Intelligence and Miscellaneous Articles. 235 



In the latter case, the geometrical type was given — the circle — to 

 determine the algebraical relations of its arcs. In the theory of 

 elliptic integrals, the relations of the arcs of unknown curves' are 

 given, to determine the curves themselves; this is the principal 

 object of the present communication. 



The problem resolves itself into twelve distinct cases, depending 

 on the magnitude of the parameter, and the sign with which it is 

 affected ; out of the discussion of these cases arise many new and 

 important relations of elliptic integrals. It would excite little in- 

 terest to give the bare enunciations of those theorems, and a mere 

 outline of the methods by which they are established would be un- 

 intelligible. Not the least interesting of those theorems is the pro- 

 position, that it is always possible to express an elliptic integral of 

 the first order as the sum of two elliptic integrals of the third order, 

 with parameters which are conjugate, reciprocal and imaginary. 



The author hopes, in a future communication to the Royal So- 

 ciety,— the present having grown under his hands beyond the limits 

 he anticipated — among other points, to extend his researches to the 

 case of elliptic integrals with imaginary parameters, and to show 

 the true geometrical meaning of such expressions. It will also be 

 shown, that imaginary expressions may be found for a logarithmic 

 elliptic arc analogous to the well-known imaginary exponential ex- 

 pressions for the sines snd cosines of circular arcs. 



XXXV. Intelligence and Miscellaneous Articles 



ON THE ARTIFICIAL FORMATION OF SEVERAL MINERALS. 

 BY M. BECQUEREL. 



I N ordinary chemical operations, when one body is made to act 

 *- upon another.it is customary to powder them, to dissolve them, or 

 to bring them to a state of igneous fusion. It is then almost impos- 

 sible to observe the results of slow action, such as nature presents 

 so often, and the electrical effects resulting from immediate contact, 

 which may in certain cases aid in bringing about the former, or 

 giving them a greater energy. Electro-chemistry, therefore, differs 

 from chemistry in employing electricity as a subsidiary means of ex- 

 citing affinity or rendering it more efficacious, and in its requiring 

 the mutual presence of three bodies, of which one at least must be 

 in the solid state and another liquid. Such is the point of view 

 under which I have constantly regarded electro-chemistry, which 

 furnishes means u;' analysis and synthesis of which advantage might 

 be taken. These researches have moreover the advantage of making 

 known the necessary conditions under which solutions containing 

 one or more combinations can react upon insoluble compounds with 

 which they are in contact. 



The weak action- which have particularly attracted my attention 



hich commence a- soofl as the rocks, the metallic and 



ubstatices which occupy veins and beds, come in contact with 



the mineral waters which rise from all parts of tin: earth's interior. 



Time then becomes an element in the growth of the crystalline sub- 



