Mathematics and General Pliysics. 419 



Sir David Brewster communicated to the Seetion the results of 

 a series of experiments on the effects of reflexion from the surfaces 

 of crystals, when some surfaces have been altered by solution, and 

 exhibited a number of singular forms, produced by different crystals, 

 or by the same crystal under different circumstances. 



Mr Graves presented a paper on the theory of exponential 

 functions, in further illustration of a memoir on the same subject, 

 which he bad laid before the Royal Society, and which had been 

 printed in its Transactions. 



Professor Hamilton explained a new method of conceiving ima- 

 ginary quantities, and the principles of a theory which he denomi- 

 nated " the theory of conjugate functions." Professor Hamilton 

 stated, that he had confirmed, by the aid of the theory, the results 

 obtained by Mr Graves. 



Mr Sang stated the results of some theoretical and experimental 

 investigations which he had made on the nature of those curves 

 traced by the extremities of vibrating wires fixed at the end, and 

 he exhibited drawings of the forms of the curves thus produced. 



Mr Sang noticed a property of the successive integer numbers, 

 intended to facilitate the discovery of those that are prime. 



Dr Williams read to the Section, a paper on the production and 

 propagation of sound. 



Mr Campbell gave an account of his views respecting the anti- 

 lunar tides. 



Professor Forbes having explained to the Section the principles 

 of the sympiesometer of Mr Adie, and the objections to which it 

 was subject, arising from the want of identity of temperature of the 

 mercury in the air; then stated a modification which he had intro- 

 duced in the construction of the instrument, whereby the correction 

 for temperature might be effectually obtained. 



Mr Dick explained a new construction of an achromatic object- 

 glass, in which, by the refraction of the cementing fluid substance, he 

 had been enabled to correct the secondary spectrum. The author ex- 

 hibited a telescope with an object-glass formed on this principle. 



Sir T. Brisbane made some verbal remarks on the subject of a 

 siliceous sand procured at New South Wales, and which has been 

 supposed to afford glass for optical purposes of a superior quality. 



Mr Murphy stated the result of some recent observations of Mr 

 Snow Harris, on the retention of electricity on the surface of bodies 

 in vacuo. 



Professor Lloyd took the advantage of the absence of other 



