PAPERS READ.

OBLITERATION FROM ILLUMINATION (STELLAR PHOTOMETRY). By HENRY M. PARKHURST, New York, N. Y.

[ABSTRACT.]

In order to establish the principle that illumination of the field tends to vary the scale of the wedge, I observed Arcturus two hours before sunset with four different apertures differing by half a magnitude. It required about twenty minutes for the approaching twilight to cause the star to become visible with an aperture half a magnitude smaller. It required only four minutes from the first glimpse of the star with each cap for the star to pass entirely across the wedge unextinguished. The effective value of the wedge under that illumination was only about m.1, whereas it had been determined to be with a dark sky about 2 m.3. Daylight illumination reduced the effect of the wedge in extinguishing stars to less than one. tenth.

The formulæ showing the effect of illumination upon obliteration, applicable to a dark sky, to moonlight, and to twilight, have been deduced by an indirect process, observing the effect of shades. From these formulæ subsidiary tables have been formed, from which it appears that there is a second difference amounting to m.2 or m.3, resulting from the illumination of the dark sky with a large aperture and low power. For stars always observed at the same point of a wedge this becomes a systematic error. Although needing further verification, the substantial accuracy of these tables has been confirmed.

The ratio of illumination to obliteration has been approximately ascertained, enabling tables for the application of the second differences to be adjusted to different magnifying powers and different apertures.

From observations at different ages of the moon and at different distances from the moon, including observations of Nova Orionis within 2° from the full moon, I have formed tables of the obliteration by the moonlight. From observations in the twilight, I have also formed tables of obliteration from twilight. But there remains to be formed a table from which the combined effect of the two can be ascertained.

Whenever the stars to be observed are sufficiently bright, I prefer to observe them with my deflecting apparatus (described in Vol. XVIII of the Annals of the Harvard Observatory, in a paper just issued) which is unaffected by illumination. But logarithmic caps cut off four-fifths of the light, so that the wedge will measure stars 1m.7 fainter. If the necessary corrections are applied, the wedge can be used for stars up to the quadrature of the moon and half an hour before the end of twilight, which could not be seen at all with the logarithmic caps.

A METHOD OF REPRESENTING THE IMAGINARY ELEMENTS OF A GEOMETRIC FIGURE AND OF USING THEM IN CONSTRUCTION. By JAMES MCMAHON,

Ithaca, N. Y.

[ABSTRACT.]

1. Point-graphs. Call the real points (a ±a', b±b') the graphs of the conjugate imaginary points (a ±ia', b±ib'). Harmonic properties. 2. Graph-locus. If a line meet a conic in two conjugate imaginary points, to find the locus traced by the graphs of these points, as the line moves parallel to itself. To find the real chords joining the imaginary intersections of conics, in certain cases.

3. Line-graphs. Call the lines (±l') x + ( m ± m') y + (n ± n') = 0 the graphs of the conjugate imaginary lines (lil') x + (m ± im') y + (n± in') = 0. These two line-pairs have the same angle-bisectors, and are cut by a transversal perpendicular to an angle-bisector in an imaginary point-pair and their real graph-pair.

4. Orthographs and skew-graphs. For transversals in a given direction not perpendicular to an angle-bisector, the graph-locus is easily constructed; it is a pair of lines, which may be called the skew-graphs for the given transverse direction, to distinguish them from the orthographs (for the orthogonal direction). All the graphs for different directions form an involution, of which the imaginary line-pair are the double lines.

5. Given the respective graph-pairs of two imaginary points, not conjugate, to construct (by means of line-graphs) the imaginary line joining them; and reciprocally.

6. Given (by means of graphs) an imaginary line and an imaginary point in it, to construct the imaginary line that passes through the point making a given angle with the first line. Special applications.

ON THE VALUE OF THE SOLAR PARALLAX DEDUCIBLE FROM THE AMERICAN PHOTOGRAPHS OF THE LAST TRANSIT OF VENUS. By Prof. Wм. HARKNESS, Washington, D. C.

[ABSTRACT.]

In this paper an account was given of the instruments and processes employed by the United States Transit of Venus Commission to determine the solar parallax from photographs of the transit of Venus which occurred in December, 1882. Let be the solar parallax, and dA and ¿Ð respectively the corrections to the right ascensions and declinations of Venus given by Hill's tables of that planet. Then, upon the assumption that Hansen's tables of the sun are correct, there resulted from measurements of the distances between the centers of the sun and Venus made upon 1475 photographs, taken respectively at Washington, D. C.; Cedar Keys, Fla.; San Antonio, Tex.; Cerro Roblero, N. M.; Wellington, South

Africa; Santa Cruz, Patagonia; Santiago, Chili; Auckland, New Zealand; Princeton, N. J.; and the Lick Observatory, Cal.;

and the corresponding mean distance from the earth to the sun is 92,385,000 miles, with a probable error of only 125,000 miles.

These numbers are doubtless close approximations to the results which will be obtained from the complete discussion of all the photographs, but they cannot be regarded as final for several reasons, chief among which is the fact that the reduction of the position angles of Venus relatively to the sun's center is still unfinished. It is likely that when these angles are combined with the distances the probable error of the parallax will be somewhat reduced.

The photographs taken at the Lick Observatory seem to indicate that for altitudes four thousand feet above the sea the values of the refraction given by the tables in general use are somewhat too large.

THE DIRECTIONAL THEORY OF SCREWS. By Prof. E. W. HYDE, Station D, Cincinnati, Ohio.

DEFLECTIONS OF THE PLUMB-LINE AND VARIATIONS OF GRAVITY IN THE HAWAIIAN ISLANDS. By ERASMUS D. PRESTON, U. S. C. and G. Survey, Washington, D. C.

ON A NEW METHOD OF CONSTRUCTION FOR EQUATORIAL DOMES. By Prof. G. W. HOUGH, Director Dearborn University, Chicago, Ill.

ON A NEW CATALOGUE OF VARIABLE STARS. By SETH C. CHANDLER, Cambridge, Mass.

A NEW SHORT-PERIOD VARIABLE IN AUTLIA. By Prof. HENRY M. PAUL, U. S. Naval Observatory, Washington, D. C.

LAWS OF FREQUENCY OF ERRORS OF INTERPOLATED LOGARITHMS, ETC., DEPENDENT ON FIRST DIFFERENCES; AND A COMPARISON OF THE THEORETICAL WITH THE ACTUAL DISTRIBUTION OF THE ERRORS OF 1000 INTERPOLATED VALUES. By Prof. R. S. WOODWARD, Geological Survey, Washington, D. C.

SOME CONSIDERATIONS ON THE FUNDAMENTAL IDEAS OF QUATERNIONS. By Prof. E. W. HYDE, Station D, Cincinnati, Ohio.

A DESIDERATUM IN THE AMERICAN EPHEMERIS. By Prof. GEORGE C. COMSTOCK, Washburn Observatory, Madison, Wis.

FUSIYAMA, JAPAN, AS A SITE FOR A MOUNTAIN OBSERVATORY. By Prof. DAVID P. TODD, Director Lawrence Observatory, Amherst, Mass.

ON THE SUPPOSED CANALS ON THE SURFACE OF THE PLANET MARS. By Prof. ASAPH HALL, U. S. Naval Observatory, Washington, D. C.

NOTE ON THE MATHEMATICS OF THE SEISMOSCOPE. By CLARENCE A. WALDO, Terre Haute, Ind.

ON SOME OLD AND NEW THEOREMS IN SOLID GEOMETRY. By H. B. NEWSON, Mt. Gilead, Ohio.

ORBIT OF BROOKS' COMET, 1888 c. By Prof. LEWIS Boss, Albany, N. Y.

PRELIMINARY ELEMENTS OF THE ORBIT OF COMETS, 1888 IX. By WILLIAM HOOVER, Athens, Ohio.

ON THE MEASURE OF INCLINATION OF TWO PLANES IN SPACE OF FOUR DIMENSIONS. By Prof. IRVING STRINGHAM, University of California, Berkeley, Cal.

ON CENSUS MAPS. By Dr. FRANZ BOAS, New York, N. Y.