305 



viz. that of the equation IJ 3 =0 with the one or other of the equa- 

 tions I1 1 =0, n 2 =0, in virtue of the equation U=0. The transfor- 

 mation depends, 1st, on a theorem used by Hesse for the deduction of 

 his second form n a =0 from the original form fI 1 = 0, which theorem 

 is given in his paper " Transformation der Gleichung der Curven 

 14ten Grades welche eine gegebene Curve 4 ten Grades in den Be- 

 riihrungspuncten ihrer Doppeltangenten schneiden," Crelle, t. lii. 

 pp. 97-103 (1856), containing the transformation in question: I 

 prove this theorem in a different and (as it appears to me) a more 

 simple manner ; 2nd, on a theorem relating to a cubic curve proved in- 

 cidentally in my memoir " On the Conic of Five-pointic Contact at 

 any point of a Plane Curve," Phil. Trans, vol. cxlix. (1859), see p. 

 385, the cubic curve being in the present case any first emanant of 

 the given quartic curve : the demonstration occupies only a single 

 paragraph, and it is here reproduced ; and I reproduce also Hesse*s 

 demonstration of the equivalence of the two forms II 1 =0 and I1 2 =0. 



V. "Notes on the Atmospheric Lines of the Solar Spectrum, 

 and on certain Spectra of Gases." By Dr. JOHN HALL 

 GLADSTONE, F.R.S. Received May 30, 1861. 



In the paper of Sir David Brewster and myself on the lines of the 

 solar spectrum *, attention was drawn to the following among other 

 phenomena : 



1st. "When the sun descends towards the horizon and shines 

 through a rapidly increasing depth of air, certain lines which before 

 were little if at all visible, became black and well defined, and dark 

 bauds appear even in what were formerly the most luminous parts of 

 spectrum/' These we termed "atmospheric lines." We did not 

 wish to express by that term anything beyond the fact above men- 

 tioned ; yet we threw out the idea that these lines may have their 

 origin "in the air that encircles our globe." 



2nd. In the case of those artificial flames whose spectra " consist of a 

 series of luminous bands separated by dark spaces . . . these luminous 

 bands sometimes coincide with the dark lines of the solar spectrum." 



About the same time Kirchhoif f published his theory that this 

 remarkable coincidence is due to the presence in the atmosphere of 



* Philosophical Transactions, I860, p. 149. 

 f Pogg. Arm. cix. pp. 148, 275 ; ex. p. 187. 



