540 Intelligence and Miscellaneous Articles. 



crystallize in our laboratories. Thus (Brewster's Journal, vol. x.) 

 llepetti observed quartz in a pasty state and in the act of crystal- 

 ling. The same kind of occurrence is said to have been observed 

 of various other substances, as beryl, opal, heavy spar." Report of 

 the First and Second Meetings of the British Association, p. 374-379. 



DIRECT DEMONSTRATION OF THE RULE FOR THE MULTIPLICA- 

 TION OF NEGATIVE SIGNS. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 No direct proof, that I am aware of, has ever been given of the 

 rule for the multiplication ofnegative signs, although proofs by Euler 

 and a hundred authors have been given by reductio ad absurdum. 

 You will oblige me by an insertion of the following direct proof, 

 especially as 1 have heard it disputed whether a direct demonstra- 

 tion is practicable, and since it will take up but a very small portion 

 of your admirable periodical. I remain, &c. J. O. H. 



A direct Demonstration of the Rule for the Multiplication of Nega- 

 tive Signs. 



This rule may be proved by the assistance of the following pro- 

 position : 



The product of a negative quantity into any other quantity is 

 equal to minus the product of the first quantity without the nega- 

 tive sign, and the other quantity. 



The product of a negative quantity into any other quantity signifies 

 that that negative quantity is to be added or subtracted as many 

 times as there are units in that other quantity, accordingly as this 

 other quantity is positive or negative, and consequently the result 

 will be the same as if the negative quantity were positive, and the 

 negative sign added to the result. 



Let the quantities to be multiplied be —a and +b. Then 



{-a)x{+b)=-{-{-a)x {+b) = -ab 

 and (-a)x(- b) = — {-\-a)x{- b) = - (— a i) = + a i. 



ON THE SOLUBILITY OF CARBONATE OF LIME, ETC. IN HYDRO- 

 CHLORATE OF AMMONIA. 

 M. Vogel, in the following notice, which is of the greatest impor- 

 tance in the analysis of many inorganic substances, remarks, that in 

 analytical researches, particularly in those which are for the purpose 

 of discovering the elements which enter into the composition of a mi- 

 neral, confidence has hitherto been placed in the statement, that 

 amongst the bases which are precipitated by the alkalies or their carbo- 

 nates, magnesia was entirely redissolved by the addition of a solution 

 of hydrochiorate of ammonia, and that this method has been generally 

 used to separate this substance from other bases, such as lime, alu- 

 mina, &c. &c. It is a well-known fact that hydrochiorate of ammonia 

 has the property of dissolving with facility many insoluble or diffi- 



