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 &rt A, 4 < B, 1 < C, 7 &rt 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.