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.