May 29, 1903.] 



SCIENCE. 



865 



the total change of vibration-frequency as we 

 pass from one end of the spectrum to the 

 other is 378 million million. Now, the width 

 of the band under consideration is 1/100,000 

 of this distance, and hence in crossing from 

 one side of it to the other there is a change 

 of frequency of approximately 3,780 millions 

 per second. Ordinarily the light from such 

 a narrow band of a ' pure ' spectrum would 

 he considered very homogeneous, i. e., of very 

 approximately a single wave-length; but 

 looked at from the point of view of number 

 of vibrations per second, this variation in 

 frequency of 3,780 millions per second, which 

 is to be foimd amongst the constituents of 

 the light, would at first sight appear so large 

 that we should not be justified in saying that 

 the light from the band is practically of one 

 w^ave-length. This view is, indeed, held by 

 Dr. Kirschmann, but I hope to show that it 

 is untenable. 



Let us look at it in another way. As we 

 pass from the blue to the red end of our 

 spectrum the wave-length increases by an 

 amount equal to itself — by 100 per cent. — this 

 increase being uniform if the spectrum is 

 normal. Hence in passing over a band 1/100 

 of a millimeter in breadth the wave-length 

 increases by 1/100,000 part of itself. Thus 

 in the light which comes from this narrow 

 space there is, if we consider the case in 

 absolute mathematical strictness, a superposi- 

 tion of waves of different lengths, but yet , 

 the waves are extremely uniform, since the 

 longest is only 1/100,000 part greater than 

 the shortest. Stated as an absolute length, 

 this difference between the longest and the 

 shortest waves is but one five-thousand-mil- 

 lionth part of an inch. 



The size of the number expressing the 

 measure of any quantity depends only on the 

 vxnX used, and may be quite meaningless when 

 we come to deal with actual sensations. For 

 example, the length of two rods may differ 

 by but the millionth of an inch, a quantity 

 smaller than the error of experiments made 

 to compare them, so that from our physical 

 measurements we should say that the rods 

 were of the same length; and yet if we chose 

 the diameter of a molecule as our unit of 



length, the infinitesimal difference between 

 the lengths of the rods would be expressed 

 by millions of millions. 



In the light under consideration there is 

 strictly a variation in the wave-lengths, but 

 relatively this is an extremely small quantity 

 — too small to be considered as an essential 

 factor in determining the nature of our sen- 

 sation. Would it be reasonable to suppose 

 that if there were absolutely no variation at 

 all the effect on the eye would be different? 

 Experiments do not indicate that the eye has 

 such marvelous delicacy that it can detect 

 any such infinitesimal changes. 



In a pure spectrum a meter long the widths 

 of the colored bands in the most sensitive por- 

 tion are given by Eood * as follows : 



Norm.il Prismatic 

 Spectrum. Spectrum. 



Orange-yellow 26 mm. 20 mm. 



Yellow 13 10 ' 



Yellow-green and green-yellow. . .97 104 *■ >^_ 



Of course it must be understood that these 

 quantities are not absolutely definite magni- 

 tudes. They are simply the careful estimate 

 of an accomplished scientist and artist. 



An attempt was made to test the sensitive- 

 ness of the eye in the following way: By 

 means of a narrow slit and a direct-vision 

 train of prisms in front of an electric_ arc 

 lamp, a spectrum 80 centimeters long was 

 thrown on an opaque screen, in which was an 

 opening about a centimeter wide and 3 centi- 

 meters long. By shifting the screen, light 

 from any desired portion of the spectral image 

 was allowed to come through, and it was then 

 received on a finely ground glass plate. By 

 means of black paper strips the portion of 

 the ground glass thus illuminated was further 

 restricted to two narrow bright bands ap- 

 proximately 1.5 millimeters in width. When 

 working in the yellow it was found that these 

 bands could be separated by a dark strip 1.5 

 millimeters wide, and still be indistinguish- 

 able from each other. A second observer, ex- 

 perienced in optical work, agreed in the above 

 result. Thus the eye was unable to distin- 

 guish between the colored bands whose centers 

 were 3 millimeters apart. Now, this distance 



* Eood, ' Modern Chromatics,' p. 24. 



