CHAPTER XXVI.

DETERMINATION OF THE LIGHT AND HEAT OF THE STARS.

One branch of observatory work is that of determining the relative _magnitude_ of stars, the word magnitude being of course used in a conventional sense for brightness. There are, moreover, stars which vary in brightness or _magnitude_ from time to time; these are called variable stars, and the investigation of the amount and period of variation opens up another use for the equatorial, and an instrument is required for finding the value of the amount of light given by a star at any instant; in fact, a photometer is necessary. The methods of determining the brilliancy of stars are so similar in principle to those employed for ordinary light-sources that the ordinary methods of photometry may be referred to in the first instance. We may determine the relative brilliancy of two or more lights, or we may employ a standard light and refer all other lights to that.

Rumford’s photometer, Fig. 165, is based upon the fact that if the intensity of the shadows of an opaque body be equal, the lights throwing the shadows are equal. Hence the lights are moved towards or from a screen until the shadows are equal; then if the distances from the screen are unequal the lights are unequal, and the intensities vary in the inverse ratio of the squares of the distances.

This method is practically carried out in the telescope by reducing the aperture till the stars become invisible, and noting the apertures at which each vanishes in turn.

The most simple method of doing this is that used by Dawes, which is simply an adjustable diaphragm limiting the available area of the object-glass; we can thus view a star, and gradually reduce the aperture until the star is _just visible_, or until it _just disappears_, the latter limit being perhaps the most accurate and most usually used; the aperture is read off on the scale attached.

The photometer of Mr. Knobel is, however, a very handy one; it consists of a plate of metal having a large V-shaped piece with an angle of 60° cut out of it; another plate slides over the first in such a manner that its edge forms a base for the V-shaped opening, thus forming an equilateral triangular hole, which is adjustable at pleasure by moving the second plate. The edge of the moveable plate is divided so that the size of the base of opening is known at once, and its area easily calculated.

The annexed woodcut will give an idea of the second method which is possible.

Let the gas flame be supposed to represent a constant light at constant distance; then the intensity of the light to be experimented upon (represented by the candle) is determined by moving it towards or from the mirror till the illumination of both the halves of the porcelain screen is equal. The instrument by which this kind of investigation is carried out by astronomers has been introduced by Zöllner, and is called the Astrophotometer.

In this the star is compared with a small image of a portion of the flame of a lamp attached to the telescope. It being found that, though the total light emitted by the flame varies with its size, the _intensity_ of the brightest part does not, appreciably. Two artificial stars are formed by means of a pin-hole, a double concave lens, and a double convex lens. These appear in the field by reflexion from the front and back faces of a plate of glass alongside the image of the real star, the light of which passes through the plate. The intensity of the artificial star is varied, first by changing the pin-hole, and finally by two Nicol’s prisms, the colour being first matched with that of the star by means of a third Nicol, with a quartz plate between it and the first of the other two Nicols. The instrument is provided with object-glasses of various sizes (and diaphragms) up to 2¾ inches, and, if fainter stars are to be examined, it can be screwed on to the eyepiece of an equatorial instrument. A second arrangement, like the first, but without the quartz plate arrangement, forms an artificial star from moonlight, for comparison of the light of that body with the artificial star.

So far there is no difficulty, but this measure must be interpreted into magnitude, and we must know what magnitude a star is which just disappears with a given aperture of, say, one inch, and secondly, the ratio of light between the magnitudes, or how much less light is received from a star of the next magnitude in proportion to the given one. If now we were able to start a new scale of magnitude, it would be easy to say that a star just visible with an inch aperture on a fine night shall be called a ninth magnitude star, and fix a certain number of ninth magnitude stars for reference, so that the errors induced by hazy nights and variable eyes might be eliminated. An observer on a bad night could limit his aperture on a known star, when he might find that double the area given by an aperture of one inch was required as a limit for one of the stars of reference, and in that case he would know that half the usual amount of light from every star was stopped by atmospheric causes, and he would make the requisite corrections throughout his observations. We might also say that a star of a whole magnitude, greater or less than another, shall give us half or double the amount of light—in fact, that _this_ shall be the ratio between magnitudes. We are not, however, able to make these rules, for an arbitrary scale has been adopted for years, and we can only reduce this scale to a law, in such a manner as not to interfere greatly with the generally received magnitudes.

Amongst the brighter stars there is a close agreement in the estimate of magnitude by different observers, but amongst the higher magnitudes a difference appears. Sir J. Herschel and Admiral Smyth, for instance, go into much higher numbers of magnitudes than Struve; the limit of Admiral Smyth’s vision with his 6-inch telescope was a 16th magnitude, while the limit of Struve’s vision with a 9½-inch telescope he calls a 12th magnitude; the estimates of the latter observer are, however, gaining greater adoption. In order to reduce the relative magnitude to a law, Mr. Pogson[21] took stars differing largely in magnitude, and compared the amount of light from each, and so reduced the ratio between the magnitudes given by Knott and all the best observers.

From this he found that a mean of 2·4 represented the ratio, and for reasons given he adopted the quantity 2·512 as a convenient ratio; as he states, “the reciprocal of ½ log. R (in his paper R = the ratio 2·512), a constant continually occurring in photometric formulæ, is in this case exactly 5.”

So far the ratio is established. The next thing is the basis from which to commence reckoning; this Mr. Pogson fixed by reference to Argelander’s catalogued stars, estimated by him at about the 9th magnitude, and with these, comparison is made with the star whose light is measured, and the above constant of ratio applied, which at once gives the magnitude of the measured star. To do this, in Mr. Pogson’s words: “If then any observer will determine for himself the smallest of Argelander’s magnitudes, just visible by fits, on a fine moonless night, with an aperture of one inch, and call this quantity L, or the limit of vision for one inch, the limit _l_, for any other aperture, will be given by the simple formula, _l_ = L + 5 × log. aperture.” The value of L founded by Mr. Pogson is 9·2; that is, a star of 9·2 magnitude, according to Argelander, is limited by 1-inch aperture, with Mr. Pogson’s eye. On different nights and with different eyes, this number, or the magnitude limited, must vary, and it varies from exactly the same causes that produce variation in the light of the stars to be measured, so that we are independent of transparency of the air, at least within considerable limits. Having found the value of L for any night, we turn the telescope on a star to be measured, then alter the aperture if we employ the first method, until the limit is found, and insert the value in the equation, the value of _l_, or the star’s magnitude, then at once appears. By this means a number of well-known stars of all magnitudes may be settled for future reference and comparison with variable stars.

The comparison stars then being fixed upon, and their magnitude accurately known, there is not much difficulty in comparing any variable star with one or more of those of approximately the same magnitude. By this means a number of independent estimates of the magnitude of the variable is obtained free from errors from the disturbing effects of mist or moonlight, which affects both the stars of comparison and variable alike. If we call the stars of comparison A B C D, we enter the comparisons somewhat as follows; (variable) 2 > A, 4 < B, 1 < C, 7 > D, the number showing how many tenths of a magnitude the variable is more or less bright than each comparison star, and the magnitude of the latter being known, we get several values of the magnitude of the variable, a mean of which is taken for the night. In order to show clearly to the eye the variations of a star, and to compute the periods of maximum and minimum, a graphical method is adopted: a sheet of cross-ruled paper is prepared, on which the dates of observation are represented by the abscissæ, and the corresponding observed magnitudes by the ordinates. Dots are then made representing the several observations, and a free-hand curve drawn amongst the dots, which at once gives the probable magnitude at any epoch in the period of observation, the change of the curve from a bend upwards to downwards, or _vice versâ_, indicating a maximum or minimum of magnitude.

So much then for the method of determining the intensity of the visible radiation. The next point to consider is the intensity of the thermal radiations—we pass from photometry to thermometry. The thermopile will in the future be an astronomical instrument of great importance. We need not go into its uses in other branches of physics, we shall here limit ourselves to the astronomical results which have been already obtained. Lord Rosse used a pile of this kind, made of alternate bars of bismuth and antimony. He attacked the moon, and by observing it from new to full, and from full to new, he got a distinct variation of the amount of heat, according as the moon was nearest to the epoch of full moon, or further from that epoch. As the moon was getting full, he found the needle moved, showing heat, and, after the full, it went down again and found its zero again at new. By differential observations Lord Rosse showed that this little instrument, at the focus of his tremendous reflector, was able to give some estimate of the heat of the moon, which may be 500 degrees Fahr. at the surface.

It may be said that the moon is very near us, and we ought to get a considerable amount of heat from it; but the amount is scarcely perceptible without delicate instruments. Still the instrument is so delicate, that the heat of the stars has been estimated. A pile of very similar construction to the one just mentioned has been attached by Mr. Stone to the large equatorial at Greenwich. The instrument consists of two small piles about one-tenth of an inch across the face; the wires from each are wound in contrary directions round a galvanometer, so that when equal currents of electricity are passing they counteract each other, and the needle remains stationary. It only moves when the two currents are unequal; we have then a differential galvanometer, showing the difference of temperature of the faces of the two piles; the image of a star is allowed to fall half-way between the two piles—then on one pile and then on another; then matters are reversed, and a mean of the galvanometer readings taken, beginning with zero when the image of a star was exactly between the two piles. The result was this, that the heat received from Arcturus, when at an altitude of 25°, was found to be just equal to that received from a cube of boiling water, three inches across each side, at the distance of 400 yards.

Arcturus is not the only star which has been observed in this way; in another star, Vega, which is brighter than Arcturus, it has been demonstrated that the amount of heat which it gives out, when at an altitude of 60°, is equal to that from the same cube at 600 yards, so that Mr. Stone shows beyond all question, that Arcturus gives us more heat than Vega.

This opens a new field, for if we get heat effects different from the effects on the eye, the stars ought to be catalogued with reference to their thermal relations as well as their visual brightness. Another valuable application of this method is due to Professor Henry, of Washington. Professor Henry imagined that, by means of a thermo-electric pile placed at the eyepiece of the telescope, so that a sun-spot, or a part of the ordinary surface, could be brought on the face of the pile, he could tell whether there was a greater, or less radiation of heat from a spot, than from any other part; and he was able with the thermopile to show that there was a smaller radiation of heat from the spots than from the other parts of the sun’s surface.

Footnote 21:

Monthly Notices, R.A.S., vol. xvii., p. 17.