The corona of Dec. 22, 1889, brings out an important circumstance. The originating belt seems to be somewhat nearer the poles than in the other coronas. If this shows that the belt moves up and down on the sun through a few degrees, we should remember that the extremities of the streamers, in consequence of the peculiar formation of the curves, will rise and fall to a greater extent, and the resultant parallels of the sun-spots will be modified in a similar manner. This accounts so well for the observed periodic changes in latitude for the spots, that it will be proper to investigate the question as far as possible.

The location of the coronal poles on one quadrant of the sun's surface will be the means of intensifying the forces that emanate from it on one side, and hence some color is given to those studies of terrestrial phenomena that point to the existence of a 27-day period, in response to the sun's rotation.

This analysis of the problem excludes all theories that ascribe the origin of the corona to extra-solar influences. We are not, however, in a position to say that the sun is magnetic because the coronal lines are similar to those surrounding a spherical magnet; nor that it is electrical, for the same reason. These phenomena are simply manifestations of the operations of the inverse of NEWTON'S Law, namely: repulsion in place of attraction. When matter attracts there is a center of attraction and of figure; when it repels, there are formed two poles of repulsion, and the body is polarized along an axis. If a name must be given to this theory of the corona, it will be more satisfactory to regard it as the polarization theory of the solar corona.

(SIXTH) AWARD OF THE DONOHOE COMET MEDAL.

The Comet Medal of the Astronomical Society of the Pacific has been awarded to E. E. BARNARD, Astronomer of the Lick Observatory, for his discovery of a Comet at 16 hours G. M. T., March 29, 1891. This is the fifteenth comet discovered by Mr. BARNARD.

The Committee on the Comet Medal,

EDWARD S. HOLDEN,

J. M. SCHAEBERLE,

CHARLES BURCKHALTER.

VISIBILITY OF INTERFERENCE-FRINGES IN THE FOCUS OF A TELESCOPE.*

BY ALBERT A. MICHELSON.

When the angle subtended by an object viewed through a telescope is less than that subtended by a light-wave at a distance equal to the diameter of the objective, the form of the object can no longer be inferred from that of the image. Thus, if the object be a disk, a triangle, a point, or a double star, the appearance in the telescope is nearly the same.

a

a

If, however. the objective is limited by a rectangular slit, or, better, by two such, equal and parallel, then, as has been shown in a former paper,† the visibility of the interference-fringes is, in general, a periodic function of the ratio of a, the angular magnitude of the source in the direction perpendicular to the length of the slits, and a, the "limit of resolution. The period of this function, and thence, may be found with great accuracy; so that by annulling the greater portion of the objective the accuracy of measurement of the angular magnitude of a small or distant source may be increased from ten to fifty times. As ordinarily understood, this increase of "accuracy" would be at the cost of "definition" (which, in this sense, is practically zero); but if by "definition" we mean, not the closeness of the resemblance of the image to the object, but the accurracy with which the form may be inferred, then definition and accuracy are increased in about the same proportion.

In almost every case likely to arise in practice, the form of the source is a circular disk; and if the illumination over its surface were uniform, the only problem to be solved would be the measurement of its diameter. But in many cases the distribution is anything but uniform. If the curve representing the distribution along the radius be i=(r), then the element of intensity of a strip y,dx will be

* Reprinted, by request, from the Philosophical Magazine.

↑ "On the Application of Interference Methods to Astronomical Measurements" (Phil. Mag., July, 1890).

and it has been shown that the visibility-curve in this case is

The intensity of the diffraction-figure of a luminous point in a telescope with a symmetrical aperture is*

I2= [SSCOS Kμ, X, COS кv ̧y ̧dx ̧dy,]2,

cos κμ.Χ.

(1)

in which k 2λ, μ, and ʊ, are the angular distances from the center of the image, and x, and y, are the co-ordinates of the element of surface of the aperture.

If μ and v are counted from the axis of the telescope and x, y, rare the co-ordinates of the luminous point, the expression becomes

If now the source is a luminous surface whose elements vibrate independently,

Ï=SSI2 dx dy.

(3)

For the case of two equal apertures whose centers are at xa,, and x,a,,,

Putting ka, 0, кa,r=k,,, and expanding,

(4)

21=SSI dx dy+cos

I cos k1x dx dy

. (5)

+sine SSI2 sin k,,x dx dy ·

Let y=4(x) be the equation of the curve bounding the lum

inous surface; or, better, let

a strip of width d.x.

*

Denoting
S

+(x)

)

(x)dr be the "total intensity" of

Idy by F(r), and omitting the factor 2,

"Wave Theory of Light," Rayleigh.

+ More generally, for m equal equidistant apertures whose total area is constant,

equation (5) becomes

or

I=fF(x)dx+cos 6(F(x) cos kx dx+sin@(F(x) sin kx dx,

I=P+C cos @+S sin 0.

(6)

If the width of the apertures is small, compared with their distance, the variations of F(x) with μ (or 0) may be neglected, and in this case the maxima or minima occur when

If now the visibility of the interference-fringes be defined as the ratio of the difference between a maximum and an adjacent minimum to their sum

In this expression, if v=o and b-length of aperture,

F(x) is nearly proportional to p(x); that is, so long as the angle subtended by the source is less than the limit of resolution of a telescope with aperture 6, the brightness is proportional to the size of the object. For larger angles the proportionality may still be made to hold by a slight alteration in the focal adjustment; and to this degree of approximation we have

[ƒ Þ(x) cos kx dx]2 + [ƒ • (x) sin kx dx]2

[f(x) dx]*

(8)

If the source is symmetrical the second term vanishes, and the expression reduces to the original form.

It is possible that, in addition to the uses already mentioned, the "visibility-curve" may have an important application in the

case of small spherical nebulæ. For from the form of this curve the distribution of luminous intensity in the globular mass may be inferred, which would furnish a valuable clue to the distribution of temperature and density in gaseous nebulæ.

When the source is so small as to be indistinguishable from a star, it would seem that this method is the only one capable of giving reliable information; but even in the case of bodies of larger apparent size it is equally applicable, may be made to give results at least as accurate as could be obtained by photometric measurements, and is far more readily applied.

REPORT MADE TO THE DIRECTOR OF THE ASTRONOMICAL OBSERVATORY OF TACUBAYA, IN REGARD TO OBSERVATIONS OF THE ZODIACAL LIGHT.*

The total eclipse of the Sun that took place on the 22d of December, 1889, presented exceptionally good conditions to study the Zodiacal light and crepuscular phenomena, on account of the fact that the zone of totality and its extension crossed our planet in the intertropical regions, where such phenomena take place with greater intensity and under better conditions for their observation; besides, the eclipse occurred at the time when the Zodiacal light shows its greatest extension and brightness. The eclipse began at sunrise for the occidental coast of America, and at sunset for the western coast of Africa. Therefore, the shadow of the Moon touched the Earth at the time when the Zodiacal light is seen distinctly, so that a rare opportunity was offered to the observers, to ascertain with certainty, whether or not the Zodiacal light is produced (at least in part) between the Earth and the Moon, or at a greater distance than that between our planet and its satellite. In order to observe the above-mentioned phenomena Sres. D. CAMILO A. GONZALEZ and D. FELIPE Valle, of the Astronomical Observatory of Tacubaya, went to Progreso, Yucatan, Mexico.

The observations of the Zodiacal light extended from the 14th to the 25th of December, i. e., seven days before and three days after the day of the eclipse, which took place on the 22d.

*Translated from the Boletin del Observatorio Astronomico Nacional de Tacubaya, by E. J. MOLERA.