4-60 Royal Society. 



riod, the coefficient of its argument will, when this period embraces 

 many years, acquire, in the process of' integration, a high multiplier, 

 and comes thus to have a sensible effect on the place of the planet. 

 Such is the origin of some of the most remarkable of the planetary 

 inequalities, and, in particular, of the great equations in the mean 

 motions of Jupiter and Saturn. It is necessary, therefore, that the 

 astronomer be furnished with the means of computing any term in the 

 expansion of the disturbing function below the sixth order j since it 

 has been found that there are inequalities depending upon terms of 

 the fifth order, which have a sensible effect on the motions of some of 

 the planets. The object of the author in the present paper is to give 

 the function such a form that the astronomer may have it in his power 

 to select any inequality he may wish to examine, and to compute the 

 coefficient of its argument by an arithmetical process of moderate 

 length. The investigation comprehends every argument not passing 

 the fifth order ; but as the formulae are regular, the method may be 

 extended indefinitely to any order. 



8. " On the Reflex Function of the Medulla Oblongata and Spi- 

 nalis, or the principle of Tone in the Muscular System." By Marshall 

 Hall, M.D., F.R.S. L. & E. 



9. " Experimental Researches in Electricity. — Fifth Series." By 

 Michael Faraday, Esq., D.C.L., F.R.S. , Fulleiian Professor of Che- 

 mLtry in the Royal Institution of Great Britain. 



The object of the author in this paper is to investigate the nature 

 of electro-chemical decomposition. From the consideration of the cir- 

 cumstances of difference that mark the electricities obtained from the 

 common electrical machine, and from the voltaic battery, and of which 

 he had already established the theory in preceding papers, be was 

 led to expect that the employment of the former in effecting chemi- 

 cal decomposition would exhibit some new conditions of that action, 

 evolve new series of the internal arrangements and changes of the 

 substance under decomposition, and perhaps give efficient powers 

 over matter as yet undecomposed. For the purpose of greater di- 

 stinctness, he divides the inquiry into three heads. In the first, he 

 treats of some new conditions of electro-chemical decomposition, and 

 shows that that effect does not depend upon the simultaneous action 

 of two metallic plates, since a single pole might be used to effect de- 

 composition j in which case one or other of the elements liberated 

 passes to that pole, and the other element to the other extremity of 

 the apparatus, the. air itself acting as a pole. In the second, he con- 

 siders the influence of water in electro- chemical decomposition ; and 

 he combats the opinion that the presence of that fluid is essential to 

 the process as erroneous, and shows that water is merely one of a very 

 numerous class of bodies, by means of which the electric influence is 

 conducted and decomposition effected. In the third, he enters at 

 large into the investigation of the theory of electro-chemical decom- 

 position ; and after discussing at some length the various theories of 

 different writers on this curious subject, he is led to consider the effect 

 in question as produced by an internal corpuscular action, exerted 

 according to the direction of the electrical current, and as being the 



