value of the inclination of the nebular plane to the line of sight, this asymmetry, when obtaining, should serve to give the quadrant of the inclination as well.

It is difficult to resist the impression, on studying carefully the original negatives of many of the nearly round spirals which lie almost at right angles to our line of sight, that there are frequent evidences of whorls of dark matter between the bright whorls of nebular matter. No definite proof of this can be adduced, and it is possible that the effect mentioned is largely one of contrast, and subjective. The narrow dark lanes in 5194 (M. 51) are worth study in this connection, particularly that alongside the longest whorl which connects with the companion nebula 5195, and which is apparently connected with the lanes shown in the latter (74). Another very marked example is afforded by the beautiful nebula 5236. There are many other, nearly round nebulae where similar narrow, clearcut dark lanes are seen; in fact the majority of such nebulae show appearances of this sort. Among these the following may be specially noted (the number following each N.G.C. number indicates the plate in L. O. Publications, vol. VIII):

While the hypothesis of occulting matter in the outer portions of the spiral nebulae seems sufficiently established by the pictorial evidence adduced for the edgewise and for many of the greatly elongated spirals, other hypotheses should be considered as well for that class of spirals which show differences of intensity on opposite sides of the major axis. Two theories, other than that which presupposes the presence of whorls of occulting matter, may be mentioned as meriting some consideration.

Phase effect. Assuming that the spiral arms are composed of finely divided matter shining by reflected light originating in the nuclear portions, the result of a phase effect in spirals making but a small angle with the line of sight, would be a marked difference in intensity on opposite sides of the major axis, that side which was nearer the observer being the fainter. So many unknown factors would enter into any calculation of such a difference in intensity, for instance, size and reflective power of the small particles, diffraction effects, illumination by scattered light, occulting effect, etc., that it would appear futile to attempt to include any such assumptions. Considering a phase effect only, for an inclination of the nebular plane of 10° to the line of sight, we should expect a thin uniform sheet of particles shining by light from a central nucleus to show roughly the following differences in brightness:

Polarisation effects. These should be expected as a consequence of any reflection theory. Because of the exceedingly faint character of the nebulae, no effects of polarization have as yet been observed.1

Phase effect, as a possible cause for differences in brightness in various parts of the spiral nebulae, is manifestly inseparably bound up with the hypothesis that the spirals shine by reflection from a central nucleus. It is impossible to exercise any dogmatism in discussing a class of objects which offer so many unexplained pecularities as do the spiral nebulae, and with regard to which we have so little precise evidence. If the differences in brightness observed on opposite sides of the major axis of elongated spirals could with probability be attributed to a phase effect, it would be a strong argument in favor of the reflection theory, as against the well

1 Reynolds, Preliminary Observations of Spiral Nebulae in Polarised Light, Monthly Notices, 72, 553, 1912. An extensive series of photographic tests has been made by Dr. W. K. Green at the Lick Observatory during the past year; no certain evidence of polarisation could be detected.

known "island universe" theory of the spiral nebulae. It may be an advantage, then, to combine such arguments as may be advanced against the phase effect as such, and the reflection theory.

1. Phase effect can not be assumed to be universal; quite a number of the greatly elongated spirals show no marked difference in brightness on opposite sides of the major axis.

2. A phase effect can not explain the lanes so frequently found showing on one side, and faint or invisible on the other. In many cases the nebular whorls on one side of the major axis seem to be of equal intensity on both sides of this axis at equal distances from the nucleus, but the dark lanes are so much more prominent on one side that this side appears much the fainter. 3. The reflection hypothesis presupposes a central star or collection of stars of sufficient brightness to produce the observed effects of illumination in the outlying parts of the nebula. Many spirals show such bright centers; in fully as many others the central star or condensation is so faint in comparison with the brighter outlying whorls as to be absolutely inadequate as a source of illumination under the reflection hypothesis. A number of large spirals appear to have no true nucleus whatever; such an example is 2403; others like 2503, have nuclei, little if any brighter than the nebular matter in some of the whorls. The nucleus of the enormous elongated nebula 253 (L. O. Publications, VIII, plate 2), if one exists at all, is very much fainter than the nebular condensations in the outer portions of the spiral.

4. On a reflection hypothesis, we should expect in general, a diminution in the brightness of the nebular material following the inverse square law. Reynolds has found that the Great Nebula in Andromeda satisfies this requirement. In most spirals such an effect is so bound up with the varying density of the nebular matter at different portions of the spiral that it would be difficult to establish the law; only the existence of polarisation effects, thus far never certainly detected, could decide the point. A study of the round or nearly round spirals of the Crossley collection leads me to the belief that in the majority of cases, a reflection hypothesis is absolutely untenable. Many nebulae show bona fide nebular matter (not apparently stellar condensations) in whorls at considerable distances from the nucleus, nearly as bright or brighter than the matter contiguous to the nucleus.

2 Monthly Notices, 74, 132, 1913.

3 It is scarcely necessary for me to emphasize at this point, that the discussion and argument is based solely upon the spiral nebulae. Diffuse nebulosity associated with bright stars, e.g., the Merope nebula in the Pleiades, the variable nebulae 2261 and 6729, seem well explained as a reflection effect.

March, 1918.