492 Mr. J. Cockle on the Method of Symmetric Products. 

 Series 11. 



The great irregularities in the last column of the above table 

 are owing to the difficulty of keeping the bulb of the thermo- 

 meter in exactly the same place over the orifice. The least varia- 

 tion would occasion an immediate and considerable change of 

 temperature ; and when the bulb was removed to only ^ of an 

 inch above the orifice, the cooling eifects w^ere reduced to the 

 amount observed when the natural pores alone of the leather 

 were employed. There can be no doubt but that the reason 

 why the cooling effects experienced by the thermometer-bulb 

 were greater in these experiments than in the former is, that in 

 these it was exposed to the current of air in localities in which 

 a sensible portion of the mechanical effect of the work done by 

 the expansion had not been converted into heat by friction, but 

 still existed in the form of vis viva of fluid motion. Hence this 

 series of experiments confirms the theoretical anticipations for- 

 merly published* regarding the condition of the air in the rapids 

 caused by flowing through a small aperture. 



LXXVII. Oil ike Method of Sijmmetric Products. By James 

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

 Law of the Middle Temple^. 



1. nnHE conclusions of Abel and Sir W. R. Hamilton respect- 

 -■- ing the impossibility of solving equations of the fifth 

 degree are rendered doubtful by recent investigations of Mr. G. 

 B. Jerrard. New fields of research thus seem to open upon us. 

 My present object is to point out the general scope of the method 

 of symmetric products, and to offer some remarks which may 

 assist in the inquiry as to how far that method is calculated to 

 throw light upon the theory of equations of the higher degrees. 



* See Dynamical Theory, § 77- Trans. Royal See. Edinb. vol. xx.p. 296j 

 or Phil. Mag. Dec. 1852. 



t Communicated by the Author. 



