TRANSACTIONS OF THE SECTIONS. 7 



3. p + ir on the cumbent, and V(p'^+r^)+iv on the sistent plane, with v 

 a function of jo and r, giving a surface, whence iuL is found on the sistent, 

 and therefore also on the cumbent plane. 



4. p + ir on the cumbent, and ^/(p~ + r')-'riu on the sistent plane, with u 

 a function oi p and r, giving a surface, whence iwL is found on the sistent, 

 and therefore also mL on the cumbent plane. 



Hence (u +iv)Lz=zh is also found on the cumbent plane, and x,y, z can 

 be fully represented for any values of ju and r. 



By this theory, all cases of impossible roots of equations with one, two, 

 or three unknown expressions admit of geometrical representation, while 

 every Cartesian case is included. 



On the conception of the Anharmonic Quaternion, and on its application to 

 the Theory of Involution in Space. By Sir W. R. Hamilton, LL.D. 



Light, Heat, Electricity, Magnetism. 

 On the Fixing of Photographs. By Dr. Adamson. 



On the Triple Spectrum. By Sir David Brewster, K.H., F.R.S. L. S^ E. 



At an early meeting of the Association the author communicated to the Associa- 

 tion an account of the experiments by which he endeavoured to estabhsh the exist- 

 ence of a triple spectrum, that is, a spectrum which, instead of consisting of seven 

 different colours, consisted of three spectra of equal length — red, yellow, and blue — 

 having different degrees of intensity in different parts, and their ordinates of maxi- 

 mum intensely incoincident. This paper, entitled "A new Analysis of Solar Light," 

 was published in 1831 in the Transactions of the Royal Society of Edinburgh. The 

 experiments were shown to some of the distinguished members of that body, who 

 honoured them by the adjudication of the Keith Medal. To objections which 

 have been raised by Mr. Airy, Dr. Draper and M. Melloni to the accuracy of these 

 results, the author has replied successively, and, he has reason to think, successfully. 



Within the last few years the subject of the triple spectrum has been studied by 

 two eminent individuals, M. Bernard in France, and M. Hehnholtz in Prussia, 

 both of whom have called in question the accuracy of his conclusions. To the obser- 

 vations of these two writers he did not think it necessary to reply ; but being obliged 

 to refer to the subject of the changes of colour produced by absorption, and conse- 

 quently to the triple spectrum, in his History of Newton's optical discoveries, he 

 found it necessary to notice the objections which had been made to it ; and he now 

 submitted to the Section a few of the remarks which he has there made upon the 

 experiments of these two foreign observers. 



To make these remarks intelligible, he first stated that his analysis of the spectrum 

 embraces three propositions, which to a certain extent are independent of eachother : — 



1. That the colours of the spectrum may be changed by absorbing media acting 

 by reflexions and transmissions. 



2. That in pure spectra white light, which the prism cannot decompose, can be 

 insulated ; and 



3. That the Newtonian spectrum of seven colours consists of three equal primary 

 spectra — red, yellow, and blue superposed, — having their maximum intensity of illu- 

 mination at different points, and shading to nothing at their extremities. 



" Now," observes the author, " the first of these propositions may be true, even 

 though we could not insulate white light at any point of the spectrum ; and both 

 the first and second may be true, without our being able to demonstrate that the 

 three spectra have the same length, and diminish in intensity from their maxima of 



