Intelligence and Miscellaneous Articles. 151 



I asked myself if the greater or less brightness of the sky ha? 

 not an influence upon the distance sought. To ascertain this I 

 requested ray son-in-law to repeat the experiment at night, illumi- 

 nating the white square by means of a lamp. He did so in the 

 middle of September, at 9 in the evening, the sky being calm and 

 without moon. To remove all lateral light, an assistant took away 

 the lamp as soon as the observer, after contemplating the white 

 square, directed his eyes to the sky. Xow, to my great surprise, 

 the result was sensibly the same as in the day experiment. After- 

 wards my second son operated, and found a value still of the same 

 order. So the brightness appears to have no notable influence 

 upon the appreciation of the distance at which the point observed 

 in the celestial vault is instinctively placed. — Bulletins deVAcademie 

 BoyaZe de Belgique, ser. 3, tome ii. nos. 9 and 10, Sept. and Oct. 

 1881. 



ON S03IE CONSEQUENCES OF GAUSS 's PRINCIPLE IN ELECTRO- 

 STATICS. BY M. CROELLEBOIS. 



M. Bertrand* has deduced from Gauss's principle several impor- 

 tant theorems relative to electrostatics ; following the same path, I 

 have obtained some interesting relations, and particularly the sim- 

 plified demonstration of Clerk Maxwell's theorem. 



I. Gauss's proposition EMV=SM7V is a pure identity if the 

 potentials be replaced by the expressions which the definition fur- 

 nishes. This relation can be arrived at independently of any ana- 

 lytical form attributed to the function T, by resting on the notion 

 of electric energv. Let us consider a conductor of charge M, at 



MY 



the potential Y, the potential energy of which is -~- ; let us 



vary the charge from M to M', the potential will vary from Y to Y', 

 and the increase of energy, equal to the electrical work expended to 

 bring the additional charge M7— M from infinite distance to the 

 conductor, will be 



Y\~e shall therefore have for the final energy, 

 MY'=MY-HM'-M)(Y+Y'), 

 from which, after simplification, and for a system of conductors, 



SBfV'=SBrV (1) 



II. Prom the two sides of the equality (1) let us subtract MY 

 and put M'— M=/i and Y'— Y=u, we shall have 



SMtt=SY/i, (2) 



* Journal de Physique, t. iii. p. 7-4. 



