1814.] Imperial Institute. 391 



sixth order inclusive. In the memoir which he has lately read to 

 the Class we see equations of five different orders, from the second 

 to the sixth, forming aUogether 35 terms, the greatest of which 

 does not amount to five seconds, and the sum total is 40"25". 



It is impossible, as we have already remarked, that these equa- 

 tions should all have the same sign, and be a maximum ; but with- 

 out seeking for the probable mean, let us suppose it to amount to 

 12" or 15". This is what will be gained by introducing these new 

 equations into the tables of Jupiter. It is doubtful, as M. Burck- 

 hardt observes, whether these inequalities be more considerable for 

 Saturn. 



In making these useful additions to the tables of the superior 

 ])lanets, if we have not yet been able to reduce the errors to what 

 may be ascribed to the observations, M. Burckhardt thinks that we 

 may be certain of the influence of the small planets on the other 

 celestial bodies ; for he has taken the greatest care to render his 

 labour complete. 



Second Memoir on the Distribution of Electricity on the Surface of 

 Conductors, by M. PoissoN. 



The author in his first memoir iiad given the equations for two 

 spheres placed at any distance whatever from each other. He had 

 shown how they might be reduced to ordinary equations with va- 

 riable differences, and then to a single independent variable quan- 

 tity. He had resolved them completely by two particular hypotheses. 

 In the one he supposed the two spheres in contact, and in the other 

 the distance between the two surfaces was very great when compared 

 with the radii. 



M. Poisson gives here the general integrals of his two equations, 

 first in the form of a scries, and then under a finite form by means 

 of definite integrals. He proves that in all cases these formulas 

 contain only quantities always determined by the state of the ques- 

 tion. They express the thickness of the coat of electricity, or the 

 intensity of tlie electricity in any point of one or other surface. 

 Provided the spheres be not too near, the series will always con- 

 verge so fast tiiat as accurate values as we choose may be easily 

 deduced. To show the use of them, he supposes two spheres, the 

 first of which has a radius triple that of the second. He calculates 

 the thickness of the coat in nine different points at equal distances 

 upon the great circle whose plane passes tlirough the line of the 

 centres from the point where that line cuts the surface to the point 

 diametrically opposite. In the table wiiich lie has formed we see 

 the law according to wlucii the electricity increases or decreases on 

 each of these spheres. We see whether the electricity is positive or 

 negative, and we can easily determine the point where the change 

 of sign takes place. 



We may make all the suppositions we please respecting the 

 nature or the quantity of electricity with which each of the spheres 



