Royal Society of Edinhurgh. 323 



tioDs are dilute no precipitation takes place, if the solution is now 

 warmed, a crystalline substance is thrown down. TJjis appears the 

 more curious, when it is known that the other salts cannot be 

 heated without decomposition. 



When the hydrochlorate is heated with potash the phosphaniline, 

 at the moment of separation, appears to undergo decomposition, for 

 the smell of aniline is apparent even in the cold, but no precipita- 

 tion takes place, so that phosphaniline must be itself soluble in 

 water. An attempt was made to obtain it in the separate state by 

 acting on the hydrochlorate with oxide of silver, a precipitate of 

 chloride of silver was formed immediately. The filtered fluid was 

 alkaline to test paper ; it clearly contained phosphaniline, but on 

 evaporating the fluid it became coloured, owing to the decomposi- 

 tion of the base, which is very changeable, and cannot be obtained 

 in the pure state. 



4. On Fermat's Theorem. By Professor Tait. 



The author stated that in consequence of Legendre's work, the 

 proof of Fermat's Theorem is reducible to showing the impossi- 

 bility of 



when m is an odd 'prime, cc, y, z being integers. 



Talbot has shown that in this case cc, y, z are necessarily com- ^ 

 posite numbers. 



The author shows, among other results of very elementary pro- 

 cesses, that if numbers can be found to satisfy the above equation, 

 X and y leave the remainder 1 when divided by m ; and that z 

 has m as a factor. Many farther limitations are given on possi- 

 ble values of x, y, z — the process being based on the consideration 

 of their prime factors, and on Fermat's Elementary Theorem 

 N"* - N = Nm. 



5. Professor Archer called attention to a curious binocular tele- 

 scope, bearing the following inscription : — 



PETRVS PETEONVS 

 SAO : C^Si= ET CAT^ 

 MAIES^? OPTICUS 

 MEDLANI 1726 



The instrument belongs to the Eoyal Institution of Liverpool, 

 and is supposed to have been part of a collection of rarities, made 

 by Wm. Koscoe, in Italy. As a telescope, it is of great power ; the 

 focus is adjusted by one portion of the case acting as a draw-tube 

 within the other part. 



