Mr. Cayley on the Solution of an Equation of the Fifth Order. 195 



The modifications which take place in cohesion-figures by the 

 mixture of one liquid with another in varied proportions are 

 very striking. For example, balsam of copaiba, when pure, 

 forms a figure consisting of very perfect concentric rings of 

 great breadth and splendid metallic colours, changing and dis- 

 appearing as the film becomes thicker. The outer edge of the 

 film is quite sharp and perfect. 



Now this balsam is soluble in alcohol, so that any adulteration 

 of it by means of a fixed oil could be easily detected, except 

 castor oil, which is also soluble in alcohol. The cohesion -figure 

 of castor oil is also well marked ; it has narrow iridescent rings 

 around a colourless disk, and is fringed with a broad perforated 

 pattern. A mixture of two-thirds balsam and one-third castor 

 oil, made under a gentle heat, forms a blank white film of large 

 size and clear edge quite destitute of colour. There is not a 

 vestige of the brilliant bands of the copaiba, or the delicate halo 

 and coloured fringe of castor. The film lies passively on the 

 water, with no other indication of its origin than the gradual 

 formation at its close of a very minute chain of colourless beads 

 or bosses gradually enlarging within its clear edge, precisely 

 similar to those which close the existence of the copaiba film, 

 and still later a partial attempt at a fringe (but without colour) 

 like castor. 



King's College, London. 

 February 13, 1862. 



XXVIII. Note on the Solution of an Equation of the Fifth Order. 

 By A. Cayley, Esq * 



I ACCIDENTALLY omitted to reply to Mr. Jerrard's re- 

 marks, May 1861, on my discussion of his alleged solution 

 of an equation of the fifth order. In his last paper, " Remarks 

 on M. Hermite's argument relating to the Algebraical Solution of 

 Equations of the Fifth Degree," February 1862, Mr. Jerrard re- 

 verts to the subject, and he says, " But although f{t)f(o 2 ) /(^ 3 )/(^ 4 ) 

 is, as well as its fifth power, a six-valued function, we cannot, 

 with the aid of Lagrange's theory of homogeneous functions, 

 establish a rational communication [? relation] between the two 

 functions 



/(o m m m, / s w / 5 (< 2 ) / vj m, 



as I pointed out to Mr. Cayley in the Philosophical Magazine 

 for May 1861." 



Putting, for shortness, a =/(t) /(t 2 ) /(t 3 ) f(t 4 ), I understand 

 Mr. Jerrard to mean that a, a 5 being given as the roots of two 



* Communicated by the Author. 

 02 



