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to obviate the danger of explosion so far as it arises from 
chances of ignition ah extra — as by the spark from a work- 
man’s pipe, of which an example was cited. The danger of 
explosions from the liberation of oxygen from the powder 
itself, by friction or otherwise, would of course remain ; but 
this, the Author inclines to believe, is a less frequent cause of 
explosion than ignition ah extra occasioned by the carelessness 
of workmen, rendered indifferent to risk by long habit, and 
emboldened by impunity. Dr. Faraday, in his comments on 
this plan, approves it as adapted to cut off one class of risks, 
and so to remove the point of danger further off, and also as 
not likely to deteriorate the quality of the powder immersed 
in the protective atmosphere. He points out, however, as a 
source of danger usually unsuspected, the possibility of the 
ignition of the gunpowder dust which collects on the beams 
of powder mills, and by which, he believes, explosions may 
be originated, as well as by the heating of the grains actually 
under trituration in the mill. Mr. Ward, in reply to Dr. 
Faraday, recognises the partial nature of the security affordc 
by the proposed plan, but lays stress on the fact that \ 
appears adapted to eliminate all the risks of the manufacture, '' 
except those which are inherent in the nature of the material 
operated on, and therefore essentially incurable. 
A Paper, entitled “ Supplementary Researches in the 
Higher Algebra,” by James Cockle, M.A., F.R.A.S., was 
read by the Rev. Robert Harley, F.R.A.S. 
In these Supplementary Researches the Author extends 
the elementary formulae given in § 2 of his original memoir ; 
compares the cyclical and the epimetric views of the function 
U ; and, following the former, is led to a new cyclical theorem 
which affords an easy demonstration of a proposition asserted 
in § 28. Mr. Cockle then applies Mr. Harley’s cyclical 
process to the deduction of certain relations between un- 
symmetric functions ; relations attained with a facility which 
