respect to a star situated at the pole of the ecliptic, the earths motion during the whole of its annual course will be perpendicular to the direction of the light coming to us from it, and will be therefore without influence on its period.
That part of the earths resolved motion which is in the direction of the visual ray, and which has alone to be considered in this investigation, may be obtained from the following formula:
Earths motion towards star=v.cos X.sin (II'),
where v is earths velocity, I the earths longitude, I' the stars longitude, and X the stars latitude.
At the time when the estimate of the amount of alteration of period of the line in Sirius was made, the earth was moving from the star with a velocity of about 12 miles per second.
There remains unaccounted for a motion of recession from the earth amownting to 29*4 miles per second, which we appear to be entitled to attribute to Sirius.
It may be not unnecessary to state that the solar motion in space, if accepted as a fact, will not materially affect this result, since, according to M. Otto Struves calculations, the advance of the sun in space takes place with a velocity but little greater than one-fourth of the earths motion in its orbit. If the apex of the solar motion be situated in Hercules, nearly the whole of it will be from Sirius, and will therefore diminish the velocity to be ascribed to that star.
It is interesting, in connexion with the motion of Sirius deduced from these prismatic observations, to refer to the remarkable inequalities which occur in the rather large proper motion of that star. In 1851 M. Peters* showed that the variable part of the proper motion of Sirius in right ascension might be represented by supposing that Sirius revolves in an elliptic orbit, round some centre of gravity without itself, in a period of 50-093 years. This hypothesis has acquired new interest, and seems indeed to have received confirmation from direct observation by Alvax Clarks discovery of a small companion to Sirius.
Professor Safford 'f and Dr. AuwersJ have investigated the periodical variations of the proper motion of Sirius in declination, and they have found that these variations, equally with those in right ascension, would be reconcileable with an elliptic orbital motion round a centre not in Sirius. The close coincidence of the observed positions of the new satellite with those required by theory, seem to show that it may be the hypothetical body suggested by Peters, though we must then suppose it to have a much greater mass relatively to Sirius, than that which its light would indicate.
At the present time the proper motion of Sirius in declination is less than its average
* Astron. Nachrichten, No. 748.
t Proceedings of the American Academy, rvol. vi.; also Astron. Notices, Ann. Arbor, No. 28; Monthly Notices, vol. xxii. p. 145.
t Astron. Nachrichten, No. 1506; Monthly Notices, vol. xxii. p. 148, and vol. xxv. p. 39.
amount by nearly the whole of that part of it which is variable. May not this smaller apparent motion be interpreted as showing that a part of the motion of the star is now in the direction of the visual ray 1 This circumstance is of much interest in connexion with the result arrived at in this paper.
Independently of the considerations connected with the variable part of the stars proper motion, it must not be forgotten that the whole of the motion which can be directly observed by us is only that portion of its real motion which is at right angles to the visual ray. Now it is precisely the other portion of it, which we could scarcely hope to learn from ordinary observations, which is revealed to us by prismatic investigations. By combining the results of both methods of research we may perhaps expect to obtain some knowledge of the real motions of the brighter stars and nebulae.
It seems therefore desirable to compare with the result obtained by the prism, the motion of Sirius which corresponds to its assumed constant proper motion. The values adopted by Mr. Main*, and inserted by the Astronomer Royal in the Greenwich Seven-year Catalogue, are 0''*035 in R.A., and +1",24 in N.P.D.
The parallax of Sirius from the observations of Henderson, corrected by Bessel, =0"-150. A recent investigation by Mr. C. Abbe f gives for the parallax the larger value of 0"-27. If the radius of the earths orbit be taken at its new value of 91,600,000 miles, the assumed annual constant proper motion in N.P.D. of lw,24 would indicate, with the parallax of Henderson, a velocity of Sirius of 24 miles nearly per second, with the larger parallax of Mr. Abbe, a velocity of 43-2 miles per second. It may be that in the case of Sirius we have two distinct motions, one peculiar to the star, and a second motion which it may share in common with a system of which it may form a part.
Observations and comparisons, similar to those on Sirius, have been made on a Canis Minoris, Castor, Betelgeux, Aldebaran, and some other stars. I reserve for the present the results which I have obtained, as I desire to submit these objects to a reexamination. It is seldom that the air is sufficiently favourable for the successful prosecution of this very delicate research.
V. Observations of the Sun.
Received April 30, 1868.
I have recently applied the large spectroscope described in this paper with some success to the examination of the spectrum of the umbra of a large sun-spot.
Before I describe the results of this examination, I will refer briefly to observations of the sun which I have made on many occasions, since 1864, with three distinct objects in view.
1. I have sought to discover if the spectrum of the light frorii near the suns limb differs in any sensible degree from that of the light from the central parts of the disk.
* Memoirs of the Royal Astronomical Society, vol. xix. t Monthly Notices of the Royal Astronomical Society, vol. xxviii. p. 2.
