508 Mr. J. Cockle on the Tlieory of Equations 



tice that cotton is mordanted with common alum, nothing is 

 gained, as far at least as concerns the theorj^ of cotton-dyeing, by 

 a statement of the behaviour of alum to solutions of colouring 

 matter. In the foregoing treatise I have therefore adverted to 

 this subject in connexion with wool- and silk-dyeing, in which 

 relation it has not yet been considered, having, however, made 

 the express reservation, that, in considering this subject, a colla- 

 teral effect (the partial decomposition of alum by the fibre) must 

 not be overlooked. 



5. The principal conclusion, that the colouring matter adheres 

 only mechanically to cotton fibres, and that the fibre itself in 

 dyeing is without any chemical effect, is correct. We have seen 

 that Persoz, as well as previous investigators, were of the same 

 opinion ; and I observe that I myself, induced by observations 

 of an entirely different nature, expressed it as my own in the 

 little communication which I published in May 1858. Whoever 

 is acquainted with the numerous and contradictory researches 

 and theories that have been made on this subject by a long 

 series of chemists, and regards the diversity of, and the difficulty 

 of becoming acquainted with the phsenomena which I have had 

 to notice in the course of this work, will clearly see that a general 

 theory of dyeing must be built on a broader foundation than the 

 investigation " On the Operation of Mordants, especially Alum, 

 in Cotton Dyeing." 



If, however, a real promoter of science agrees with me in cer- 

 tain observations which tend to the decision of the foregoing- 

 question, and, although proceeding on another course of investi- 

 gation and induction, comes to the same conclusion on a pi'in- 

 cipal point, this must assist all who take an interest in the sub- 

 ject in coming to a decided opinion, and to myself can only be 

 a source of satisfaction. 



LXXV. Observations on the Tlicory of Equations of the Fifth 

 Degree. By James Cockle, M.A, F.R.A.S., F.C.P.S. ^c* 

 [Continued from p. 344. J 

 70. T ET (1) and the 15-ic whose roots are the values of 

 J-^ §1 + ^2 + ^3 be written, respectively, 



A = . . . (1), A' = . . . (1'), 



and let the roots not common to (1) and (1') be written 



/33= eA+OA+^-A> «3= OA+^A+^s^e, 

 ^,=e,e,+dA+0A> '^A=eA-^&A+dA; 



* Communicated by the Author. 



