4 t 1 Mr. J. Cockle on Multiplicity of Values. 



It follows from this theory, that hurricanes are most likely to 

 be produced by such volcanic eruptions as succeed seasons of 

 great heat, and that the eruption of a low volcano is more likely 

 to produce a hurricane than that of a high one, since the whole 

 of the insulating atmospheric shell is pierced through in the 

 former case, and only the upper portion of it in the latter. 



April 18, 1853. 



LXIX. Fragment on Multiplicity of Values. By James Cockle, 



M.A., of Trinity College, Cambridge; Barrister -at-Law of 



the Middle Temple*. 



I. TN the Introduction to his Memoir e sur le nombre devaleurs 



-*- que peut prendre une fonction quand on y pe?'mute les 



lettres qu'elle renferme, published in Liouville's Journal for 



January 1850, M. J. A. Serret has given an outline of the 



history of the question. Were it sought to add to the learned 



analyst's sketch indications of collateral, but allied, researches, 



we should have to make mention of the names of Descartes, 



Hudde, Saunderson, Le Sueur, Euler, Foncenex, Vandermonde, 



Lagrange, Laplace, Malfattif, Abel J, Sir W. K. Hamilton §, 



Badano||, Bronwin^f, and G. B. Jerrard**, as well as of 



others tf. 



II. Some suggestions may perhaps arise from the following 

 mode of considering the subject. Let 



0i(2/) + My)+ • + a ™ (2/) = a(y) 



e \ (y) + e 2 (y) + • +«* (y) =e (y) 

 *i(y) +*«(y) + • *vW =«(y)> 



* Communicated by the Author. 



t Mem. delta Soc. Ital. vol. xi. Peacock, ' Report/ p. 312. Lagrange 

 has noticed the writers who precede him in the list given in the text 

 (Thtorie des Equations, &c. pp. 178-186, 269-272). His memoir in the 

 Berlin Memoirs for 1770 (Berl. 1772) was (see p. 134) read to the Academy 

 'dans le courant de Vannte 1771.' 



\ Crelle's Journal, vol. i. pp. 65-84. (Berlin, 1826.) 



§ Trans. Royal Irish Acad. vols, xviii. (pp. 171-259) and xix. The latter 

 contains (pp. 329-376) the criticism on Badano's admirable researches. 



|| Nuove Ricerche sidla Risoluzione Generate delle Equazioni Algebriche 

 del P. Gerolamo Badano, Carmelitano Scalzo, Professore di Matematica 

 nella R. Universita di Genova. Genova, Tipografia Ponthenier, 1840. 



1T Phil. Mag. for November 1847 (S. 3. vol. xxxi. pp. 341-346). 



** Phil. Mag. Suppl. for June 1845 (S. 3. vol. xxvi. pp. 545-574) ; for 

 January 1846 (S. 3. vol. xxviii. p. 63); for February 1852 (S. 4. vol. iii. 

 pp. 112-116); for June 1852 (Ibid. pp. 457-460) ; for December 1852 

 (S. 4. vol. iv. p. 434). I have pointed out certain objections which, as it 

 appeared to me, might be taken to Mr. Jerrard's views (see Phil. Mag. for 

 December 1849, pp. 436, 437), and I have further pursued the subject of 

 quintics at pp. 505-507 of vol. Iv. of the Mechanics' Magazine. I may 

 mention that in the last line but one of the second column of the page last 

 mtntioned (507) *"- r should be put in place of of. 



ft Woolhouse, Kirkman, Mease, Cayley, Salmon, and, I think, others. 



