by Runge and Paschen, that each member of a trunk or of a branch behaves alike, not only as regards the general type of subdivision but also as regards the amount of separation in a given magnetic field, provided the separation is measured on the frequency scale. The same is T.I. T. II. M.B.I. M.B.II. MB.M. Fig. 174. true for all series which correspond to each other. Thus M.B. I. II. and III., Fig. 174, give the magnetic separation of the lines in each of the three main branches, in all cases where there are three main branches associated with each other (zinc, cadmium, mercury, calcium). The figure represents the observations when the line of sight is at right angles to the magnetic field, each line being split up into the group shown in the figure. The dotted lines represent the compo nents vibrating parallel to the field, and the full lines those at right angles to the field. The portions of the figure marked T. I. and T. II. represent the separation observed in the two sodium lines, and also apply in all cases where twin trunks exist (e.g. copper, silver), T. I. representing the type of the least refrangible component. The same type is observed in a doublet found in each of the spectra of magnesium, calcium, strontium and barium (e.g. H and K of calcium), and we may therefore conclude that these doublets belong to a previously unknown trunk. The distances between the Zeeman components of each line are found by Runge and Paschen to be small multiples of a number, which is the same for each of the two members of the twin trunks. It is also the same for each of the main branches of the mercury and allied triplets. Thus in Fig. 174 the distances between the lines of the rows marked T. I. and T. II. are all capable of being represented as small multiples of a difference in period which for the field used by Runge and Paschen (31000) was measured by them to be 0:459 (the unit here is the number of waves spread over one centimetre). Referred to the same scale and the same intensity of field, the common factor of the subdivision of the triplets marked M.B. I. II. and III. is 0.702. Runge and Paschen point out that these numbers are very nearly in the ratio of 2: 3. Comparing the types marked T. II. and M.B. I. the figure shows that the smallest displacement of the vibrations at right angles to the field is the same in the case of the loublet and the triplet. The types found in the twin trunk are also found in the main branches of the alkali metals with the difference that the type of the most refrangible member of the twin trunk is the same as the type of the least refrangible member of the branch doublet. The lines of the side branches of copper, silver, thallium and S.B.S. S.B.I. S.B.II. Fig. 175. aluminium are doublets, the less refrangible member being accompanied by a satellite, which shows a complicated structure in the magnetic field. Fig. 175 shows the appearance (S.B.S.) of the satellite in the magnetic field, and also the types belonging to the least refrangible (S.B. I.) and most refrangible (S.B. II.) components of the side branches Much remains to be done in extending the investigation to other metals. Iron has been investigated pretty carefully. Among the various types of separation Fig. 176 shows three remarkable ones given by H. Becquerel and H. Deslandres*. In this figure the components vibrating perpendicularly are drawn above those which are parallel to the magnetic field. The peculiarity of the type marked A is that the vibrations parallel to the field are more affected than those at right angles to it. According to Berndt the green line of Helium is divided in accordance with this type A, but the experiment is difficult in the case of permanent gases and further measurements are much needed. It will be noticed that in some cases the same component appears, whether the direction of vibration is at right angles to the field or parallel to it. It would be interesting to notice whether in such cases the light is really elliptically polarized, as it should be if the coincidence were absolute. In Table XIV. I have collected the calculated Zeeman coefficients for a few of the important types. * C. R. CXXVII. p. 18 (1898). The members of the doublets and triplets are numbered in the order of diminishing wave-lengths, thus "Main Branch III." means the most refrangible member of a triplet belonging to the main branch series. The table is entirely based on the measurements of Runge and Paschen* and the wave-lengths given in the second column as examples belong to lines from which, among others, these authors have derived their results. The last column gives under the heading the alteration in frequency (multiplied by 10-) of the vibrations which are parallel to the field. Where several numbers are given in the third or fourth column, it means that the original vibration is split into more than two components. * Berl. Abh. (Anhang) 1902. Sitzungsber. d. Berl. Ak. xix. p. 380 (1902) and XXXII. p. 720 (1902). On the simple assumption under which equation (19) has been deduced, (20) allows us to calculate the important ratio e/p from the Zeeman coefficient. Taking z from Table XIV., the values of 4% are found to range from 34 × 107 to 10'. Independent measurements of elp founded on the properties of kathode rays, give values between 3 and 1.86 × 107; the correct value lying probably nearer the higher than the lower of these numbers. The average apparent mass of the electron vibrating in the magnetic field calculated on the simple Lorentz theory is therefore not far different from that obtained by observation on kathode rays. There seem however, undoubted cases (probably the majority) where the constraint or mutual influence of the vibrating electrons diminishes their apparent mass. The simplest form of resolution in which each line, looked at transversely to the lines of force, is separated symmetrically into three components, of which the outer ones vibrate at right angles to the field, is found in the case of the side branch doublets of Copper, Silver, Aluminium, Thallium and Copper as well as in certain doublets of Calcium, Strontium, Magnesium and Barium. In all these cases the magnetic effects are identical when measured on the frequency scale. The values of e/p deduced from Runge and Paschen's measurements are 18 × 107 and 14 × 107 for the least and most refrangible members respectively. These numbers agree very well with those obtained by electrical measurement. On the other hand, the third main branch of the magnesium series, also showing the simplest resolution, gives a number about twice as great for e/p. It is a significant fact that no Zeeman effect has yet been observed in the case of spectra of fluted bands such as those of carbon and nitrogen*. The magnetogyric properties of gases giving by absorption spectra of fluted bands render it very possible that such effects exist but have not been detected owing to their smallness. A slight increase in power may bring them to light. 168. Photo-gyration in the magnetic field. If an electron attracted to a fixed centre with a force varying as the distance moves in a magnetic field, its equations of motion are where H1, H2, and H, are the components of magnetic induction due * C. R. cxxvII. p. 18 (1898). to the external field. The right-hand side of the equations which express the components of electromagnetic force may easily be proved from the consideration that the force is at right angles both to the direction of the field and the direction of motion*. If we take the magnetic field to be of uniform strength H, the lines of force being parallel to the axis of a, the above equations may be written more simply If a plane wave be propagated parallel to a line of force, P and έ vanish, and by elimination of and between (23) and (24) we may obtain two equations which only contain P and Q. For the sake of simplicity, we shall confine ourselves to the simple periodic motion. ỡ, and ỡ may now be eliminated, and we derive thus from (25) and (26), 4π Ne2 Tew) 4π Ne2 = d2II dx2 This gives for v, the velocity of right-handed circularly polarized |