32 



SCIENCE 



[N. S. Vol. LIV. No. 1384 



can be seen witli an ordinary small telescope, 

 show that the sun is not of uniform shape 

 and density. While exact measurements of 

 the shape of the sun are extremely difficult to 

 make, yet every series of measures, heretofore 

 made, show distinct departure from a true 

 spherical form. The sun is not a sphere. 



Passing outward from the sun itself one 

 finds the corona. At times of eclipse this halo, 

 or brilliant crown, about the sun can be seen 

 by the unaided eye. It has been sketched 

 many times; it has been photographed times 

 without number. Its presence proves the sun 

 to be surrounded by an envelope of matter 

 of irregular shape and of vast size. This en- 

 velope is in general lens-shaped and it ex- 

 tends far out beyoim.d the orbit of the earth. 

 On clear dark nights the extreme outer por- 

 tions of it can be seen after sunset as a faint 

 glow in the western sky, — a glow that is well 

 known under the name of the zodiacal light. 



While matter is thus known to exist in the 

 vicinity of the sun and the inner planets, 

 yet its effect upon the motions of these planets 

 cannot be accurately calculated. Until its 

 distribution is fully known, its effect can not 

 be reduced to figures. It is perfectly clear 

 that the figure, 537.6" per century, does not 

 accurately represent the motion of Mercury's 

 perihelion under the Newtonian law; but, in 

 the present state of our knowledge as to the 

 solar envelope, it is impossible to correct defi- 

 nitely this figure and to state finally what the 

 true figure should be. 



The whole question of the effect of this 

 matter upon the motions of the planets has 

 been made the subject of several recent in- 

 vestigations, notably by Jeffreys and Seeliger.^ 

 As the actual distribution of this matter is 

 unknown, the problem is attacked in reverse: 

 that is, from the discordances is found a 

 general distribution of matter, which will ac- 

 count for the motions, and this calculated dis- 



2 ' ' The secular perturbations of the four inner 

 planets," bj Harold Jeffreys, Month. Notices, B. 

 A. S., Vol. LXXATEI., p. 112. 



"Das ZodiakaUicht und die emperischen glieder 

 in der bewegung der planaten, " by Seeliger. 



De sitter, Ohservatory , Vol. XXXVI., 1913. 



tribution is then compared with the known 

 facts. This procedure is analogous to the 

 method by which the planet Neptune was 

 discovered. 



The matter in the immediate vicinity of 

 the sun would tend to group itself about a 

 plane somewhere near that of the solar 

 equator, or that of the orbit of Mercury; 

 whilst matter at a considerable distance from 

 the sun would tend more towards the in- 

 variable plane of the planetary system, which 

 is nearly the same as that of the orbit of 

 Jupiter. Further the density of the matter 

 will decrease as the distance from the siin in- 

 creases. This general distribution can be ap- 

 proximated to by assuming the whole mass to 

 be made up of ellipsoids of revolution, each 

 ellipsoid to be of uniform density, but the 

 larger ones to be of much less density than 

 the inner ones. 



An ellipsoid, or ring, of matter wholly 

 within the orbit of a planet will give a direct 

 motion to the perihelion. But if the orbit 

 actually lies in the matter composing such 

 ellipsoid, then the effect is the opposite and 

 the motion of the perihelion will be retro- 

 grade. This, of course, upon the assumption 

 that the density is rmiform throughout; if 

 the density is much greater in the central por- 

 tions of the ellipsoid, then the retrograde effect 

 of the outer portion may be overcome and the 

 total effect upon the perihelion may be di- 

 rect, but the motion will be less than that due 

 to the central portion alone. By adjusting 

 the rate at which the density is assumed to 

 decrease, any motion of the perihelion, direct 

 or retrograde, within limits can be obtained. 

 To changes in the density of the envelope sur- 

 rounding the sun may thus be attributed the 

 discordant motions of the perihelia of the 

 four inner planets, and especially the retro- 

 grade discrepancy in the motion of Venus. 



The entire mass of matter, which is known 

 to exist, may for the purposes of computation 

 be considered as made up of three ellipsoids, 

 or as showing two abrupt changes in density. 

 The small central dense portion lies whoUy 

 within the orbit of Mercury, the intermediate 

 portion wholly within the orbit of the earth. 



