Intelligence and Miscellaneous Articles, 549 



pound body may be calculated as a function of the union of ele- 

 ments which it is often impossible to obtain in a direct manner. By 

 equating the values found by experiment, an equation is obtained 

 which contains in fact several unknown quantities ; but other com- 

 pounds containing the same simple substances in different propor- 

 tions furnish new equations ; and provided their number is sufficiently 

 great, not only the numbers sought, but also very valuable verifica- 

 tions are obtained. This research, which will be communicated com- 

 pletely to the Academy when finished, has already given a most 

 important law. 



The forces of union of simple substances reduced to the unit 

 of surface and of specific gravity are inversely proportional to their 

 equivalents. 



For hydrogen we have obtained 27 milligrammes per millimetre, 

 and that by four methods : 



(1) By means of mercury. 



(2) By means of bromine. 



(3) By means of oil of turpentine and benzole. 



(4) By means of water, wood-spirit, and benzole. 



But we only propose this figure as the result of a primary study 

 of the fundamental number ; it will probably undergo some correc- 

 tions after the experiments have been renewed, and the products 

 completely purified. The experiments to be made are long and 

 delicate ; great precautions must be taken to avoid serious errors. 



The facts already confirmed refer to definite integrals ; hence it is 

 probable, though not quite certain, that 



At the same very small distance, and with an equal specific gra- 

 vity, two elements of volume of a simple substance exert on each 

 other an attraction the value of which must be simply multiplied by 

 the ratio of the equivalents if it is to be applied to another simple 

 substance. 



This law of attraction evidently reproduces the experimental law 

 of the forces of union. It leads directly to several other laws 

 which we shall examine experimentally, of which the following are 

 the enunciations : — 



In simple substances the attractions on contact, reduced to the 

 unit of surface and of specific gravity, are inversely as the equivalents. 



In simple substances the ratio of attraction on contact to the force 

 of union is — 



( 1 ) Independent of the specific gravity. 



(2) Independent of the chemical nature. 



(3) Independent of the molecular grouping. 



For all simple substances taken in the fluid state, a constant pro- 

 duct is obtained when the following four numbers, referred to the 

 same temperature and pressure, are multiplied together : — 



(1) The chemical equivalent. 



(2) The coefficient of expansion for constant pressure. 



(3) The inverse of the coefficient of compressibility. 



(4) The inverse square of the density. 



The attractions on contact of two different simple substances 

 acting one upon another, and therefore of any two compounds, are 

 obtained by calculations resembling those we have used for the forces 

 Phil Mag. S. 4. No.212. Svppl Vol. 31. 2 



