XIII.

THE WEDGE PHOTOMETER.

BY EDWARD C. PICKERING.

Presented May 10, 1882.

MUCH attention has recently been directed to the use of a wedge of shade glass as a means of measuring the light of the stars. While it has been maintained by various writers that this device is not a new one, the credit for its introduction as a practical method of stellar photometry seems clearly to belong to Professor Pritchard, Director of the University Observatory, Oxford. Various theoretical objections have been offered to this photometer, and numerous sources of error suggested. Professor Pritchard has made the best possible reply to these criticisms by measuring a number of stars, and showing that his results agreed very closely with those obtained elsewhere by wholly different methods. His instrument consists of a wedge of shade glass of a neutral tint inserted in the field of view of the telescope, and movable so that a star may be viewed through the thicker or thinner portions at will. The exact position is indicated by means of a scale. The light of different stars is measured by bringing them in turn to the centre of the field, and moving the wedge from the thin towards the thick end until the star disappears. The exact point of disappearance is then read by the scale. The stars must always be kept in the same part of the field, or the readings will not be comparable. By a long wedge the error from this source will be reduced. A second wedge in the reversed position will render the absorption uniform throughout the field. Instead of keeping the star in the same place by means of clockwork, the edges of the wedge may be placed parallel to the path of the star, when the effect of its motion will be insensible. To obtain the best results the work should be made purely differential, that is, frequent measures should be made of stars in the vicinity assumed as standards. Otherwise large errors may be committed, due

to the varying sensitiveness of the eye, to the effect of moonlight, twilight, &c., and to various other causes.

A still further simplification of this photometer may be effected by substituting the diurnal motion of the earth for the scale as a measure of the position of the star as regards the wedge. It is only necessary to insert in the field a bar parallel to the edge of the wedge and place it at right angles to the diurnal motion, so that a star in its transit across the field will pass behind the bar and then undergo a continually increasing absorption as it passes towards the thicker portion of the wedge. It will thus grow fainter and fainter, until it finally disappears. It is now only necessary to measure the interval of time from the passage behind the bar until the star ceases to be visible, to determine the light. Moreover all stars, whether bright or faint, will pass through the same phases, appearing in turn of the 10, 11, 12, &c., magnitude, until they finally become invisible. For stars of the same declination, the variation in the times will be proportioned to the variations in the thickness of the glass. But since the logarithm of the light transmitted varies as the thickness of the glass, and the stellar magnitude varies as the logarithm of the light, it follows that the time will vary as the magnitude. For stars of different declinations, the times of traversing a given distance will be proportional to the secant of the declination. If 8, 8' are the declinations of two stars having magnitudes m and m', and t, t' are the times between their transits over the bar and their disappearances, it follows that m' -m =A (t sec 8-t' sec 8'). For stars in the same declination calling A sec 8 =A' we have m' — m — A' (t-t'). Accordingly the distance of the bar from the edge of the wedge is unimportant, and, as in Professor Pritchard's form of the instrument, it is only necessary to determine the value of a single constant, A. Various methods may be employed to determine this quantity. Professor Pritchard has recommended reducing the aperture of the telescope. This method is open to the objection that the images are enlarged by diffraction when the aperture is diminished; constant errors may thus be introduced. Changing the aperture of a large telescope requires some time, and in the interval the sensibility of the eye may alter. These difficulties are avoided by the following method, which may be employed at any time. Cover the wedge with a diaphragm in which are two rectangular apertures, and place a uniformly illuminated surface behind it. Bring the two rectangles into contact by a double image prism, and measure their relative light by a Nicol. From

=

the interval between the rectangles and the focal length of the telescope the light in magnitudes corresponding to one second, or A, may be deduced. Perhaps the best method with a small telescope is to measure a large number of stars whose light has already been determined photometrically, and deduce A from them.

The great advantage claimed for this form of wedge photometer is the simplicity of its construction, of the method of observing, and of the computations required to reduce the results. It may be easily transported and inserted in the field of any telescope like a ring micrometer. The time, if the observer is alone, may be taken by a chronograph or stop-watch. Great accuracy is not needed, since if ten seconds correspond to one magnitude, it will only be necessary to observe the time to single seconds. The best method is to employ an assistant to record and take the time from a chronometer or clock. If the stars are observed in zones, the transits over the bar serve to identify or locate them as well as to determine their light. A wedge inserted in the field of a transit instrument will permit the determination of the light of each star observed without interfering with the other portion of the observation. If the stars are all bright, time may be saved by dispensing with the thin portion of the wedge. In equatorial observations of asteroids the light may be measured photometrically with little additional expenditure of time. Perhaps the most useful application would be in the observation of zones. When the stars are somewhat scattered it would often happen that their light might be measured without any loss of time. By this instrument another field of usefulness is opened for the form of horizontal telescope advocated at a former meeting of this Academy (Proc. Amer. Acad. XVI. 364). Very perfect definition would not be required, since it would affect all the stars equally. To an amateur who would regard the complexity of an instrument as a serious objection to it, a means is now afforded of easily reducing his estimates of magnitude to an absolute system, and thus reudering them of real value.

XIV.

ON THE COLOR AND THE PATTERN OF INSECTS.

BY DR. H. A. HAGEN.

Presented April 12, 1882.

"PROBABLY there is scarcely a dash of color on the wing or body of an insect of which the choice would be quite arbitrary, or which might not affect its duration for thousands of years." These words were written by Sir Charles Lyell in a letter to Sir John Herschel in 1836.* This letter, which is a real treasure of thought, asserts clearly that the writer assumes "such contrivances must sometimes be made, and such relations predetermined between species," for the protection of their existence.

Though it has been accepted generally that certain colors and patterns of insects might be a protection against enemies, these interesting facts have been mentioned only occasionally, and a general review is still a desideratum. Professor Weismann † has given a very elaborate paper on the origin of the pattern of caterpillars. The paper, as stated in the preface, intends an examination of the pattern strictly for the purpose of finding out whether all patterns can be accepted as the consequences of selection and adaptation, and as produced in a purely mechanical manner, or whether some unknown power has to be accepted in part or entirely to explain the pattern. The writer reaches the conclusion that the latter is not the case, and that the known principles of selection and adaptation explain the different patterns. The choice of caterpillars was made purposely to

*Life, Letters, and Journals of Sir Charles Lyell, Bart., London, 1881, vol. i. p. 469; Nature, No. 633, Dec. 15, 1871, p. 147.

† Dr. A. Weismann, Studien zur Descendenz-Theorie, Leipzig, 1875, vol. i.; 1876, vol. ii. Die Entstehung der Zeichnung bei den Schmetterlings Raupen.

exclude entirely a third factor, sexual selection. Everybody will follow Professor Weismann's careful and elaborate study with interest, though it is probable that the examination of a larger number of exotic species (he has chiefly used European) will change, or at least modify, some of his statements.*

Nevertheless, if it is to be assumed with Professor Weismann that the colors and the pattern originate in a purely mechanical manner, there seems to be a large gap still to be filled. The statement that color and pattern appear in a caterpillar by selection and adaptation as a beneficial protection, without showing how they have been produced, where they come from, which part of the body, and what kind of chemical process brings them out, represents simply a belief. Belief is, as it is well known, beyond discussion, as long as it is based upon views which cannot otherwise be proved. But as the author has prominently advanced that the origin of the color and the pattern is only the consequence of mechanical arrangements, excluding entirely predetermining power, the possibility of such mechanical arrangements should have been proved satisfactorily.

If we compare side by side Sir Charles Lyell's letter with the accepted predetermination and Professor Weismann's work with the denied predetermination, there seems to be no difference except in the belief of both authors.

The conviction that color and pattern are the consequence of existing laws and actions in the body of the insect, induced the present writer to extend his study in that direction. May it not be considered too assuming, if the result shall prove inadequate to the purpose. The first step in all such questions is the most difficult, and often nothing more is left to be said about it, except that it was the attempt of the first step.†

* Of North American Sphingidæ the previous stages of fifty-four species are known, and of fifteen species all stages. With very few exceptions all were published before 1874. Of the European species all stages were described long ago of eight species: Sphinx ligustri by Schwarz; Sph. pinastri by Sepp, Ratzeburg, Hartig, Schwarz, Klopsch; Deil. euphorbiæ by Sepp, Rösel, Schwarz; Deil. porcellus by Sepp; Smer. tiliæ by Rösel, Reaumur; Smer. ocellata by Sepp; Smer. populi by Sepp, Schwarz; Deil. nerii by Rossi. With few exceptions excellent figures are given. The literature is therefore not so scanty as has been assumed, though not sufficient for the purposes of the author.

† Some parts of the present paper were published in the Amer. Natural. 1872, pp. 388-393, and Entom. Monthly Mag. 1872, ix. pp. 78-83, Mimicry in the Colors of Insects.