456 Mr. Horner's new Demonstration of an 



in cold alcohol, more easily in cold aether, and still more so 

 in either of them when hot; from its alcoholic solution it was 

 precipitated in white flakes by water ; this was a mechanical 

 mixture of galactin and water. It dissolved in sulphuric acid, 

 and when heated caused its decomposition. 



The action of nitric acid on galactin was very remarkable ; 

 at common temperatures it did not immediately act on it, but 

 when left for some days it converted it into an opake, yellow, 

 friable mass ; this same substance was obtained more rapidly 

 when the acid was heated, effervescence ensued, and on dilu- 

 tion, a pale yellow precipitate fell. This substance resembled 

 a resin : it was fusible, combustible, soluble in aether, brittle, 

 and friable; it had a resinous odour, and was insoluble in hot 

 or cold water : during this action no oxalic acid was formed. 



Galactin resembles wax in being fusible, volatile, combus- 

 tible, and insoluble in water, but it differs in the following 

 effects of reagents. 



Action of On wax On galactin. 



Cold sulphuric acid none dissolves it. 



Hot ditto combines with decomposed by. 



Nitric acid forms oxalic acid forms no oxalic acid. 



Alkalies saponify no action. 



Cold alcohol no action dissolves it. 



Cold aether no action dissolves it. 



LXII. New Demonstration of an original Proposition in the 

 Theory of Numbers. By W. G. Horner, Esq. 



To Richard Phillips, Esq., F.R.S., L. $ E. 9 $c. 



My dear Sir, 



I WILL not trouble you with an array of corollaries and 

 practical deductions, for which I hope to find a fitting 

 place elsewhere, but trust that you will regard the succinct 

 statement which I send as not unsuitable to the purposes of 

 your Magazine. I am, yours very sincerely, 



W. G. Horner. 



" If c is a prime number, and N any number not divisible 

 by c, the quantity N c_1 — 1 will be divisible by c, so that 



1ST- 1 -! 



will be an integer." 



c 



This theorem, which is due to Fermet, is justly described 

 by Legendre as " one of the most important in the theory of 



