Intelligence and Miscellaneous Articles. 397 



,.. ,1 ./ ^ 1— cos 2a;, , 1— cos6.«, , 1— cos 10a;, p 



(/)• — 9 log A(c, w)=— p- + s"--jr — 7. h + '-T^; — = + &C., 



^-^ ' 2 o V ' / Sin 7ra ^ Sin S^a •" Sin 57r« 



/ X , ^ . sin .r , sin 3a; , sin 5a; „ 



(i^). ^Ccsm(.i= + C,- . + g. , +&C.... 



Sin ^ira Sin y-7r« bin ^vra 



ri\ 1/^ COS a; , cos 3a; , cos 5a; , „ 



(A). ^Cccosw=p^ — J — +- — 3 — + p; — -. h&c.... 



CosgTra Cos-fT" CosfTra 



^.. ip /I— ^_ sin a; . sin 3a; sin 5a' „ 



(.M- T <^^^ r+A~"Sin7ra Sin37ra Sin57ra '^"" 



Moreover, Jacobi's two celebrated theorems follow as a corollary from 



the general propositions here established. 



LXI. Intelligence and Miscellaneous Articles. 



ON THE PKODUCTION OF AZtlRITE. BY H. DEBRAY. 



AZURITE may be easily produced by bringing in contact a solu- 

 tion of nitrate of copper and carbonate of lime in sealed tubes. 

 The reaction takes place at the ordinary temperature, and under a 

 very slight pressure. In the author's experiments, the pressure has 

 never exceeded seven or eight atmospheres, and it sometimes de- 

 scended to three. 



A tube of about 20 to 25 millims. in diameter, closed at one end, 

 is charged with sticks of chalk and crystals of nitrate of copper 

 weighed beforehand, so as to furnish an evolution of gas, the pressure 

 of which, calculated for the volume given to the tube on closing it, does 

 not exceed a certain number of atmospheres. There is always an 

 excess of carbonate of lime in pro])ortion to the nitrate of copper. 

 The tube is then constricted nearly at the calculated height, after 

 having introduced into it a mercurial manometer; water is poured 

 into it through a funnel drawn out to a fine point, when the solution 

 of the nitrate of copper takes place slowly enough to allow the tube 

 to be closed without danger from the internal pressure. The tube 

 may also be closed after the dry substances have been placed in it, 

 together with another tube containing water; by reversing the ap- 

 paratus, the water flows out and the reaction is produced. 



The chalk is first seen to become covered with a greenish substance ; 

 by degrees, and after the liquid has lost its colour, this green matter 

 becomes converted into mammillated crystals of azurite. By the con- 

 tact of nitrate of copper, the chalk is slowly converted into tribasic 

 nitrate of copper, 

 3(CuO, N05) + 2(CaO,C02) = 3CuO, N05 + 2(CaO,NO^) + 2CO^ 



When the neutral nitrate of copper has once disappeared, there 

 remain the tribasic nitrate and carbonate of lime dissolved in car- 

 bonic acid ; there is then a production of azurite by the following 

 reaction : — 



3CuO, NO^ + CaO, 2C0^ HO = 3CuO, 2C02, HO + CaO, N0\ 



Carbonate of lime cannot be replaced by alkaline carbonates. If 

 tribasic nitrate of copper be mixed with an excess of l)icarbonate of 

 soda, a paste made of the mixture with a little water, and then the 

 whole be heated to about 320° F. in a sealed tube, a well-crystallized 

 substance of & fine blue colour is obtained, which might be taken at 



