110 MEMOIRS OF THE NATIONAL ACADEMY OF SCIENCES. 



vision. Witli any maguifyiiig power {p) from to the brightness is invariable; and if we set 



= P, the brightness for powers greater than P is proportional to -2- Evidently the cases of ]) 



between and 1 correspond to an inverted telescope audjj = 1 to naked eye vision. 



But She mere brightness of a snrface does not alone determine its visibility ; it must not be 

 too small, or, in the case of Spectral lines, too narrow. The apparent width of a line is determined 

 by the width of the slit and the magnifying power of the telescope. If the spectrnm consists 

 only of bright lines it is a matter of perfect indifference whether the necessary width is secured in 

 one way or the other provided that their separation is sufficient. In the case of such a spectrum as 

 that of the corona — and it is that which interests us here — the conditions are dirterent. If the slit 

 be widened, the continuous spectrum, upon which the bright lines are ])rojected, is brightened so 

 that the contrast is lessened. Hence we must, if we choose to secure sufiflcient width for the lines 

 by this method, use more jiowerfnlly dispersive apparatus to assure contrast. With greater power 

 in the telescope, which implies a greater value for the aperture, it is not necessary to use a wide 

 slit, and consequently fewer prisms may be used. The relation of the two methods for securing 

 the same result may be perfectly definitely stated. If the observing telescope always has the 

 power expressed by the quotient obtained by dividing its aperture by the diameter of the pupil, 

 then n prisms with aperture a is exactly equivalent to one x>ris'm with aperture na as regards con- 

 trast between bright lines, of the same apparent width in each case, and their background. 



This, however, is not all that we demand in a spectroscope for observing the corona. There 

 are dark lines in the spectrum the width of which does not depend upon the width of the slit, con- 

 sequently their visability does not depend upon the laws which we have just considered. In order 

 to render such lines visible with any dispersive power the slit must have a very moderate angular 

 width, hence with a small aperture it might be impossible to have the slit wide enough to show 

 the bright lines and at the same time the dark ones. Suppose, for example, that the bright 

 lines are so faint that in order to be distinctly visible they must not be less than 10' in width. If 

 no telescope were used with the prisms, a form which has often been employed, this would render all 

 but the strongest lines of the solar spectrum invisible ; if on the other baud a dispersive mem- 

 ber of a tenth of the power but tenfold the aperture the same apparent spectrum would be ob- 

 tained with a slit 1' in width. This admits of a sharply defined spectrum. That a considerable 

 angular width in the bands, with the exception of 1474 K, is requisite, has been proved in many 

 observations of past eclipses, as well as in my own observations. In the latter, bands correspond- 

 ing to C, D3, and F were not seen, although Mr. Upton's observations prove that they were pres- 

 ent. Since they were carefully looked for and must have been as intrinsically brilliant as in the 

 prismatic telescope, the only explanation is the wholly sufficient one of too narrow a slit. Had it 

 been wider, however, the more important observations as regards dark lines would have been un- 

 satisfactory. We see from these last considerations that for corona observations a spectroscope 

 of large aperture is far superior to one of small aperture which would be regarded as equivalent to 

 it by the rule in the preceding paragraph. 



The principles developed above will be valuable to us in explaining the apparently contra- 

 dictory evidence on record as to the spectroscopic nature of the corona. They can only be regarded 

 as novel in so far as they direct attention to the fact that the conditions which must be satisfied 

 in an apparatus designed for this particular use differ from those governing other spetroscopic 

 observations ; nor should I venture to give them here were there not most positive proof that they 

 are not universally understood. Not oidy have some eminent authorities mistakenly laid stress 



