234 MR. R. HAftLEY ON IMPOSSIBLE 



contributions to Algebra will ever occupy a conspicuous 

 position in the history of that science. An interesting and 

 instructive letter on the subject of surd equations, from 

 Mr. Homer to Professor T. S. Davies, was published in 

 vol. viii. s. iii. (pp. 43 — 50) of the Philosophical Magazine. 

 In that letter, the mode in which foreign roots are introduced 

 by the elimination of radicals is very clearly explained, and 

 the existence of rootless or impossible equations satisfactorily 

 demonstrated. 



Some interesting remarks on the impossible equation 

 2 iF -I- V^' — 7 = 5, 

 will be found on pp. 34, 35 of the Gentleman's Diary for 

 1837. This equation is also very elegantly discussed by 

 Professor J. R. Young in the fourth edition of his valuable 

 Elementary Treatise on Algebra* 



Assuming that the symbol V niay be always interpreted, 

 either positively or negatively, as circumstances may require, 

 Mr. W. S. B. Woolhouse seems to contend that the doc- 

 trine of impossible equations is founded upon too restricted 

 a view of that symbol. This question I have already 

 suflSciently discussed, and only call attention now to Mr. 

 Woolhouse's views, in order to make an opportunity of re- 

 marking, that much as I differ in opinion from that highly 

 accomplished mathematician in the present instance, I con- 

 sider his views on every mathematical subject as entitled to 

 our best attention. 



Of Mr. Cockle's researches I have already spoken. I 

 believe he is the only mathematician who has taken any 

 thing like a general or extended survey of the subject, and 



♦ See pp. 131-2 of that admirable little work. It may be proper here 

 to state, that Mr. Cockle, in the Mechanics' Magazine, vol. xlvii. p. 331, 

 has taken objection to certain parts of Prof. Young's argument in relation 

 to the equation noticed in the text, and that the Professor, with his cha- 

 racteristic frankness, has admitted the validity of Mr. Cockle's objections. 

 — See Mechanics* Magazine, vol. xlvii. p. 546. 



