The difficulty of reaching strict results in this way is increased by the fact that stars are different in color. Two lights can be estimated as equal with greater precision when they are of the same color than when their colors are different. An additional source of uncertainty is brought in by what is known as the Purkinje phenomenon, after the physicist who first observed it. He found that if we took two lights of equal apparent brightness, the one red and the other green, and then increased or diminished them in the same proportion, they would no longer appear equal. In other words, the geometrical axiom that halves or quarters of equal quantities are themselves equal, does not apply to the effect of light on the eye. If we diminish the two equal lights, we find that the green will look brighter than the red. If we increase them in the same proportion, the red will look brighter than the green. In other words, the red light will, to our vision, increase or fade away more rapidly with a given amount of change than the green light will.
It is found in recent times that this law of change does not extend progressively through all spectral colors. It is true that as we pass from the red to the violet end of the spectrum the yellow fades away less rapidly with a given diminution than does the red, and the green still less rapidly than the yellow. But when we pass from the green to the blue, it is said that the latter does not fade out quite so fast as the green.
One obvious conclusion from all this is that two stars of different colors which look equal to the naked eye will not look equal in the telescope. The red or yellow star will look relatively brighter in a telescope; the green or bluish one relatively brighter to the naked eye.
In recent times stars have been photographed on a large scale. Their magnitudes can then be determined by the effect of the light on the photographic plate, the impression of the star, as seen in a microscope, being larger and more intense as the star is brighter. But the magnitude thus determined is not proportional to the apparent brightness as seen by the eye, because the photographic effect of blue light is much greater than that of red light having the same apparent brightness. In fact, the difference is so great that, with the chemicals formerly used, red light was almost without photographic effect. Even now, what we measure in taking the photograph of a star is almost entirely the light in the more refrangible portions of the spectrum. It appears, therefore, that when a blue and a yellow star, equally bright to the naked eye, are photographed, the impression made on the negative by the blue star will be greater than that made by the yellow one. A distinction is therefore recognized between photographic and visual magnitudes.
The photographic magnitudes of the stars are now being investigated and catalogued on a scale even larger than that on which we have studied the visual magnitudes. Yet we have to admit the non-correspondence of the two systems. The bluer the star, the brighter will be its photographic as compared with its visual magnitude. The most that can be done is to bring about the best attainable agreement between the two systems in the general average of all the stars.
Fortunately the differences between the colors of the stars are by no means so great as those between the colors of natural objects around us. All the stars radiate light of all colors; and although the difference is quite appreciable either by the eye or by the photograph, it is not so great as it would have been were the variations in color as wide as in the case of terrestrial objects.
Two comprehensive surveys of the heavens, intended to determine as accurately as possible the magnitudes of all the brighter stars, have recently been undertaken. One of these is the Harvard photometry, commenced by Professor Pickering at the Harvard Observatory, and now extended to the Southern Hemisphere by the aid of a branch establishment at Arequipa, Peru.
The instrument designed by Professor Pickering for his purpose is termed a meridian photometer, and is so arranged that the observer can see in the field of his telescope a reflected image of the Pole Star, and, at the same time, the image of some other star while it is passing the meridian. By a polarizing apparatus the image of the star to be measured is made to appear of equal brightness with that of the Pole Star, and the position of a Nicol prism, which brings out this equality, shows the ratio between the magnitudes of the two stars.
The other survey, with the same object, is now being made at the Potsdam Astrophysical Observatory, near Berlin. In the photometer used by the German astronomers the image of one star is compared with an artificial star formed by the flame of a candle. The work is performed in a more elaborate way than at the Harvard Observatory, and in consequence, only that part of the heavens, extending from the equator to 40° north declination, has been completed and published. A comparison of the results thus obtained with those of Professor Pickering, shows a curious difference depending on the color of the star. In the case of the reddest stars, the estimates are found to be in fairly close agreement, Pickering’s being a little the fainter. But in the case of the white or bluish stars, the estimates of the German astronomers are more than one fourth of a magnitude greater than those of Pickering. This corresponds to an increase of nearly one fifth in the brightness. Whether this difference is to be regarded as purely psychological or due to the instruments used, is an interesting question which has not yet been settled. It is difficult to conceive how different instruments should give results so different. On the other hand, the comparisons made by the Germans make it difficult to accept the view that the difference is due purely to the personality of the observers. There are two German observers, Drs. Müller and Kempf, whose results agree with each other exactly. On the other hand, Pritchard, at Oxford, made quite an extensive photometric survey, using an instrument by which the light of one star was cut down by a wedge-shaped dark glass, whereby any gradation of light could be produced. A comparison shows that the results of Pritchard agree substantially with those of Pickering. It is quite possible that the Purkinje phenomenon may be the cause of the difference, the source of which is eminently worthy of investigation.
This fact simply emphasizes the lack of mathematical precision in photometric measurements of star light. Even apart from this difference of color, the estimates of two observers will frequently differ by 0.2 and sometimes by even 0.3 of a magnitude. These differences correspond roughly to 20 or 30 per cent in the amount of light.