460 Bmjal Society. 



by resolution of the proposed equation into a system of equations of 

 an inferior order. This method applied to the linear equation under 

 its usual forms leads to the well-known solution of equations with 

 constant coefficients : and when applied to the same equation under 

 the exponential form, it gives a result embracing the solution not 

 only of equations with constant coefficients, but also of a large 

 class of equations with variable coefficients. 



The author treats, — 1st, of the solution of linear differential equa- 

 tions, total and partial, in series ; 2ndly, of their finite integration ; 

 3rdly, of the theory of series, or inverse method of development ; 

 4thly, of linear equations of differences, total and partial, of certain 

 miscellaneous applications, chiefly in the field of definite integrals, 

 single and multiple. 



January 25. — " A Description of an extensive Series of the Water 

 Battery ; with an account of some Experiments made in order to test 

 the relation of electrical and chemical action which takes place 

 before and after completion of the Voltaic Circuit." By John P. 

 Gassiot, Esq., F.R.S. 



In a former paper, which was printed in the Philosophical Trans- 

 actions for 1839, the author described a series of experiments made 

 with some powerful voltaic batteries, for the purpose of determining 

 the possibility of obtaining a spark before the completion of the cir- 

 cuit. This anticipated effect was not, however, produced. A short 

 time after, Mr. Cross stated that he had succeeded in procuring a 

 spark from a battery of 1626 cells of copper and zinc, acted upon by 

 river water. The author, pursuing his researches, constructed a bat- 

 tery consisting of 3520 pairs of copper and zinc cylinders, each pair 

 being placed in a separate glass vessel, well covered with a coating 

 of lac varnish, and insulated by being placed on slips of glass covered 

 on both sides with a thick coating of lac. The cells were placed on 

 44 separate oaken boards, also covered with lac varnish, each board 

 carrying 80 cells, and sliding into a wooden frame, where they are 

 further insulated by resting on pieces of thick plate-glass, similarly 

 varnished. 



In describing the effects which this apparatus has produced, the 

 author endeavours to draw a distinction between the static and the 

 dynamic effects of the developed electricity, and treats of each se- 

 parately. The conclusions to which he is led from the series of ex- 

 periments narrated in this paper, are the following : — 



1. The elements constituting the voltaic battery assume polar ten- 

 sion before the circuit is completed, even in a single cell ; this polar 

 state being shown to exist by the action exerted on the electroscope 

 being different at each polar extremity of the battery. 



2. The tension, so produced, when exalted by a succession of series, 

 is such, that a succession of sparks passes between the polar extre- 

 mities of the battery before their actual contact. 



3. The static effects precede, and are independent of the com- 

 pletion of the voltaic circuit, as well as of any perceptible develop- 

 ment of chemical or dynamic action. 



4«. When the current is established, either by actual contact of the 

 extremities, or merely by their approximation, so as to admit of a 



