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not be without its advantages, and he thought that the 
Chetham Society would do well to include the collection in 
their valuable series. 
A Paper was read by the Rev. Robert Harley, F.R. A.S., 
entitled, “ The Method of Symmetric Products, and its 
Application to the Finite Algebraic Solution of Equations.” 
This Paper is divided into three sections. The first 
contains a systematic exposition of Mr. Cockle’s Method of 
Symmetric Products, with illustrations of its power and 
efficiency when applied to the lower equations. In the 
second, the Author discusses the resolvent product { 0 ) for 
quin tics, and defines a new cyclical symbol (S'). He shows 
that 0 has six, and only six, values, and that when any one 
of these values vanishes, the equation of the fifth degree 
admits of finite algebraic solution : its roots are actually 
exhibited. Mr. Cockle’s new solvible form is verified, and 
shown to include, as particular cases, the quadrinomials of 
De Moivre and Euler. The third section contains a direct 
calculation of the equation in 6 . The coefficients are 
followed, one by one ; the calculation being carried on by 
means of the cyclical symbol S', which is shown to possess 
peculiar working properties. The resulting sextic is found 
to coincide with Mr. Cockle’s equation, obtained by a wholly 
different method, which was laid before the Society a few 
months ago in his “ Researches in the Higher Algebra.” 
The Author notices the steadiness with which the Method of 
Symmetric Products mounts up to the higher equations, and 
concludes by expressing his belief that the equation in & — the 
verification of which has involved prodigious labour — will be 
found to be a canonical equation in the theory of quintics. 
A paper was also read by the Rev. W. N. Molesworth, 
M.A., “On Comparative Sociology, or the Application of 
the Comparative Method to the Investigation of Social 
Laws.” The Author, after adverting to the present state of 
social science, and accounting for its backwardness by the 
difficulty and complexity of its phenomena, as well as the 
