108 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



should be equivalent to the quotient obtained by dividing the diameter of the object-glass by the 

 diameter of the pupil of the eye. If we assume tlie diameter of the pupil at | of an inch, which 

 cannot be far from the truth unless special precautions have been taken to dilate it, we should 

 choose a power equal to eight times the numerical value of the available aperture in inches. If 

 the coronal light contains an excess of definite wave-lengths, the fact will be indicated by colored 

 images of the corona arranged according to their wavelengths upon an impure spectrum as a back- 

 ground. It is well known that such rings are ordinarily seen corresponding iu place to the lines 

 C, D:i, 1474rK, and F. With a dispersive power less than that of a 60° flint-glass imsm they over- 

 lap; with a much greater power they are distiuct rings. With a high dispersive power, also, the 

 contrast between the rings and the background is increased, at least until the absolute loss of light 

 incident to all highly dispersive apparatus becomes considerable. It is veiy important to observe, 

 however, that the C ring alone is free from admixture. with light of other refraugibilities, and that 

 only on the side farthest removed from the blue end of the spectrum. On the other hand, the green 

 ring, the liTJtK, is least favorably situated for distinctness. We must expect, therefore, to find in 

 such an instrument the C ring relatively much too strong. This peculiarity evidently makes the 

 instrument a defective one for observing the corona; but the defect is partly balanced by its show- 

 ing large surfaces instead of narrow spectral lines, thus enabling the observer to sometimes recog- 

 nize the presence of light of definite wave-lengths, which the ordinary spectroscoiie would fail to re- 

 veal. There are a number of cases on record where just this advantage has been rendered evident. 



(b) Integrating spectroscope. — This term has been applied to that form of instrameut where the 

 spectrum is that of the sum of all tbe sources from which raj^s passing through the slit fall upon 

 any x>oint of the effective aperture. Bearing iu miud that the effective aperture is determined by 

 the angular dimensions of the source of light, as well as by the linear aperture and focal length of 

 the collimator, the theory does not differ from that of the analyzing spectroscope. The proper ratio 

 of focal length to aperture has been discussed in the description of the instrument used by Ensign 

 Brown. From what I shall prove in the theory of the remaining form of spectroscope, it follows 

 that an integrating spectroscoi)e with large available aperture is far superior for this particular 

 purpose to oue with equivalent dispersive power and smaller lenses. 



(c) Analyzing spectroscope. — This differs from the instrument just described only in having an 

 additional lens, which forms an image of the source of light upon the slit-plate. This lens is ordi- 

 narily called the " condensing lens." The term is objectionable, not only because it fails to define 

 the function of the lens, but because it is misleading. For example, if we may speak of the " con- 

 densing" power of a lens, it is evidently a measure of the brightness of the image formed by it, 

 and this depends solely upon the angular aperture of the lens. Now, I shall show that the bright- 

 ness of the spectrum in the instrument under discussion is absolutely independent of the angular 

 aperture of the " condensing lens." It follows, then, that the use of the lens is not to " condense" 

 light upon the slit. It seems that a much better name for this lens is one which describes its office 

 at once, namely, " image lens." This name I shall venture to use to replace the old term in the 

 following discussion : 



Let A — effective aperture of image lens. 

 F = focal length of image lens. 

 a ~ effective apertui'e of collimating lens. 

 /= focal length of collimating lens. 

 d = diameter of pupil of eye. 



g — quantity of light incident on unit surface of image lens from one minute square of 

 source. 



