Mr. De la Rue on Cochineal* 471 



On the probable existence of such a class of equations I 

 hazarded a conjecture at the conclusion of my last communi- 

 cation to this Magazine. As 1 hope shortly to bring out a 

 paper on this subject in a more complete form, I shall con*- 

 tent myself at this time with merely stating a theorem of much 

 importance to the completion of the theory of insoluble and 

 of Monogenous equations of the third degree; to wit, that the 

 equation in integers 



a{a,^ + j/3 _j. 2:3^ ^ ^ ^^.2^ ^^2^ _^ ^2^ ^ ^^2 4.^^2 ^. ^^2^ _(_ ^^^ __ q 



may always be transformed so as to depend upon the equation 



Ji^ +gv^ + hisfi = {Qa — e)uvw, 



wherein fgh —ae^— {f + 3a2)^+ 9a^— Sac^— gc^. 



By means of the above theorem, among other and more 

 remarkable consequences, we are enabled to give a theory of 

 the irresoluble and monogenous cases of the equation 



when m is some powet of 2, or of certain other numbers. 



26 Lincoln's Inn Fields, J J S 



Nov. 17, 1847. 



Erratum. — In the October Number, at page 295, a little below the 

 middle, for _y= 11 7949000 read the same with the number 1 added at 

 the end. At page 293, last line, omit the words after ** provided " as far 

 as " divisible by 9 " on the following page, and read in lieu, " provided in 

 the second case that ABC is of the form 9»z+l and that D is divisible by 9." 



LXXII. On Cochineal (Coccus Cacti). First Memoir, 

 By Warren De la Rue, Esq.'^ 



T^HE beautiful theoretical results which have been lately 

 * obtained by a closer examination of indigo blue and its 

 products of decomposition, made it desirable to undertake 

 similar investigations with other colouring matters. I made 

 choice of the colouring principle of cochineal {Coccus Cacti), 

 hoping that a detailed research might not only prove of in- 

 terest in a scientific point of view, but also throw some light 

 on its practical applications, and the more so, as the recent 

 investigations of Preisser had seemed to point out a very close 



* Communicated by the Chemical Society ; having been read June 21, 

 1847. 



