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form a fair Annual Catalogue. A few words of explanation may be necessary.

me.

About the middle of the month of July, 1880, when one-third of the total number of observations for the year had been made, Dr. GOULD was called away for the remainder of the year upon a special mission, and the temporary Directorship was assigned to As this was to be the last year of special observing for the General Catalogue, the desire to signalize the event by an extraordinary effort that should produce the maximum result compatible with exactness, grew into a purpose with me, and a method was tentatively elaborated and perfected which gave the result mentioned above, without being in the least degree irksome to any of the participants, since they all accepted the idea with

eagerness.

It seems rather extraordinary now, after this accumulated weight of years, but it was pure enthusiasm with all of us then, free from any taint of vainglory or disregard of the rigorous requirements of orthodox observing. The idea simply was to demonstrate what four carefully trained specialists in this kind of work, acting in perfect accord, could accomplish with our Meridian Circle in a given time.

The programme required the presence of three men in the circle room: The observer, who reclined in a comfortable position upon the chair throughout the observations; the microscope reader, who also made the pointings of the telescope; and the recorder, temporary chief of the party, who was seated at a small desk before the dial, and whose duty it was to give out the settings from the programme, record the readings of the microscopes, take their means, and give such information to the observer as was needed to identify the star.

In this arrangement, the greatest physical strain fell upon the one at the miscroscopes, and consequently the recorder exchanged places with him at intervals of an hour and a half. When the night was a long one (eight hours), the observer for the second half came at midnight, and thereafter the first observer would alternate with the recorder and miscroscope reader. Each observer began and ended with a time star, and observed others at

* As a means of comparison, the catalogue of the Royal Observatory of the Cape of Good Hope, which contains 40,000 observations of 12,441 stars may be taken. This was observed by Mr. STONE with the aid of four assistants, in eight years (1870-78), and was the most notable production up to that time.

intervals of an hour. Barometer and thermometer readings were taken hourly throughout the night. Six circumpolars, at least, three at upper culmination and three at lower, were always observed upon a long night, and three nadir, level and collimation determinations were made. Readings were also made upon the south collimator at the beginning and end of the work, to serve as a check upon the azimuth in case the last pair of circumpolars should be lost by clouds.

The routine from beginning to end of the night-twilight to twilight-was practically uninterrupted; the chronograph was never suffered to run down, and I could easily substitute a new sheet while the cylinder was making one-third of a revolution. Usually, however, two sheets, corresponding to four hours' work, were fastened upon the barrel at a time, and it was then the work of a few seconds only to strip off the upper one. During the day, the transits—more than 4000-upon the chronograph sheets were read off, the stars were identified and the observations were recorded, and a new programme was arranged for the coming night. The basis of the programme was our Zone Catalogue, of course, but all the anonymous stars of which the observer gave any note during the observations were also incorporated.

The above was the rigorous procedure during the month of December, not omitting readings for runs and any other desirable operation that could be performed in daylight. During all this time there was neither strain, nor hurry, nor fret over a failure, but every operation was in the charge of an assistant who knew how to do it well in the least possible time. The longest nights were those of December 23, 24, 25 and 26-32 hours in allaggregating 1549 complete determinations. The gentlemen who assisted me were Messrs. BACHMANN, DAVIS and STEVENS, but in the circle room there was no distinction of person and we alternated according to rule. I had employed the same method during the four preceding months, also, but in less degree, and by way of practice."

ARGENTINE NATIONAL ORSERVATORY,

CORDOBA, June 24, 1891.

GIFT TO THE LICK OBSERVATORY FROM PROF. MICHELSON.

In Vol. III of the Publications (page 274) Prof. MICHELSON describes an apparatus devised by himself for making measures of very small angles by interference methods and gives observations

of the diameters of Jupiter's satellites made by himself during the summer of 1891 with such an apparatus applied to our 12-inch equatorial.

Since that time Prof. MICHELSON has had a similar device constructed by WARNER & SWASEY to fit the 36-inch telescope, with which it is hoped to measure the diameters of some of the smaller satellites, and of some of the asteroids. The apparatus is now completed and has been presented to the observatory through the kindness of Prof. MICHELSON.

December 25, 1891.

E. S. H.

HANDBOOK OF PRACTICAL OPTICS BY STEINHEIL & VOIT. [Handbuch der Angewandten Optik von Dr. A. STEINHEIL und Dr. E. VOIT, Band I, pp. 314 (Leipzig, 1891.)].

Messrs. STEINHEIL & VOIT need hardly have remarked in the preface to their recently published Handbuch that the work was the outcome of thirty years' experience in grinding lenses. For whether the reader approve their methods or not, he must see that these bear the stamp of practicability. We have before us a product of this well-known Munich atelier, which gives ample evidence that if lens grinding be an art, it is also more than an art.

The interested readers will be rather the users than the makers of telescopes; for, though the work is professedly written for the latter class, it contains general methods, illustrated by many special cases, for computing, with great accuracy, the efficiency of a lens either as regards its correction for color or spherical aberration, its definition, distortion, fulfillment of Gaussian condition, flatness of field, etc. What strikes one most in this treatment is perhaps the rigidity of the methods employed. There is a refreshing absence of approximations; focal lengths are never measured save from principal points; thicknesses of lenses are never disregarded; the air-space of separation in double objectives receives its full share of attention.

A rigid adherence to a clear and simple notation adds immensely to the lucidity of the discussion. To feel the importance of this, one has only to recall that in a corrected glass there are three media each with its own refractive index and thickness, besides four refracting surfaces each with its own radius, its own angles of incidence and refraction. The notation adopted is that of SEIDEL in which the successive surfaces and quantities asso

ciated with them, have for subscripts the successive even numbers; while the media in order are marked by the odd numbers. Constants are connoted by small Latin letters; points, by German capitals; lengths, by Latin capitals; angles, by small Greek letters, each carrying the subscript of its own refracting surface.

The first three chapters, devoted to reflexion, refraction and the Gaussian cardinal points, have nothing to distinguish them from the ordinary text-book treatment. Indeed, we are surprised to find that the only method recommended, or even mentioned, for the determination of refractive indices is one which must be considered decidedly inferior. If the search be for the sixth decimal of a refractive index, one can hardly hope to find it by allowing the parallel beam which leaves his collimator to divide on the refracting edge of the prism, and by then measuring the divergence between the two beams which are simultaneously reflected from the two faces of the prism: for one has no guarantee, ordinarily, that the beam furnished by one-half the collimator objective will have an identical direction with that furnished by the other half. We venture to suggest the use of the Gaussian eye-piece in the view telescope, thus measuring the divergence of the two normals to the prism-faces, as being the most accurate method in use. Here but one objective is employed and that with full aperture, while for delicacy of setting one can scarcely exceed the coincidence of a fine pair of cross-hairs with its "ghost."

The remaining chapters are peculiarly the authors' own. In them, single and double objectives are discussed in great detail. The general method of the writers is to compute a series of lenses, each of the same linear aperture and focal length, but each member of the series differing from its neighbor in some small degree; say in the distribution of refraction between the surfaces of the flint, perhaps in the thickness of the air-space, or possibly the flint instead of the crown may be turned so as to face the incident beam, etc. Each of these changes of condition produces a change in the character of the image, which latter the author is thus enabled to discuss in a purely inductive manner.

If, for instance, a reading telescope be desired, where the all important condition is that spherical aberration be eliminated for divergent as well as for parallel light, the designer has only to run through the series and pick out that form (all forms not workable are excluded), for which the spherical error is least, provided, of course, that the glass is reasonably corrected in other respects.

From the tables having dispersions and refractive indices for arguments, a color curve for any ordinary lens might be easily predicted. In this connection, to be sure, the want of homogenity in commercial glasses might have been touched upon. Irregularities of this kind justify Sir HOWARD GRUBB in his remark that "object-glasses cannot be made on paper."

On page 184, we have a sample of what may be hoped for in the second volume, viz., some general considerations regarding the choice of lens for any particular work; in other words, a weighting of the different corrections for various lines of work.

The pages of the first volume, interesting as they are, might have been considerably enlivened by bringing the discussions of the above type into closer juxtaposition with the mathematical

treatment.

While the work, as it stands, is far from arid, one might easily finish its reading with the impression that all the errors mentioned were of equal importance. The appearance of the next part is expected with pleasure. HENRY CREW.

ON VARIATIONS OF SHORT PERIOD IN THE LATITUDE* [BY SIR WILLIAM THOMSON, PRESIDENT R. S.].

NOTE: At the anniversary meeting of the Royal Society of London, November 30, 1891, Sir WILLIAM THOMSON presided and delivered his annual address. An abstract of the address is given in Nature for December 3. From this abstract the following paragraphs are taken.

"A fundamental investigation in astronomy, of great importance in respect to the primary observational work of astronomical observatories, and of exceeding interest in connection with tidal, meteorological and geological observations and speculations, has been definitively entered upon during the past year, and has already given substantial results of a most promising character. The International Geodetic Union, at its last meeting in the autumn of 1890, on the motion of Professor FOERSTER, of Berlin, resolved to send an astronomical expedition to Honolulu, which is within 9° to the opposite meridian to Berlin (171° west from Berlin), for the purpose of making a twelve months' series of observations on latitude corresponding to twelve months' analogous observations to be made in the Royal Observatory, Berlin. Accordingly Dr. MARCUSE went from Berlin, and, along with Mr.

* See Publications A. S. P., vols. II, p. 135, III, p. 254.

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