On the Resolution of Equations of the Fifth Degree. 469 



fore inclined to think that our friend Liebig is right in asserting 

 that no plant wants any artificial supply of ammonia, or of mat- 

 ters producing that compound, there being enough of it offered 

 by natural means. Having communicated the results of my 

 researches on the subjects mentioned above to the Academy of 

 Munich, I hope they will soon be published. 



[In relation to the peculiar circumstances under which oxygen 

 and nitrogen combine, it may be worth while here to refer to the 

 results obtained by Dr. Bence Jones (Phil. Trans. 1851, p. 407, 

 &c), where the direct union of these gases in all cases of com- 

 bustion in air is described. Schonbein^s results depend upon 

 evaporation. — M. F.] 



LXV. Supplementary Remarks on M. Hermite's Argument rela- 

 ting to the Algebraical Resolution of Equations of the Fifth 

 Degree, % 6. B. Jerrard*. 



9. TN art. 8 of my " Remarks on M. Hermite's Argument t/' 

 -*- I stated that his conclusion was such as to indicate that 

 an error must somewhere have found its way into his calculus. 

 The reasons in support of my statement, which are there only 

 glanced at, I proceed to explain. 



10. Putting his final result under the form 



N 



it is clear that N may be regarded as an integral function of the 

 coefficients A v A 2 , . . A 5 , and such as not to involve any radi- 

 cals except those characterized by the symbols -y/, %/ ; while S 

 may be supposed to be a rational as well as an integral function 

 of the coefficients in question. 



11. Let now 



N. 



2>, 



N 



2> 



A 2 , . . A 5 that the equation in x shall be a solvible equation of 

 the fifth degree, the expressions for whose roots shall involve irre- 

 ducible radicals of the form f/7 How can this case be explained ? 



12. Here, you will say, ®j = 0; so that we may obtain an 

 independent solution into which quintic radicals shall enter. A 



denote what p^ becomes when we assign such values to Aj, 



* Communicated by the Author. 



t See the Philosophical Magazine for last February. 



