lorentz. 
 
 Equations (6) and (7) are sufficiently general to cover all 
 hitherto observed phenomena. Thus to explain the case where 
 
No. i.] 
 
 INTERFEROMETER STUDY. 
 
 I 3 
 
 the central line of the triplet (line 2, Fig. 2) is doubled, it is only 
 necessary to write the equation for Z in the form Z— A sin Q t 
 where A is a periodic function of t of the form A — a sin nt. Sub- 
 
 stituting this in the equation 
 
 cPz_ 
 
 dF 
 
 = — Q 2 z and integrating we get 
 
 Z— a sin nt sin Q t — 0/2 [cos (Q — n) t — cos (J 2 -f n) t ] , 
 which represents two vibrations of frequency 
 
 (£2 dt n)/27T. (8) 
 
 The case of reversed polarization may be covered by supposing 
 the value of n to be such as to separate the components sufficiently 
 to place them outside the other lines of the triplet. In a similar 
 manner the doubling of the outer members of the triplet may be 
 accounted for which would also cover the case of a quartet when 
 viewed parallel to the magnetic field. In this way all the various 
 cases of multiple lines are satisfactorily explained. 
 
 Reverting to equations (2) and (3) we see that the change of 
 period of the ion is expressed by the equation, 
 
 27is/ m e H 
 
 ~K~' 2 Ks/m 
 
 The proportional change will then be 
 
 T- T' eH e HT 
 
 T 2 Ks/m m 4~ 
 
 27i s/ m 
 
 since K = — y~ • 
 
 X )/ 
 
 Finally, since T = — and T 9 — — where v = velocity of light, this- 
 
 becomes 
 
 / - // _ e H 
 
 X 2 m 47IZ> * 
 
 ( 9 > 
 
 Where A = wave-length of the spectral line for zero magnetic field. 
 /' = wave-length of the spectral line with magnetic field. 
 v = velocity of light, 300,000,000 cm. 
 
 H = intensity of magnetic field in C. G. S. units. 
 
14 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Equation (9) may be written 
 
 e X — 4 . 7 TV 
 
 77 
 
 and it is seen that a measurement of the change of wave-length en- 
 ables us to determine the ratio of the ionic charge to the ionic mass. 
 
 Zeeman 1 finds for this ratio, in the case of the blue line of Cd 
 (A = 4800) 24 x io 6 , while Preston 2 has found that this value 
 must be determined separately for each line, but that a possible 
 classification of lines may be made similar to the chemical classifi- 
 cation of Keyser and Runge. 3 
 
 Another interesting and significant observation is that of Ames 4 
 et. alt. who find that in the case of some iron lines, there appears to 
 be no magnetic effect, while those lines which show the greatest 
 magnetic shift are the ones which show the greatest pressure shifty 
 aud those which show but little magnetic shift are the ones of little 
 pressure 5 shift. 
 
 The present status of the subject may be summarized as follows : 
 
 1. In general, spectral lines are influenced by the magnetic field 
 when the radiations emanate from a source of light in the magnetic 
 field. 6 The magnetized system of lines is symmetrical with respect 
 to the original unmagnetized line. New spectral lines may be pro- 
 duced by the magnetic field. 7 
 
 2. Viewed parallel to the magnetic field the spectral line is, in 
 general, doubled, but it may become a single or multiple line. In 
 the case of a single line there is no polarization ; 8 in all other cases 
 the components are circularly polarized ; the shorter wave-length in 
 the direction of the magnetizing current, the longer wave-length in 
 the opposite sense. 
 
 3. Viewed in a direction perpendicular to the magnetic field the 
 
 1 Acad. Amsterdam, 1S97-1898, p. 260. 
 
 2 Phil. Mag. (5), 45, p. 337. 
 
 3 Wied. Ann., Bd. XLIII., p. 394, 1891. 
 
 4 Astro. Phys. Jr., 8, p. 50, 1898. 
 
 5 Astro. Phys. Jr., 6, p. 169, 1897. 
 
 6 Astro. Phys. Jr., 8, p. 49. 
 
 7 Astro. Phys. Jr., 9, p. 47. 
 
 8 This would be true of the lines seen by Becquerel and Ames, showing reversed 
 po’arization, when viewed parallel to the magnetic field. 
 
No. i.] 
 
 INTERFEROMETER STUDY. 
 
 J 5 
 
 outer components are plane polarized so that their vibrations are per- 
 pendicular 1 to the magnetic field ; the inner components having their 
 vibrations parallel to the magnetic field. 
 
 4. The general form of the line viewed perpendicularly to the 
 magnetic field is a triplet, but it is sometimes of complex structure. 
 
 5. The amount of magnetic action, measured in change of period 
 of the spectral line, is not a simple function of the wave-length ; nor 
 is it a constant for all wave-lengths ; nor a constant for all lines of 
 a given substance ; nor is it a simple function of wave-length for 
 the lines of a given substance. 
 
 6. The magnetic action is proportional to the field strength (being 
 limited, however, by temperature and pressure) ; and there appears 
 to be a possible classification following the chemical classification of 
 Mendelejeff and of Kayser and Runge. 
 
 Part Two. Experimental Work. 
 
 Introductory Note. — From the foregoing survey of the subject we 
 are led to believe that a comprehensive study of the problem con- 
 sists essentially of two parts : 
 
 1. A qualitative analysis of as many spectral lines, emanating 
 from as many different substances as possible, with a classification 
 according to the type of line produced. 
 
 2. Quantitative measurements of the change of wave-length and 
 of the ratio e/m, and a classification based upon these measurements. 
 
 All spectral lines belonging to the same group in both classifica- 
 tions may then be regarded as possessing related properties, and 
 the ratio elm as determined from such a group of lines should have 
 the same value. 
 
 Such a series of observations would as Preston remarks “ afford 
 a valuable means of inquiry into the so far hidden nature * * * of 
 the radiation from a luminous body, and also give us some clearer 
 insight into the structure of matter itself.” 
 
 Outline of Work. — In the following research the complete study 
 of the subject was not attempted, this being manifestly too great a 
 task for the limited time available. The preliminary ground has, 
 however, been cleared and a beginning made. 
 
 1 Exception, see Astro. Phys. Jr., 8, p. 50, 1898. 
 
JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 16 
 
 The work was subdivided as follows : 
 
 Section I. A preliminary survey of the field with a view of de- 
 termining the conditions limiting the observation of the magnetic 
 phenomenon. 
 
 Section II. A comparison of the ease of manipulation and range 
 of the two methods outlined above. 
 
 Section III. To ascertain whether the magnetic effect is radi- 
 cally different at different temperatures. 
 
 Section IV. To measure the magnetic shift of as many lines 
 as the time available would permit ; studying, also, the state of 
 polarization of the components. 
 
 Section I. A Preliminary Survey to Determine the Conditions 
 Limiting the Observation of the Magnetic Phenomena. 
 
 Apparatus. I. Magnet . — This was of the usual upright type ; 
 the base, cores, coils, pole heads, and cores to pole heads are all 
 separable ; the base and cores to the pole heads are of mild steel, 
 the rest of the magnetic circuit being made of that form of cast iron 
 known as Mitis Metal. An elevation of the magnet is shown in 
 Fig. 4, drawn to yi scale. 
 
 The cores to the pole heads are one inch in diameter, and it soon 
 became apparent that they, together with the mass of iron behind 
 them, tended to lower the temperature of the flame. A second 
 
No. i.] 
 
 IN / ERFER OME TER S TUB Y. 
 
 17 
 
 Fig. 5. 
 
 pair of cores was made of the form shown in Fig. 5. This form 
 also concentrated the magnetic field, thereby increasing its strength. 
 A third core was prepared similar 
 to those shown in Fig. 4, with a 
 J^-inch hole throughout its length ; 
 this core was for use in viewing the 
 flame parallel to the magnetic field. 
 
 II. The Flame . — The flame of a small Bunsen burner was first 
 used but was found to be too large. A small blast lamp was then 
 made of glass, and a foot bellows used. This gave a small conical 
 jet of flame about 3 inches high when the blast was inactive, and 
 about ^ inch high with the blast. This form of lamp, shown in 
 Fig. 6, proved highly satisfactory. 1 
 
 To color the flame a strip of asbestos wick supported by platinum 
 wire was first used. A bead of fused sodium carbonate was also 
 
 
 h^GAS 
 
 used, and, finally, a rod of 
 sodium glass was adopted 
 as needing the least atten- 
 tion. When a very bright 
 flame is used recourse to 
 the fused bead may be had, 
 but such a flame generally 
 gives rise to spontaneous 
 reversals. In the latter ex- 
 periments the glass lamp 
 was set aside for the burner 
 of an oxy-hydrogen lamp, 
 and the foot-blast was re- 
 placed by an oxygen tank. 
 
 III. Dispersion Apparatus . — The first trials were made with a 
 plane grating spectroscope ; the higher spectra were especially dim. 
 No success was attained with this apparatus. Next a Rowland 
 concave grating of 14,436 lines to the inch and’ five feet focal dis- 
 tance was mounted at one end of the table, the magnet being at the 
 other end. The spectrum was viewed with a telescope. It was 
 
 1 In time the glass about the opening cracks away but the whole lamp is easy of con- 
 struction. 
 
 Fig. 6. 
 
i8 
 
 JOHN C. SHEDD. 
 
 [VOL. IX. 
 
 with this mounting and with an oxygen gas flame that the first re- 
 sults confirmatory of Zeeman’s work were obtained. 
 
 The arrangement of apparatus is shown in Fig. 7. The lines 
 D x D 2 were very sharp and bright. When the current was turned 
 
 Fig. 7. 
 
 on each line grew broad and after a few seconds became distinctly 
 double, a sharp dark line separating the components throughout 
 their whole length. The lines were visibly brightened, as was also 
 the whole flame. 
 
 When the current was interrupted the lines appeared to collapse, 
 and after a second or so would again become sharp. Frequently 
 the doubling of the lines would persist for a few seconds after the 
 current was broken and the dark dividing line could be seen, 
 though narrower than with the full field. 
 
 For the doubling a field strength of about 18,000 C. G. S. units 
 was used, with weaker fields only a broadening of the line could be 
 observed. 
 
 Polarization . — With zero field the light was found to be slightly 
 polarized by reflection from the grating. The polarization with 
 
 full field is represented in Fig. 8, the ac- 
 celerated components D x , D 2 2 harmon- 
 ize in their sense of rotation with the 
 magnetizing current. The \ plate 
 reduces the circular polarization to plane 
 polarization. 
 
 Viewing the flame in a plane perpen- 
 dicular to the magnetic field the pole cores shown in Fig. 5 were 
 used. The tripling can best be observed by means of the nicol ; 
 without the nicol the tripling could be faintly seen, but the strength 
 of field necessary and the instrumental difficulties present make the 
 
No. i.J 
 
 INTERFEROMETER STUDY. 
 
 19 
 
 observation of the phenomena far from satisfactory. The planes' of 
 vibration of the components are shown in Fig. 9. As no quarter 
 wave plate is used this is the state of vibration in the ray of light 
 itself. 
 
 It being apparent that no measurements could be taken without 
 resorting to photography, the study was concluded at this point 
 and work with the interferometer begun. 
 
 Summary. The following points may be noted as covering the first 
 point aimed at in the work : 
 
 1. The magnetic separation of the sodium lines D Y D v as given 
 by a naked flame, cannot be distinctly observed at the temperature 
 of the Bunsen flame, nor of the air-blast flame, nor even at the tem- 
 perature of the oxygen gas flame, unless precautions are taken 
 against spontaneous reversals. 
 
 2. The phenomenon can be much more satisfactorily observed 
 parallel to the magnetic field when perpendicular to it, as the 
 strength of field necessary to produce a pure (or visual) triplet is 
 twice that necessary to produce the doublet. 
 
 3. There is a very perceptible time lag both when the magnet 
 is excited and when the current is broken, during which period the 
 lines show an inertia effect. This lag does not seem to be wholly 
 due to the self-induction of the fields, but may be partially vis- 
 ual and partially ionic. 
 
 4. A field ^strength of at least 15,000 C. G. S. units seems to be 
 necessary for satisfactory observation. 
 
 5. Spectra above the second order are too faint for good effects. 
 
Part Two. The Interferometer Method. 
 
 Professor Michelson 1 has shown the peculiar adaptability of the 
 interferometer for the class of research here considered . 
 
 The instrument used in the present case was received March i, 
 1898, and has proved highly satisfactory for the work under- 
 taken. 
 
 The instrumental difficulties attending the use of the Interferom- 
 eter are such as perhaps to warrant a word about them. These 
 difficulties arise from two sources : (1) defective workmanship in the 
 instrument, and (2) those due to the observer. These will be con- 
 sidered in order : (1) the most serious error that can be present is 
 a lack of parallelism in the ways along which the mirror carriage 
 moves. This is generally manifested by a shifting of the system of 
 fringes in the field of view, and a more rapid loss of visibility on 
 the part of the fringes than should take place. 2 A second defect is 
 sometimes present in the optical quality of the glass, due either to a 
 defective surface, or to internal stress in the glass. This defect is 
 manifested by a distortion of the fringes which under^ proper adjust- 
 ment should appear as circles. A third defect, easily overlooked, 
 is in the silvering of the surfaces. The two end mirrors (see Fig. 
 10) M' M" should be heavily silvered, and brightly polished. - 
 The half-silvered surface (Tf), however, should have such a film 
 as will transmit and reflect equal amounts of light. If this be true, 
 
 1 Astro. Phys. Jr., 6, p. 48, also 7, p. 131. 
 
 2 Phil. Mag. (5), 34 p. 286. 
 
No. 2.] INTERFEROMETER STUDY. 2 1 
 
 50 jo of the incident light is effective in the two interfering beams, 
 and the fringes are of maximum brightness. There is no direct 
 method of estimating this defect, and experience is the only proper 
 guide. (2) A very considerable amount of patience is necessary to 
 eliminate or minimize personal errors. Fringes are often obtained 
 which appear satisfactory, but from a lack of exact adjustment have 
 a variable focus, are distorted, and rapidly fade out as the movable 
 mirror recedes. If the instrument be in adjustment the fringes 
 appear as concentric circles, and Michelson has shown 1 that if the 
 incident light be parallel then the fringes are at infinity. 2 If, how- 
 ever, the light be not parallel, then the fringes are in front of the 
 interfering surface (M, Fig. 10), upon it or behind it, according as 
 A is greater than, equal to, or less than zero, where A is the dif- 
 ference in the paths traversed by the two beams of light. In gen- 
 eral it may be said that the incident beam is not parallel, and 
 hence, that the fringes recede as A increases. If a telescope is 
 used to view the fringes, the focus will have to be altered slightly, 
 and must soon be adjusted for parallel light. If, on the other hand, 
 the naked eye is used, there is a tendency to focus the eye upon 
 the mirror, instead of upon the fringes. Hence an observer is apt 
 to lose sight of the fringes altogether, or to view them out of focus 
 unless considerable care is exercised upon this point. The real 
 work of the interferometer consists in an eye estimate of the visibility 
 of the fringes as A is increased. There is a manifest liability to error 
 in these eye estimates, unless a comparison set of fringes of known 
 intensity is available ; but the process in such a case is not only 
 tedious 3 but adds to the amount of apparatus to be looked after. 
 On the whole, it is more practicable, and perhaps, as reliable to de- 
 pend upon the training of the eye that comes from long practice, and 
 in testing the eye from time to time by means of comparison fringes. 
 However, even after a correction 4 curve is obtained and applied, 
 there is room for a considerable margin of personal error, which is, 
 perhaps, the chief drawback to the method as a whole. 
 
 1 Phil. Mag. (5), 13, p. 239, 1882. 
 
 2 Except when A =°> when the fringes are on the mirror. 
 
 3 Astro. Phys. Jr., 7, p. 133. 
 
 4 Phil. Mag. (5), 34, p. 283. Such a curve is shown in Fig. 14. 
 
22 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Adjusting the Interferometer} 
 
 The general disposition of apparatus for the present work is shown 
 in Fig. io. 
 
 JT T M' 
 
 Fig. 10 . 
 
 M, M', M // . Interferometer mirrors. 
 
 Q. X ^ plate. 
 
 N. Nicol. 
 
 S. Slit. 
 
 E. Eye or telescope. 
 
 First Adjustment. To Find the Fringes. — The mirror M n is set 
 so as to be within two or three mm. of the zero of the scale, and 
 a Bunsen flame 1 2 colored with a piece of sodium glass is so set with 
 reference to the lens C that the field of the mirrors is uniformly 
 bright. Then a pin, or bit of glass fiber, is fastened by a bit of wax 
 onto the lens, so that its image is in the center of the field. It is 
 preferable to have the image lie obliquely across the field, not hori- 
 zontally or vertically. The mirror M' is then adjusted until the 
 two images of the pin, made by the two mirrors, M and M f , are super- 
 posed. When the images lie obliquely the movements of the adj usting 
 screws can be easily followed. When the adjustment is very close, 
 if the room is partially darkened, and the eye focused for a point 
 behind the mirror, the fringes should appear as fine lines covering 
 the field. The eye should now be focused on these fringes, and 
 
 1 The Adjustments of the Interferometer are discussed at length by Professor Wads- 
 worth in Phys. Rev., Vol. 4, p 480. See also p. 400 of same vol. 
 
 2 The Bunsen flame occupies the position of slit S in Fig. 10, the rest of the system to 
 ^he right of S being absent. 
 
No. 2.] 
 
 INTERFER OME TER STUD Y 
 
 23 
 
 the screws adjusted so that the fringes grow broader and more dis- 
 tinct. The final adjustment is reached when they appear as con- 
 centric circles, which do not change in appearance, when the eye is 
 shifted in any direction. Under these conditions the two mirrors, 
 M and M", are optically parallel to each other. 
 
 Second Adjustment. To Find Zero of the Instrument. — The zero 
 of the instrument is the position of zero difference of path between 
 the two interfering beams of light. It is found by obtaining fringes 
 with white light and adjusting on the central black fringe of this 
 system. To obtain fringes with white light the mirror M f should 
 first be adjusted so as to give the fringes as vertical lines of small 
 curvature. If now the mirror M " be moved back and forth by slow 
 motion, the fringes will be seen to change curvature at one region. 
 The exact point of this change of curvature is the point sought. 
 Having adjusted approximately for this, a candle flame should be 
 set before the Bunsen flame, giving the white image of the candle 
 flame with a background of sodium fringes. The mirror M" may 
 now be slowly moved by means of the tangent screw, the motion 
 being followed by the eye, in the progression of the (faint) sodium 
 fringes. When the zero point is approached brilliant chromatic 
 fringes, from ten to twenty in number, will appear in the image of 
 the candle flame. If now the candle be removed, and the air cut 
 off from the Bunsen flame the chromatic fringes are very distinct and 
 brilliant. 
 
 The zero point will shift a little with change of temperature, and 
 still more by a change in the distance of the mirror M' from M due 
 to difference in the manipulation of the adjusting screws. The zero 
 should therefore be observed before each set of observations. 
 
 Visibility Curves. 
 
 The theory of the visibility curve has been given by Michelson, 
 and its adaptation shown to problems where the distribution of light 
 as a source of radiation is to be determined. 
 
 The following curves were taken using sodium light as source of 
 illumination, and viewing the light first perpendicular to the field, 
 and than parallel to it. 
 
24 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 I. Perpendicular to the Field. The curves taken are shown in 
 Fig. ii , A, and the corresponding distribution of light in Fig. 1 1, B 1 . 
 
 In this curve the nicol prism was not used, and the loss of light 
 by the central component (which is known to be present), is such 
 as to render the line an apparent double. 2 In the curves B, in those 
 marked B, C } D the main components seem accompanied by small 
 companions some having negative ordinates. Now since this would 
 indicate negative intensities, they indicate errors in observing the 
 curves A. The analysis of the curves A then furnish a valuable 
 check upon their correctness. 
 
 II. Light Viewed Parallel to the Magnetic Field. Curves were 
 taken for this position both with and without the nicol. The re- 
 sults are shown on Figs. 12 and 13. These are substantially iden- 
 tical and show first a broadening and then a doubling of the spectral 
 lines. The presence of the negative ordinates is also seen and yet 
 the substantial results are clear. 
 
 1 Acknowledgment is due to Professor Michelson who kindly facilitated the analysis 
 of these curves on the Harmonic Analyzer at the University of Chicago. 
 
 2 See part I, also Michelson, Astro. Phys. Jr., 6, p. 49. 
 
No. 2 .] 
 
 INTERFER OME TER S TUD Y. 
 
 25 
 
 Fig. 12. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \' 
 V V 
 
 
 
 
 
 A 
 
 
 
 
 Na 
 
 li 
 
 FLA 
 
 MAGN. 
 
 ME yiE 
 
 ETIC FIEI 
 
 LWED 
 -D 1 
 
 
 
 CURV 
 
 A- 
 
 E H 
 
 0. 
 
 V 
 
 V 
 
 \ \ 
 
 
 
 — - 
 
 
 \ 
 
 f4 
 
 
 A) 
 
 <1S Vi| A PLATE VERTIC/j 
 
 “ NICOL | | “ 
 
 kL 
 
 
 Ef- 
 
 c- 
 
 — 300 
 
 — 770 
 
 0 
 
 0 
 
 
 \ 
 
 c' 
 
 B 
 
 \ 
 
 
 
 
 
 
 v 
 
 LINES PI 
 
 RESENT 1 
 
 3 1 D 1 °2 
 
 
 
 
 
 
 mm. 
 
 A 
 
 i i 
 
 
 
 5 1 
 
 0 1 
 
 2 1 
 
 1 1 
 
 6 
 
 S ;2 
 
 
 d 
 
 
 
 
 
 
 
 
 0 2 
 
 12 2 
 
 1 20 
 
 -28=3 
 
 0 3 
 
 2- 
 
 
 
 
 \ 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 B DISTRIBUTION 
 
 M 
 
 CURVES 
 
 l 
 
 
 'a' ~ e 
 
 i ~ c 
 
 
 Fig. 13. 
 
26 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Having analyzed these curves a comparison curve was then taken 
 to observe what correction was necessary to reduce the eye esti- 
 mates shown in the full line curves of Figs. 11,12 and 13. The re- 
 sulting curve is shown in Fig. 14 and the corrected visibility curves 
 are shown in the dotted curves of Figs. 12 and 13. These corrected 
 curves were not analyzed, but their distribution curves would be 
 more nearly correct than those shown. We have then in the curves 
 shown all observational errors present ; the result, though not satis- 
 factory, is by no means bad. This form of error is very hard to 
 avoid and long practice alone can eliminate it. 
 
 100 
 
 Fig. 14. 
 
 Polarization . — The interferometer was found to be capable of 
 showing the state of polarization in the most elegant manner, not 
 only identifying the plane of polarization, but also immediately 
 identifying the accelerated from the retarded ray. 
 
 Thus with the axis of the X plate vertical the nicol was ro- 
 tated and the action and character of the fringes observed. The 
 following were the results obtained : 
 
No. 2 .] 
 
 INTERFEROMETER STUDY. 
 
 27 
 
 Table II. 
 
 Position of Axis 
 of Nicol. 
 
 Action of Fringes on 
 Magnetization. 
 
 Character of Central Fringe 
 with Magnetic Field. 
 
 0° Vertical. 
 
 Become hazy. 
 
 Hazy. 
 
 4- 45° 
 
 Expand and remain distinct. 
 
 Distinct, dark. 
 
 -(- 90° Horizontal. 
 
 Become hazy. 
 
 Hazy. 
 
 135° 
 
 Contract and remain dktinct. 
 
 Distinct, light. 
 
 180° Vertical. 
 
 Become hazy. 
 
 Hazy. 
 
 —135° 
 
 Expand and remain distinct. 
 
 Distinct, dark. 
 
 — 90° Horizontal. 
 
 Become hazy. 
 
 Hazy. 
 
 1 
 
 4* 
 
 Ln 
 
 0 
 
 Contract and remain distinct. 
 
 Distinct, light. 
 
 0° Vertical. 
 
 Become hazy. 
 
 Hazy. 
 
 It is evident that the haziness at o° db 90° and 180° is due to the 
 simultaneous contracting and expanding of the fringes. Further 
 analysis shows us that when the 
 fringes expand the retarded compon- 
 ent is present and when the fringes 
 contract the accelerated (or shorter 
 wave-length) component is present. 
 
 This is shown in Fig. 15. Unpol- 
 arized light is represented by the su- 
 perposition of the two perpendicular 
 planes of vibration. 
 
 From this general survey of the in- 
 terferometer we derive the following- 
 generalizations : 
 
 1 . The interferometer is capable of showing the magnetic effect 
 for field strengths below 1,000 C. G. S. 
 
 2. The visibility curves, even under unfavorable circumstances, 
 show clearly the general character of the magnetic effect and when 
 checked through a long series, by means of an harmonic analyzer, 
 furnish an incomparable method of analysis. 
 
 3. When unaccompanied by such a check errors are not readily 
 eliminated and for quantitative measurements of change in wave- 
 length another use of the interferometer furnishes a better method. 
 
 Inasmuch as the visibility curve analysis was, not under the cir- 
 cumstances, entirely available, attention was tufned to the develop- 
 ment of point 3 above and carried out as follows : 
 
 Fig. 15. 
 
 Axis of ^ 1 plate vertical, 
 Nicol rotated. 
 
28 
 
 JOHN C. SHEDD. 
 
 [VOL. IX. 
 
 Measurements of Change of Wave-length. 
 
 Method. — Professor Michelson 1 in determining the difference in 
 wave-length between the components of the magnetic line makes 
 use of what he calls the “period of coincidence due to doubling.” 
 This may be defined as follows : Consider two systems of fringes 
 produced by light sources differing but little in wave-length. Then 
 the residtant system due to both sources, will be the resultant of 
 the overlapping of the component systems, and at certain points 
 destructive interference will take place, and at others reinforcement. 
 The fringes will then run through a series of maxima and minima 
 as A is increased. The distance from maximum to maximum is the 
 “period.” If A be measured from “zero” to the first point of re- 
 inforcement, then the following equation holds 
 
 Ap = M=(N+ i)V (II) 
 
 where N is the total number of fringes ; and A and A are measured 
 in mm. In the case of the lines D l D 2 these maxima occur every 
 988 fringes and A J; = 0.58242 mm. In the case, however, of the 
 magnetic shift the difference of wave-length is so small that Michel- 
 son finds the values of A to range from 58 mm. to 14 mm. as the 
 magnetic field increases to 4,000 C. G. S. units. The same method 
 is also described by Perot and Fabry 2 and is especially applicable 
 where the difference of wave-length is sufficient to give a differ- 
 ence of color to the two sets of fringes. 
 
 When applied to the magnetic components the method is open to 
 improvement. In the first place the fringes, at a point where A = 
 50, or even 30, are so narrow and frequently so faint that an accu- 
 rate determination of points of reinforcement (i. e. y where both sys- 
 tems agree in phase) is not easy. Secondly, since the magnetized 
 and unmagnetized fringes cannot be simultaneously observed, the 
 above determination consists in finding the value of A at which the 
 closing of the magnet shifts the system the double width of one 
 fringe. This determination for high values of A is not as easy as 
 might be wished. 
 
 1 Astro. Phys. Jr., 6, p. 50. 
 
 2 Astro. Phys. Jr., Feb., 1899. See Appendix III. 
 
No. 2.] 
 
 INTERFEROMETER STUDY, \ 
 
 2 9 
 
 There are, however, two possible modifications. If the nicol be 
 not used, it has been seen that the magnetized components draw 
 apart, one being retarded and the other accelerated. The corre- 
 sponding effect on the fringes is to cause the original system simul- 
 taneously to contract and expand. If now the point is found at 
 which the two systems of fringes are tangent to each other, each 
 fringe will have shifted its own width, showing that the acceler- 
 ated system is period in advance of the retarded one, or ^ 
 period removed from the original system. We then have the 
 equation 
 
 A m ,-M-(N+%)X’. (.2) 
 
 The second modification consists in using the nicol and in thus 
 quenching one of the component systems. Now concentrate the 
 attention upon one fringe, either adjusting a pointer (fastened to 
 lens c, Fig. 10) to its edge, setting the fringe tangent to a line drawn 
 on the mirror M, or by merely observing the central fringe of the 
 system. Let it be supposed that the central fringe is dark, and the 
 field unmagnetized. On turning on the current the system contracts, 
 and for a certain value of A will be the exact complement of the 
 first, the center being now light instead of dark. 
 
 Under these conditions the fringes have shifted over their own 
 width, and the following equation is obtained. 
 
 a , Ap = m = {N+y 2 )i'. (13) 
 
 Still a third modification would be as follows : Let the field re- 
 main magnetized and set the fringe, with the nicol in a given posi- 
 tion, tangent to the fixed line. Then let the nicol be rotated 90°, so 
 ' as to bring the other system of fringes into view ; then that value 
 of A which renders the line a common tangent to both systems 
 gives a difference of period such that 
 
 A =M i ==(N+ i)X 2 
 
 where ^ and X 2 are the component lines. Also since X x and X 2 lie 
 symmetrically with respect to X (the unmagnetizedTine) we have 
 
 A = NX x = [N + y 2 )X=(N+ i)X 2 
 
JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 30 
 
 or, putting the equation in terms of X, 
 
 a =m=(N±y 2 y (14) 
 
 which is identical with equation (13). 
 
 Since in the above equations N is the total number of fringes 
 passed over from the position A = o, some means must be had of 
 knowing its value. This is obtained very simply as follows : If X be 
 given in mm. then i/X equals the number of fringes per mm., 
 and N — A /^, A being measured in mm. Substituting this value 
 in the above equations and solving for X—X', the following equa- 
 tions are obtained 
 
 For A equation (11) 
 
 
 X 2 
 
 (11') 
 
 i X' 
 
 
 ~ _ A 
 
 ~ A 
 
 For A^ equation (12) 
 
 , ,, //' 
 
 X 2 
 
 
 x - x r = - — 
 
 — 
 
 (12') 
 
 4 A 
 
 4 A 
 
 For A y 2p equation (13) 
 
 xx' 
 
 X 2 
 
 (13') 
 
 X — A' = r 
 
 
 2 A 
 
 ~ 2 a 
 
 For a given, value of X — X' we have the relation 
 
 ^ P = 4 ./ tp = 2 A Hp . (16) 
 
 This last equation would indicate that the second method given 
 by equation (12') would be the most accurate since it gives the 
 smallest values of A and hence the widest and brightest fringes. 
 It must, however, be noticed that the condition expressed by 
 equation (12) is that the two systems of fringes shall differ by y 
 period and hence that the dark rings of one system shall coincide 
 with the light rings of the other. Hence the field will be uni- 
 formly illuminated and the fringes disappear. In practice there is 
 found to be a region over which the fringes are blurred and the ex- 
 act point of extinction is difficult to determine. 
 
 On the other hand, in the third method the fringes are always 
 sharp and for values of H above 2,000 C. G. S. units the values 
 of A are small enough to render the fringes sufficiently wide for 
 satisfactory observation. 
 
No. 2.] 
 
 INTERFER OR/E TER S TUD V. 
 
 3 * 
 
 With a little practice the method of observing the central fringe 
 was found to give concordant readings and hence was used in prefer- 
 ence to setting the fringe tangent to a line. 
 
 A comparison of the three methods is given by equation (16). 
 
 j ^ 
 
 Still further light is given by substituting the value of — from 
 
 equations (13) in equations (9). 
 
 Making this substitution we get 
 
 1 st method. 
 
 2d 
 
 3d 
 
 m 
 
 H A =4 xv — 
 
 m 
 
 H A = xv — 
 
 H A 
 
 m 
 
 2TC V — 
 
 e 
 
 (n") 
 
 (12") 
 
 (13") 
 
 07 ) 
 
 If m/e be regarded as constant, these equations all represent rec- 
 tangular hyperbolae asymptotic to H and A taken as axes. 
 
 It is thus seen that curves expressing the relation of H and A 
 furnish a ready means of comparison both by equations (16), and 
 by their form as indicated by equations (17). Such a set of com- 
 parison curves was taken with an oxygen gas flame colored with 
 sodium. In Table III. the values of H A for different parts of the 
 curve are given, and the curves themselves are given in Fig. 16. 
 
 Table III. 
 
 Method II. Method III. Method I. 
 
 I Z 1 
 
 A 
 
 HA 
 
 (curve A.) 
 
 A 
 
 HA 
 
 (curve B.) 
 
 A 
 
 HA 
 
 (curve C.) 
 
 2,300 
 
 15.4 
 
 354 
 
 21.4 
 
 492 
 
 13.1 
 
 300 
 
 3,000 
 
 12.0 
 
 360 
 
 16.7 
 
 500 
 
 12.0 
 
 360 
 
 4,000 
 
 9.0 
 
 360 
 
 13.3 
 
 530 
 
 11.0 
 
 440 
 
 5,000 
 
 7.3 
 
 365 
 
 10.5 
 
 526 
 
 10.0 
 
 500 
 
 6,000 
 
 6.2 
 
 370 
 
 8.2 
 
 490 
 
 9.0 
 
 540 
 
 7,000 
 
 5.5 
 
 385 
 
 6.8 
 
 475 
 
 8.2 
 
 575 
 
 8,000 
 
 4.8 
 
 384 
 
 5.8 
 
 465 
 
 7.4 
 
 590 
 
 9,000 
 
 4.3 
 
 386 
 
 5.2 
 
 470 
 
 6.7 
 
 602 
 
 10,000 
 
 3.8 
 
 380 
 
 4.8 
 
 480 
 
 6.1 
 
 610 
 
 11,000 
 
 3.5 
 
 386 
 
 4.5 
 
 496 
 
 5.6 
 
 615 
 
 12,000 
 
 3.4 
 
 408 
 
 4.4 
 
 528 
 
 5.3 
 
 635 
 
 1 H throughout these experiments was determined by the balistic method. 
 
32 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Curves A and B corresponding to Methods II. and III. show a 
 close correspondence with equation (17) while curve C is manifestly 
 unreliable. 
 
 Comparing curves A and B we see that equation (16) is not ful- 
 filled, and hence that either one or both curves are displaced. From 
 the fact already pointed out as to the difficulty of making settings for 
 curve A we have no hesitation in concluding that the readings for 
 this cure are uniformly too high. 1 Assuming that curve B is cor- 
 rect, the dotted curve D gives the corresponding position for 
 curve A. 
 
 Section III. Comparison of Magnetic Shift at Different 
 
 Temperatures. 
 
 To investigate this the sodium flame was used and reversal curves 
 taken, by Method III., under the following conditions : I. Bunsen 
 flame, II. Oxy-gas flame, III. Vacuum tube. 
 
 1 It is not to be supposed that curve A represents the greatest accuracy attainable by 
 Method II. Continued observation would undoubtedly render this method quite avail- 
 able. 
 
No. 2.] 
 
 INTERFER OME TER S TUD Y 
 
 n 'i 
 
 OO 
 
 The light was viewed parallel to the magnetic field as giving the 
 most uniform structure of line (see Fig. 3, B), and a mica plate 
 used. The following tables are selected as representative. 
 
 Table IV. 
 
 Reversal Curves. Na in Bunsen Flame. 
 
 H 
 
 C. G. S. units. 
 
 A mm . 
 
 A — A ' A. U. 
 
 0,000 
 
 00 
 
 0.000 
 
 3,000 
 
 12.80 
 
 0.135 
 
 4,000 
 
 11.65 
 
 0.155 
 
 5,000 
 
 10.60 
 
 0.168 
 
 6,000 
 
 9.60 
 
 0.180 
 
 7,000 
 
 8.50 
 
 0.205 
 
 8,000 
 
 7.70 
 
 0.230 
 
 9,000 
 
 6.40 
 
 0.274 
 
 9,500 
 
 5.40 
 
 0.325 
 
 9,600 
 
 5.00 
 
 0.350 
 
 9,700 
 
 4.90 
 
 0.370 
 
 9,800 
 
 4.80 
 
 0.375 
 
 10,000 
 
 4.70 
 
 0.380 
 
 11,000 
 
 4.65 
 
 0.380 
 
 12,000 
 
 4.65 
 
 0.380 
 
 13,000 
 
 4.65 
 
 0.380 
 
34 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Table IV. is platted in Fig. 17. The part of the curve lying be- 
 tween 8,000 C. G. S. and 11,000 was checked up with special care 
 and the knee in the curve verified. For all readings where A is 
 less than 3 mm. a small change in A indicates a large change in 
 X — X', and hence the readings become less sensitive. The departure 
 of the reversal curve from the normal hyperbolic form would in- 
 dicate, as is shown in curve B , Fig. 17, an ionic inertia or lag, due 
 either to low temperature or high density of the gas, or to both 
 This constraint retards the change in wave-length but suddenly 
 gives way at a field strength of about 9,500. Above a value of 
 H, of 10,000 the mean wave-length of the lines do not seem 
 further to change, increase in H beyond this point being effective in 
 broadening the lines rather than in separating them. 
 
 In curves A and B (Fig. 18) a small flame 2 cm. high was used 
 with the tip of the inner cone opposite the aperture. In curve C 
 the jet was 15 cm. high and the base of the flame opposite the 
 opening. The flame in both cases was colored with a bead of fused 
 sodium carbonate. 
 
 Curve C shows the same “lag” as does the Bunsen flame, and 
 the maximum value of X — X' is not so large. In curves A and B , 
 
 Table V. See Fig. 18. 
 
 Reversal Curves. Na in Oxygen-gas Flame. 
 
 H 
 
 mm. 
 
 A b mm. 
 
 A e mm. 
 
 U-a') a 
 
 (*-*')* 
 
 ( A.+V ) c 
 
 0 
 
 00 
 
 00 
 
 00 
 
 0.000 
 
 0.000 
 
 0.000 
 
 2,500 
 
 17.20 
 
 18.50 
 
 19.40 
 
 0.105 
 
 0.097 
 
 0.090 
 
 3,000 
 
 16.00 
 
 17.15 
 
 18.00 
 
 0.111 
 
 0.105 
 
 0.100 
 
 4,000 
 
 13.30 
 
 14.35 
 
 15.35 
 
 0.135 
 
 0.125 
 
 0.115 
 
 5,000 
 
 10.80 
 
 11.70 
 
 12.80 
 
 0.164 
 
 0.151 
 
 0.140 
 
 6,000 
 
 8.25 
 
 9.00 
 
 10.70 
 
 0.212 
 
 0.197 
 
 0.165 
 
 7,000 
 
 6.20 
 
 6.95 
 
 9.10 
 
 0.285 
 
 0.251 
 
 0.197 
 
 8,000 
 
 5.10 
 
 5.80 
 
 7.80 
 
 0.345 
 
 0.304 
 
 0.228 
 
 9,000 
 
 4.55 
 
 5.10 
 
 6.90 
 
 0.390 
 
 0.345 
 
 0.254 
 
 9,500 
 
 4.40 
 
 4.90 
 
 6.50 
 
 0.400 
 
 0.360 
 
 0.275 
 
 10 , 000 . 
 
 4.30 
 
 4.70 
 
 6.00 
 
 0.410 
 
 0.375 
 
 0.310 
 
 10,500 
 
 4.25 
 
 4.50 
 
 5.40 
 
 0.420 
 
 0.402 
 
 0.334 
 
 11,000 
 
 4.15 
 
 4.40 
 
 5.15 
 
 0.430 
 
 0.402 
 
 0.345 
 
 12,000 
 
 4.05 
 
 4.40 
 
 5.10 
 
 0.442 
 
 0.402 
 
 0.345 
 
 12,700 
 
 4.00 
 
 4.40 
 
 5.10 
 
 0.442 
 
 0.402 
 
 0.345 
 
No. 2.] 
 
 INTER PER OME 7ER S TUD Y 
 
 35 
 
 Fig. 18. 
 
 which are at a higher temperature, this lag is overcome at a lower 
 value of H, and the maximum value of / — // is larger. 
 
 Table VI. See Fig. 19 . 
 
 Reversal Curve. Na in Vacuum Tube. 
 
 H 
 
 A mm. 
 
 A — y A. u . 
 
 0 
 
 00 
 
 0.000 
 
 5,000 
 
 11.20 
 
 0.160 
 
 6,000 
 
 9.50 
 
 0.186 
 
 7,000 
 
 7.90 
 
 0.225 
 
 8,000 
 
 6.30 
 
 0.280 
 
 9,000 
 
 5.00 
 
 0.352 
 
 9,500 
 
 4.60 
 
 0.384 
 
 10,000 
 
 4.25 
 
 0.415 
 
 10,500 
 
 4.10 
 
 0.431 
 
 11,000 
 
 4.00 
 
 0.441 
 
 12,000 
 
 4.00 
 
 0.441 
 
 13,000 
 
 4.00 
 
 0.441 
 
JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 
 Fig. 1 9 would seem to show that at the temperature of the vacuum 
 tube the change of 7 — // is nearly proportional to H up to 7,000 C. 
 G. S., at which point the “ lag ” is overcome. At 1 1,000 the maxi- 
 mum for X — is reached. 
 
 In the case of the vacuum tube, the tube 
 was arranged as shown in Fig. 20. The 
 brass tube T is made to fit over the pole 
 heads of the magnet, and is capped at either 
 end, thus forming a metal box. Into this 
 box the vacuum tube is placed, being held 
 from contact with the metal by asbestos 
 wool. 
 
 A Bunsen flame is so supported as to 
 play horizontally upon the tube. Small glass tubes enter the caps 
 and convey wires to the terminals of the vacuum tube which was 
 energized by an induction coil of the usual type. The substance 
 whose spectrum was to be examined was placed in the tube, in the 
 form of filings, and the tube then exhausted to between 1 mm. and 
 2 mm. pressure. The brass tube was then heated by means of the 
 
No. 2.] 
 
 INTERFEROMETER STUDY. 
 
 37 
 
 Bunsen flame, until the spectral lines appeared sharp and bright. 
 In some cases the heating was pushed too far, resulting in chemical 
 action on the glass. 
 
 Upon using the vacuum tubes it was found that the glass of the 
 tube itself acted as a retardation plate, adding its effect to that of 
 the X mica plate. It was thus found impossible to produce an 
 exact retardation of period. With reversed positions of the nicol 
 prism, however, the two systems of fringes were found to be clear 
 and sharp so that the arrangement was satisfactory if not ideal. The 
 mica plate was used part of the time, and part of the time discarded. 
 
 In the preceding curves the effect of pressure cannot be separated 
 from the temperature effect. The combined effect is what is ob- 
 served. An interesting detail yet to be studied is the case where 
 the pressure is gradually varied, and a pressure curve obtained. 
 
 Summary . — From a study of these curves we draw the following 
 conclusions with regard to the effect of temperature. 
 
 I. At the temperature of the Bunsen flame there is a distinct 
 ionic “lag” or constraint which is overcome, suddenly, at a field 
 strength of 9,500 C. G. S. units. 
 
 II. This ionic lag becomes less as the temperature rises and is 
 practically absent at the hottest temperature of the oxygen-gas flame 
 or of the vacuum tube. 
 
 III. The change in wave-length reaches a maximum value depend- 
 ing upon the temperature (and pressure); the maximum is reached 
 at about 1 1,000 C. G. S. For values of H above this the magnetic 
 effect is to broaden the lines and not to separate them further. 1 
 
 This latter point receives support from Michelson’s echelon spec- 
 troscope which shows the sodium lines to belong to type II. (See 
 
 Fig. 3, B. 
 
 Note. An attempt was made to take observations witli the spark gap. A glass tube 1 
 mm. bore was taken, and metallic sodium crowded into it until 2 or 3 cm. of the tube at the 
 center was filled. The tube was then cut at the middle of the sodium, and the free ends 
 used as spark terminals. 
 
 On turning on the magnet the electro-dynamic action of the field caused a spark to fan 
 out showing in a very pretty manner the magnetic equipotential surfaces. This has also 
 been observed by M. Cornu. (Astro. Phys. Jr., 7, p. 166, note 2.) 
 
 1 This may be peculiar to the sodium lines, and be due to the simultaneous presence of 
 the lines D x and D r No observations have yet been made upon them separately, the 
 dispersion necessary to isolate them being too great. 
 
JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 8 
 
 Section IV. Measurements of Magnetic Shift. 
 Equation (9) may be put into the form 
 
 showing that for a given value of \ the change in wave-length should 
 be proportional to H provided no constraint is present. We have 
 seen that in the case of sodium (and presumably for all sub- 
 stances) a constraint is present at low temperatures, but that it 
 disappears as the temperature rises. In the measurement of mag- 
 netic shift it is important that the temperature be high, and, pre- 
 ferably, that the pressure be low. These conditions are fulfilled by 
 the vacuum tube ; hence it was used as a source of illumination. 
 
 It was primarily intended to make an extended series of observa- 
 tions upon the spectral lines of different substances, but the difficul- 
 ties encountered of breaking tubes, deposits in the capillary, and 
 chemical action within the tube, were such as to reduce the number 
 of satisfactory observations to sodium, zinc, mercury and cadmium. 
 Difficulty was also rqet with in getting readings upon lines lying 
 near either end of the visible spectrum. 
 
 The following are the data taken : 
 
 Sodium. Yellow lines (D X D ^. — The probable linear relation 
 of / — /' to H can be derived from Fig. 21, curve B, by drawing a 
 line from the origin tangent to the curve. This is given in Fig. 24. 
 
 Zinc. Blue line. / = 4810.724. (For arrangement of appa- 
 ratus, see Fig. 10.) 
 
 Table VII. 
 
 H. C. G. S. 
 
 A mm. 
 
 hx a 
 
 4,000 
 
 10.2 
 
 408 
 
 5,000 
 
 8.30 
 
 415 
 
 6,000 
 
 6.80 
 
 408 
 
 7,000 
 
 5.80 
 
 406 
 
 8,000 
 
 5.05 
 
 404 
 
 9,000 
 
 4.40 
 
 396 
 
 9,500 
 
 4.15 
 
 394 
 
 10,000 
 
 3.95 
 
 395 
 
 10,500 
 
 3.85 
 
 405 
 
 Aver. =403. 
 
No. 2.] 
 
 INTERFEROMETER STUDY. 
 
 39 
 
 The average of column three is the product of H x A of the 
 equivalent hyperbola, and this, divided by any given value of H f 
 gives a corrected value for A, which may be used in determining 
 the value of X — X' . In this way a double check is secured, first, in 
 drawing a smooth curve through the original data, and thus getting 
 the readings of column two; and second, in “averaging” these 
 readings in the manner shown. 
 
 In Table VII. the average of column three is 403 ; the value of A 
 corresponding to ff= 5,000, is 8.06, and X — X' is 0.144 A. U. 
 This is given in Fig. 21. 
 
 Mercury . — Readings were obtained on the yellow, green and violet 
 lines as follows : 
 
 Table VIII. 
 
 H 
 
 Yellow line. 
 
 Green line. 
 
 Violet line. 
 
 K = 5790-49- 
 
 A. = 5460.97. 
 
 A = 4358.56. 
 
 
 A 
 
 //A 
 
 A 
 
 HA 
 
 A 
 
 HA 
 
 3,000 
 
 20 
 
 600 
 
 
 
 
 
 4,000 
 
 15. 
 
 600 
 
 12.0 
 
 480 
 
 
 
 5,000 
 
 11.9 
 
 595 
 
 9.5 
 
 475 
 
 
 
 6,000 
 
 9.85 
 
 591 
 
 8.0 
 
 480 
 
 
 
 7,000 
 
 8.25 
 
 578 
 
 6.8 
 
 476 
 
 5.7 
 
 399 
 
 8,000 
 
 7.00 
 
 560 
 
 5.8 
 
 464 
 
 4.8 
 
 384 
 
 9,000 
 
 6.20 
 
 558 
 
 5.2 
 
 468 
 
 4.3 
 
 387 
 
 10,000 
 
 5.70 
 
 570 
 
 4.8 
 
 480 
 
 3.8 
 
 380 
 
 11,000 
 
 5.45 
 
 560 
 
 4.7 
 
 517 
 
 3.5 
 
 385 
 
 Aver. = 579. Aver. = 480. Aver. = 387. 
 
 The magnetic shift for H = 5,000 is, yellow line o. 128 A. U., green 
 line, 0.155 A. U., violet line 0.120 A. U. 
 
 Lines are then drawn through zero and this value, thus giving 
 the magnetic shift for any value of A. This is done on Fig. 22. 
 
 Cadmium . — Readings were taken on the red, green and blue lines 
 as shown in Table IX., and platted on Fig. 23. 
 
40 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 Table IX. 
 
 H 
 
 Red line. 
 
 A =6438.9. 
 
 Green line. 
 
 A = 5086.3. 
 
 Blue 
 
 A = , 
 
 line. 
 
 4800. 
 
 
 A 
 
 HX A 
 
 A 
 
 HX A 
 
 A 
 
 HX A 
 
 3,000 
 
 . 
 
 . 
 
 15.8 
 
 475 
 
 13.9 
 
 418 
 
 4,000 
 
 18.6 
 
 745 
 
 13. 
 
 520 
 
 10.7 
 
 432 
 
 5,000 
 
 14.15 
 
 708 
 
 10.8 
 
 540 
 
 8.4 
 
 420 
 
 6,000 
 
 11.4 
 
 685 
 
 9. 
 
 540 
 
 6.85 
 
 411 . 
 
 7,000 
 
 9.8 
 
 685 
 
 7.8 
 
 546 
 
 5.9 
 
 413 
 
 8,000 
 
 8.75 
 
 700 
 
 7. 
 
 560 
 
 5.3 
 
 424 
 
 9,000 
 
 8. 
 
 720 
 
 6.6 
 
 594 
 
 • • 
 
 • • 
 
 Aver. = 707. 
 
 Aver. = 539. Aver. = 420. 
 
 The magnetic shift for H — 5,000 is red line, 0,131 A. U.; green 
 line, 0.120 A. U.; blue line, 0.137 A. U. 
 
 The results may be summarized as follows : 
 
 Table X. 
 
 Substance. 
 
 Line. 
 
 Magnetic Shift for 
 
 H= 5000 H = 10.000 
 
 
 
 A. U. 
 
 A. u. 
 
 Sodium. 1 
 
 Yellow line D x . 
 
 0.207 
 
 0.414 
 
 Mercury. 
 
 Yellow line. 
 
 0.128 
 
 0.256 
 
 a 
 
 Green “ 
 
 0.155 
 
 0.310 
 
 i 6 
 
 Violet “ 
 
 0.120 
 
 0.240 
 
 Cadmium. 
 
 Red 
 
 0.131 
 
 0.262 
 
 << 
 
 Green “ 
 
 0.120 
 
 0.240 
 
 < i 
 
 Blue “ 
 
 0.137 
 
 0.274 
 
 Zinc. 
 
 Blue “ 
 
 0.144 
 
 0.288 
 
 This table is shown graphically on Fig. 24. 
 
 1 The echelon shows that the separation of the components of D 2 to be about two- 
 thirds of that of D v The value here found belongs to Z) v the line having the greater 
 magnetic shift. 
 
No. 2 .] 
 
 INTERFEROMETER STUDY. 
 
 41 
 
 Fig. 21. 
 
 Fig. 22. 
 
42 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 0 0.1 0.2 0.3 
 
 MAGNETIC SHIFT A" A' IN A.U.- 
 
 Fig. 23. 
 
 Fig. 24. 
 
No. 2.] 
 
 INTER PER OME TER S TUB Y 
 
 43 
 
 RATIO OF IONIC CHARGE TO IONIC MASS. 
 
 (I 
 
 for the case of circularly polarized light. This must be slightly 
 modified for plane polarized light as the period of single vibration 
 will be half that of the complete vibration of the circularly rotating 
 ion. Equation (io) will then be written 
 
 X — )J 2TCV 
 e/m = -jj- ' 
 
 The numerical value in electromagnetic units may now be calcu- 
 lated from the values of \ — 1 ' and H. 
 
 For the lines so far examined the values are as follows : The lines 
 may be grouped according to the value of e/m ; this gives the fol- 
 lowing interesting table. 
 
 Equation (io) gives the relation 
 
 X — /' AfiV 
 e ! m — yi yy 
 
 Table XI. 
 
 Substance. 
 
 Line. 
 
 e[m 
 
 Sodium. 
 
 Yellow. 
 
 22.45 X 10 s 
 
 Mercury. 
 
 Vio et. 
 
 23.81 
 
 Cadmium. 
 
 Blue. 
 
 22.41 
 
 Zinc. 
 
 Blue. 
 
 23.46 “ 
 
 Mercury. 
 
 Green. 
 
 18.59 “ 
 
 Cadmium. 
 
 Green. 
 
 17.48 
 
 Mercury. 
 
 Yellow. 
 
 14.35 
 
 Cadmium. 
 
 Red. 
 
 11.93 
 
 1 
 
 Type of line. 
 (Michelson.) 
 
 Type II. 
 
 Type III. 
 Type I. 
 
 It is thus seen that the groupings according to Michelson’s chart 
 (see Fig. 3 ) and according to the value of ejm are the same. 
 
 The data furnished by Preston 1 are too meager to furnish a just 
 comparison, but it is to be said that his classification is not so well 
 defined as is that furnished by the interferometer. 
 
 Polarization . — The method of observing the state of polarization 
 has been outlined. In the lines examined the state of polarization 
 1 Ph.il. Mag. (5), 45, p. 330. See part I. 
 
44 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 was found to be normal with the exception of two cases, that seem 
 deserving of notice. 
 
 I. Violet Line of Mercury. — In the readings of Table VIII. the set- 
 tings were taken successively on the yellow, green and violet lines for 
 the same value of H, by shifting the slit 5 in Fig. io. The nicol 
 was so set as to cause the fringes to expand, thus giving the re- 
 tarded component. For high values of A the behavior of the fringes 
 in the case of faint lines is not readily observed, and it was not until the 
 value A = 5-14 mm. was reached that it was noticed that the violet 
 line contracted, while the yellow and green lines expanded. This 
 behavior was carefully observed for the balance of the readings 
 and persisted throughout. This peculiar state of polarization would 
 indicate that the component of the violet line which agrees in rota- 
 tion with the magnetic whirl is retarded instead of accelerated, as in 
 the other lines. Hence we must have present a species of diamag- 
 netic ion in contrast to the ordinary or “ magnetic ” ion. The above 
 observations were taken with the greatest of care, and yet the con- 
 clusion seemed so unusual as to call for repeated verification. All 
 attempts, however, to secure the same observations proved unavail- 
 ing so far as reversed polarization was concerned. 
 
 II. In the case of the cadmium lines the following observations 
 were made : The red , green and blue lines were examined, the nicol 
 being set so as to cause the fringes to contract, thus giving the ac- 
 celerated ray. The observations were begun with H — 2,900 C. G. 
 S. units. At the second reading with H — 6,600 the fringes all ex- 
 panded, and so also for H= 7,900. At the last reading with H — 
 8,800 all the fringes again contracted. The apparent conclusion to 
 be drawn is that a reversal of the state of polarization takes place 
 during the progress of the experiment. It is more likely, however, 
 that in this case, since (as already stated) the glass of the vacuum 
 tube acts as a retardation plate, some change of stress due either to 
 variation in temperature or to the magnetic field, is responsible for 
 the observed effect. This fact, in connection with the difference 
 in wave-length between the violet and the green and yellow lines of 
 mercury, may, perhaps, also explain the unusual behavior observed 
 in this line. Both these cases illustrate the necessity of carefully 
 watching the instrumental factors present. 
 
No. 2.] 
 
 INTERFEROMETER STUDY. 
 
 45 
 
 Summary . — The study of the magnetic shift and the values of elm 
 lead to the following conclusions : 
 
 I. A classification of lines according to the amount of magnetic 
 shift is of little value. 
 
 II. A classification of lines according to the value of e\m is 
 significant. 
 
 III. Such a classification groups the lines according to the type 
 of line produced, as given by the analysis of visibility curves. 
 
 IV. The smaller the value of ejm the less the broadening of the 
 component lines and the simpler their structure ; vice vei'sa the 
 larger the value of ejm the more the broadening, and the more 
 complex their structure. 
 
 Recapitulation. 
 
 In the preceding pages the history of the subject has been traced, 
 from the first experiments of Faraday to the present time. The 
 bearing of the Maxwell-Lorentz theoiy upon the progress of Zee- 
 man’s experiments is noted, and the reacting influence of experiment 
 upon theory is shown, so that in the papers of Larmor, Lorentz and 
 others the mathematical exposition of the subject has kept pace with 
 the experimental observations. In the experimental development of 
 the problem two well-marked methods have been presented and com- 
 pared. It has been found that the spectro-photographic method is 
 (i) limited in range by reason of the small resolving power of the 
 ruled grating when so minute changes are to be measured ; and (2) 
 is limited in accuracy by reason of the wide margin of error in the 
 settings of the micrometer, especially when nebulous lines are to be 
 measured. 
 
 On the other hand, the interferometer method has been seen to 
 possess a resolving power greatly in excess of the photographic 
 method, and hence is applicable to low values of H as well as to high 
 values. 
 
 The results accomplished so far consist in 
 
 I. By the spectro-photographic method. 
 
 (1) A classification of lines according to the type of line produced 
 by the magnetic field. 
 
46 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 (2) The measurement of the distance between outside compo- 
 nents of magnetic triplets and a determination of the value of the 
 ratio e\m. 
 
 The number of lines so far examined is not large, nor do the 
 values of the magnetic shift obtained by different observers seem to 
 agree very well ; but enough has been done to suggest a classifica- 
 tion of lines parallel to that obtained by Kayser and Runge. 
 
 II. With the interferometer Professor Michelson has presented, 
 
 (1) Three well-marked types of lines, with a possible fourth type. 
 
 (2) He has concluded that the magnetic shift is to be regarded 
 as approximately independent of substance or color. 
 
 The chief value to be attached to his work is contained in (1), 
 and it would seem to us better to leave (2) unformulated rather than 
 to state it as an approximate law. 
 
 The experiments described in this paper have sought to deter- 
 mine, 
 
 (1) The relation, at different temperatures, of the magnetic shift 
 to strength of field. 
 
 (2) To present a method of measuring the magnetic shift that 
 shall be as free as possible from objections involved in existing 
 methods. 
 
 The method adopted is similar to existing interferometer methods, 
 but is believed to be especially adapted to the present problem. 
 
 (3) To measure the magnetic shift and determine the ratio ejtn. 
 
 The values obtained for magnetic shift show that any classifica- 
 tion based upon this alone is of relatively small value ; but that a 
 classification based upon the value of e\m is significant. 
 
 This classification is seen to give groups of lines identical with the 
 groups presented by Michelson’ s three types of lines. 
 
 The complexity of structure is also seen to depend upon the 
 value of this ratio e\m. 
 
 The preceding experiments were carried on in connection with 
 the Fellowship in Physics from 1897 to 1899 at the University of 
 Wisconsin, under the direction of Professor Benjamin W. Snow ; 
 whom, in conclusion, I desire to thank for his helpful and continued 
 encouragement throughout the progress of this investigation. 
 
 Physical Laboratory, University of Wisconsin, April, 1899. 
 
No. 2.] 
 
 INTERFER OME TER STUD Y 
 
 47 
 
 Appendix I. 
 
 Extract from Life of Faraday by Dr. Bence Jones, Vol. II., p. 44. 
 
 “ 1862 was the last year of experimental research ; Steinheil’s ap- 
 paratus for producing the spectrum of different substances gave a 
 new method, by which the action of magnetic poles upon light 
 could be tried. In January he made himself familiar with the appa- 
 ratus, and then he tried the action of the great magnet on the spec- 
 trum of NaCl, BaCl, StCl and Li Cl, 
 
 “ On March 12 he writes : 
 
 “ ‘Apparatus as on last day (January) but only ten pairs of voltaic 
 battery for the electromagnet. 
 
 “ ‘ The colorless gas flame ascended between the poles of the mag- 
 net, and the salts of sodium, lithium, etc., were used to give color. 
 A Nicol’s polarizer was placed just before the intense magnetic field, 
 and an analyzer at the other extreme of the apparatus. Then the 
 electromagnet was made, and unmade, but not the slightest trace of 
 effect on or change in the lines of the spectrum was observed in 
 any position of polarizer or analyzer. 
 
 “ ‘ The other pierced poles were adjusted at the magnet, the colored 
 flame established between them, and only that ray taken up by the 
 optic apparatus which came to it along the axis of the poles, i. e., 
 in the magnetic axis or line of magnetic force. 
 
 “ ‘ Then the electromagnet was excited and rendered neutral, but 
 not the slightest effect on the polarized or unpolarized ray was ob- 
 served.’ 
 
 “This was the last experimental research that Faraday made.” 
 
 II. 
 
 Extract from M. Ch. Fievez (Astronome a l’Observatoire Royale 
 de Bruxelles), Bulletins de /’ Ac ade mi e Royale de Belgique , 3d serie, 
 tome ix., p. 381 (1885). 
 
 “ L’installation spectroscopique de l’Observatoire, disposant d’un 
 appareil dispersif de tres grande puissance et d’un electro-aimant 
 Faraday, construction Ruhmkorff, pouvant etre active par un cou- 
 rant de 50 ampres d’intensite, a permis d’aborder ce probleme. 
 
48 
 
 JOHN C. SHEDD. 
 
 [Vol. IX. 
 
 “ La flamme oxyhydrique d’un petit chalumeau etait dirigee 
 horizontalement sur un charbon sode place entre les armatures 
 coniques de l’electro-aimant, distantes Tune de l’autre de io milli- 
 metres. Une image de la flamme etait projetee sur la fente du 
 spectroscope par un objectif double. La quantite d’oxygene intro- 
 duce dans cette flamme permettait de regler la temperature de facon 
 a donner aux raies spectrales et D 2 l’apparence voulue. 
 
 “ Dans ces conditions, les raies sodiques D x et D 2 etant d’abord 
 peu larges et non renversees avant le passage du courant d’aiman- 
 tation, deviennent immediatement plus brillantes , plus longues et plus 
 larges aussitot que l’electro-aimant est mis on activite. 
 
 “ Si les raies brillantes D x et D 2 sont deja elargies, 1 ’ electro -aimant 
 etant inactif, elles deviennent plus larges encore et se renversent 
 (c’est-a-dire qu’ une raie noire parait au milieu de la raie brillante 
 elargie) pendant le passage du courant d’aimantation. 
 
 “ Si les raies sont deja elargies et renversees, l’elargissement de 
 la raie brillante et de la raie noire devient beaucoup plus considerable. 
 
 “ Ces phenomenes, qui disparaissent instantanefnent lors de V inter- 
 ruption du courant, peuvent etre observes, mais avec moins d’in- 
 tensite, sur la raie rouge du potassium, du lithium, sur la raie verte 
 du thallium, etc., lorsqu’ une minime quantite de ces metaux ou 
 d’un de leurs sels est placee sur le support de charbon. 
 
 “ Enfin, les armatures coniques de l’electro-aimant etant rem- 
 placees par les armatures meplates, de maniere que toute la 
 longueur de la flamme sodique seit comprise entre ces armatures, 
 les raies D x et D 2 , prealablement renversees et elargies, presentent un 
 double renversement (c’est-a-dire l’apparition d’une raie brillante au 
 milieu de la raie noire elargie), lorsque l’electro-aimant est en 
 activite.” 
 
 III. 
 
 Extract from article in Astro. Phys. Jr., February, 1899, by 
 Perot and Fabiy. 
 
 “ * * * when the light is complex it is easy to obtain a precise 
 measure of the ratio of the wave-length of the radiations which 
 constitute it; let there be two radiations of nearly equal wave- 
 length / and X — £. The distances between the silvered surfaces is in- 
 
No. 2.] 
 
 INTERFEROMETER STUDY. 
 
 49 
 
 creased until the discordance between the two systems of rings is 
 complete. Then if e is the distance between the surfaces (which is 
 given with sufficient accuracy by the micrometer) we have 
 
 _i- A 
 
 l 4 £ 
 
 “ * * * This method is also readily adapted to the study of the 
 change of wave-length of a given line, on condition that the radia- 
 tion be sufficiently monochromatic ; in such a case a comparison 
 can be made of two sources emitting, for instance, in the one case 
 the altered radiation and in the other the normal radiation, atten- 
 tion being directed to the change in the appearance of the rings 
 produced by the two sources successively.” 
 
 Note. — With the interferometer the ray travels the distance be- 
 tween the plates twice and hence J = 2e. Therefore the equation 
 for the interferometer becomes 
 
 e A A 2 
 
 — = -or e = — . 
 
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