motus peculiaris of each star was subject to no law, but might equally probably be directed to any point of the sky. If, however, we do not regard the aggregation of the stars in the Milky Way as a merely accidental circumstance, it is logical to suppose that the true motion. of a star must stand in some relation to the plane in which the Milky Way lies. This consideration led Sir JOHN HERSCHEL to the hypothesis of a Rotation of the stellar system in the plane of the Milky Way, according to which each star was supposed, in general, to revolve in a somewhat eccentric orbit about the centre of the Milky Way, this orbit being only slightly inclined to its plane. The author has included in his equations (which are in the form first proposed by Professor SCHOENFELD) terms which express such a rotation, as well as the usual terms which express the corrections to the precession constants and the terms which express the Sun's motion in space. The same form of equations has previously been adopted by Dr. BOLTE and by Dr. L. STRUVE. In order to take the next step it would be convenient to make some hypothesis as to the relative distances of the different classes of stars used in the discussion. In Dr. STRUVE'S memoir he has supposed the stars used to be situated at certain relative distances from the Sun depending directly on their magnitudes; Dr. BOLTE has divided the stars used by him into three classes according to their magnitudes, namely: 1st, 5.5 to 7.4 mags.; 2d, 7.5-8.2 mags.; 3d, 8.3-10 mags., and has solved the equations for each class separately, thus determining, from the data, the relative average distances of each of his classes. (Dr. BOLTE'S results did not, however, show a certain law of increase of distance with increase of faintness.) Dr. STUMPE has chosen another method of estimating the distance of the stars of his list, that is, he has divided them into four classes according to the magnitude of the observed proper motions, thus:

Class I contains 551 stars whose proper motions are between 16" and 32′′ in a century.

Class II contains 340 stars whose proper motions are between 32" and 64" in a century.

Class III contains 105 stars whose proper motions are between 64′′ and 128′′ in a century.

Class IV contains 58 stars whose proper motions are over 128" in a century.

These data lead to 2108 equations containing 5 unknown quantities, which are to be solved by least squares. Dr. BOLTE and Dr.

STRUVE, in their investigations, made use of certain simplifications which materially reduced the enormous labor of the solution, but, as it is by no means sure that such simplifications did not somewhat influence their final results, Dr. STUMPE has valiantly rejected all simplifications, and has solved these equations just as they stand. This labor is not lost, for it gives his investigation a high authority, since his results are the pure outcome of observed facts, free from all hypothesis.

The solution of the equations shows no sign of any systematic rotation of the stars about the Milky Way. Dr. STUMPE points cut that this result may not be due to the absence of such a general rotation, but that it may simply be caused by the fact that most of the stars of his list are northern stars. When the stars of the southern sky have been as completely investigated as those of the northern hemisphere, this work should be repeated in the same thorough manner. Leaving, then, the question of a general rotation of the stars and solving the equations for the Right-Ascension and Declination of the point towards which the Solar System is moving (R. A.; Decl.), and for the velocity of the sun's motion as seen from each group of stars

C

Dr. STUMPE obtains

The comparison of the column () with the last column shows

not only that the stars with large proper motion are nearer to us than the rest, but the numbers agree well with the hypothesis that the distance of a star is inversely proportional to its proper motion. There is no relation between the magnitudes and the distances of the stars used in the investigation.

The foregoing abstract gives the main results of Dr. STUMPE'S work, but it fails to do justice to the thoroughness and rigorously

scientific spirit of the plan of investigation. The final figures set down in the last table would have the highest authority, if the systematic corrections of the original star-places were revised and the work repeated. E. S. H.

ADDENDUM TO LUDLAM'S ASTRONOMICAL OBSERVATIONS (1769). In 1769, the Reverend W. LUDLAM printed a volume, whose title-page is as follows:

Astronomical observations made in St. John's College, Cambridge, in the years 1767 and 1768, with an account of several astronomical instruments, by the Reverend Mr. LUDLAM. Printed by J. ARCHDEACON, printer to the University, for T. CADELL, successor to Mr. MILLER, in the Strand, London, MDCCLXIX.

The copy of this work in the library of the U. S. Military Academy at West Point, which I used in the years 1871-2, is full of manuscript corrections, and it contains also a manuscript note, in which the Reverend author sets forth his grievances. I have thought that this should not be unknown, and I copy it below, with the reminder that a considerable part of the income of the Universities of Oxford and Cambridge was and still is derived from their exclusive privilege of printing the Authorized Version of the Bible. E. S. H.

MANUSCRIPT NOTE BY THE AUTHOR.

"The university printer being very ignorant, and the press meanly "provided with types for books of science, there are many inaccuracies “in the printing of this book; some of which are corrected with the "pen.

The gainful monopoly of printing bibles and common prayer "books, is the only object that engages the attention of the University "officers and their greedy printer.

THOLLON'S MAP OF THE SOLAR SPECTRUM.

W. L."

The third volume of the Annals of the Observatory of Nice is accompanied by a magnificent folio-atlas, containing a map of the solar spectrum. This atlas is the fruit of some six or seven years' work by M. THOLLON; and, after his death, M. PERROTIN, the Director of the observatory of Nice, employed parts of three or more years in completing it for publication. It is not possible to give in this place an adequate review of this great work. An excellent short

account of it is given in Knowledge, for Sept. 1, 1890. The observatory of Nice was founded by M. BISCHOFFSHEIM of Paris, and he has already spent more than $1,000,000 for buildings and instruments. Among the latter is the great telescope of 30 inches aperture. The publication referred to is, I believe, also made at M. BISCHOFFSHEIM's private cost. A brief description of the Nice Observatory will probably be printed in these Publications during the current year. E. S. H.

SATELLITES OF MARS, 1890.

During the present opposition the maximum theoretical brightness of the satellites of Mars was 1.15, if their brightness at mean opposition be taken as 1.00.*

Under good circum

Their brightness at discovery was 1.91. stances they have been readily visible in the same field of view with Mars, when the planet was not hidden by an occulting bar. They have been several times re-discovered by visitors who were looking at the planet, and who did not know of their existence.

During April and May two observers made a conscientious search for new satellites. The weather conditions were rather unfavorable. The general conclusions reached were that no new satellite exists within the orbit of Deimos, which is anything like as bright as onefourth the brightness of that satellite. It is possible, though not very likely, that so faint a satellite as this may exist outside of Deimos' orbit, or within that of Phobos. E. S. H. AND J. M. S.

SOLAR PARALLAX FROM THE TRANSIT OF VENUS PHOTOGRAPHS OF 1882.

Professor HARKNESS, U. S. N., reports that the photographs of the last transit of Venus (more than 1400 photographs being available) lead to the following value of the solar parallax; = 8′′.842 ± o".0188. With 3963.296 miles as the equatorial radius of the earth, the resulting mean distance of the sun is 92,455,000 miles, with a probable error of 123,400 miles. —(From the Report of the Supt. U. S. Naval Observatory, June 30, 1889.

SPECTROGRAPHIC OBSERVATIONS OF SPICA AT POTSDAM.

In No. 2995 of the Astronomische Nachrichten Professor H. C. VOGEL considers at length all the photographs of the spectrum of a Virginis which have been made at Potsdam, and finds that they

* See a paper by Mr. KEELER, in the Astronomical Journal, Vol. VIII, p. 74.

accord closely with his earlier observations of the same star, showing that it is a close binary, having a period of only a little more than four days. The same apparatus was employed as in the determination of motions of stars in the line of sight, described by Professor VOGEL in Astronomische Nachrichten, No. 2896. In the method followed at Potsdam, the spectrum of the star and that of terrestrial hydrogen are photographed together, and the displacement of the star lines on the photograph in the neighborhood of the Hy line, is afterwards measured under a microscope. Stars of the second and third spectral types gave results of great accuracy, as the lines in such stars are sharp and are very numerous. In the case of a Virginis, the difficulties of observation were considerably greater, the hydrogen lines being broad and diffuse, without any definite maximum of intensity, and there were no distinct lines in the vicinity of Hy to which the measurements could be referred.

Measurement of twenty-four photographs, obtained during the spring of the present year, showed that the star lines were displaced alternately toward the upper and the lower end of the spectrum in a complete period of about four days, the maximum displacement toward the violet indicating a motion of the star toward the sun of 65.9 English miles, and that toward the red a receding motion of 47.5 miles per second. These observations are completely explained by supposing that Spica is a binary star having a period of about four days, the orbital velocity of the larger component being 56.7 miles per second, and that the system is approaching the sun at the rate of 9.2 miles per second. The more exact elements, as determined by Professor VOGEL, are as follows:

Potsdam Mean Time.

Epoch (no orbital motion in line of sight) 1890, May 4 10. 50. Period p 4.0134 days. Motion of System in line of sight

=

9.2 Eng. miles.

Motion in the line of sight, at time t, after deducting the motion

A comparison with the Greenwich results for this star in preceding years was made with the aid of this formula, but it was unsatisfactory, owing to the uncertainty of the English observations.

On the assumption of a circular orbit, equal mass of the components, and the data given by observation, the mass of the system is 2.6 times that of the sun, and the distance between the components