116 British Association. 



penetrable to light as charcoal. Sir John Herschel had also noticed 

 many cases of absorption without any trace of reflection ; and only 

 in the cases of some vegetable colours did he ever experience the 

 contrary. — Professor Lloyd asked whether the changes might not re- 

 sult from partial changes of density caused in the substances by 

 changes of temperature ? — Sir David Brewster stated that it was im- 

 possible there could be any change of density in the case of the ni- 

 trous gas, as the changes in its temperature took place while its vo- 

 lume was secured from enlargement by its being sealed up in glass 

 tubes. At one time he was inclined to think that some chemical 

 change might have been effected upon the glass, but the phaenomena 

 did not long warrant this conclusion. The phaenomena of absorption 

 could be all had from plates of partially decomposed glass, such as 

 that which had been long buried in the earth, but this w^as a case 

 of real opalescence. — Sir W. Hamilton conceived that the views of 

 Wrede required the confirmation of more exact numerical exami- 

 nation before they could be adopted; and he trusted that Sir David 

 Brewster would give the inquiry the advantage of his great skill and 

 experience. 



Sir W, Hamilton then gave an account of his Exposition of the 

 argument of Abel respecting equations of the fifth degree. Sir Wil- 

 liam stated that the celebrated young Swedish philosopher, Abel, 

 whose labours (unfortunately for the cause of science) had lately 

 terminated with his life, had at one time supposed that he had found 

 a method of solving generally equations of the fifth degree, but soon 

 finding that this solution was illusory, it occurred to him that perhaps 

 under the conditions of ordinary algebra such a solution was an im- 

 possibility ; as soon as he had started this thought he pursued it 

 through a most intricate argument, and at length achieved what any 

 one upon first hearing it would be apt to consider most chimerical — 

 an H priori argument to prove that the solution of an equation of the 

 fifth degree was, under the limitations of ordinary algebra, an im- 

 possibility. 



The argument of Abel consisted of two principal parts ; one inde- 

 pendent of the degree of the equation, and the other dependent on 

 that degree. The general principle was first laid down, by him, that 

 whatever may be the degree noi any general algebraic equation, if it 

 be possible to express a root of that equation, in terms of the coeffi- 

 cients, by any finite combination of rational functions, and of radicals 

 with prime exponents, then every radical in such an expression, when 

 reduced to its most simple form, must be equal to a rational (though 

 not a symmetric) function of the n roots of the original equation 5 

 and must, when considered as such a function, have exactly as many 

 values, arising from the permutation of those n roots among them- 

 selves, as it has values when considered as a radical, arising from the 

 introduction of factors which are roots of unity. And in proceeding 

 to apply this general principle to equations of the fifth degree, the 

 same illustrious mathematician employed certain properties of func- 

 tions of five variables, which may be condensed into the two follow- 

 ing theorems : that if a rational function of five independent variables 



