MR SWAN ON THE CONSTITUTION OF FLAME. 29 
These observations completely verify the results obtained with the flames of 
coal-gas and of alcohol. It will be seen that the greatest observed difference in 
breadth between the red and blue regions of the spectrum was only -003 inch, a 
discrepancy fairly within the limits of errors of observation. The observations, 
therefore, lead to the conclusion, that the structure which Professor DRAPER sup- 
poses to occur in flame has really no existence. 
The question now arises, how are we to explain the inequality in breadth of 
the spectrum, as observed by him? There seems certainly considerable difficulty 
in accounting for the “ rapid inclination of the sides at the red end of the spec- 
trum,” which he describes. From the effect of irradiation, every spectrum will 
appear slightly broader towards the middle, where the light is more brilliant, than 
towards the ends where it is comparatively feeble; a fact illustrated by my own 
observations, which exhibit a greater observed breadth at the line } of the spec- 
trum than at the lines Band G. Now, as the brightest point,—about the line 
D,— occurs in the spectrum of a flint-glass prism much nearer the red than the 
violet extremity, the variation in brightness will be much more rapid from the 
extreme visible red rays to the line D, than from the line D to the extreme violet 
rays. Hence we may expect any apparent inequality of breadth, due to irradia- 
tion, to be most conspicuous at the red end of the spectrum, where the brightness 
of the light varies most rapidly. Ihave not, however, observed any contraction in 
breadth at the red end of the spectrum, which I should describe as “rapid ;” and 
any notable contraction certainly did not extend beyond the line B. 
The apparent want of parallelism which Professor Draper conceives he has 
discovered by instrumental means in the more refracted portions of the spectrum 
admits however of an easy explanation, if I have rightly understood his method 
of observation. It will be recollected that this seems, from his description, to 
have consisted in measuring the difference of azimuths of the two sides of the 
spectrum. | Now, such a process could not fail to give erroneous results; for it 
may be easily shown, that if 
d=the angular horizontal breadth of the spectrum at any point, 
z=the zenith distance, and 
6=the observed difference of azimuths of the sides of the spectrum, 
Sin 4 6=sin 3 d cosec z; 
or if d and @ be small, 
d=d cosec 2. 
Now, 2 varies from point to point of the spectrum; whence the observed 
breadth 6 would also vary, even although the true breadth d remained constant. 
Moreover, the flame would probably be placed about the same level with the 
observer's eye, so that its zenith distance, when viewed directly, would be nearly 
90°. According, therefore, as the light was refracted upwards or downwards, z 
VOL. XXII. PART I. H 
