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single independent variable, and the simultaneous determination of 

 the singular solutions, if such exist ; the generalisation of the trans- 

 formed types, and the application of the result to the integration of 

 a large variety of partial differential equations in any number of in- 

 dependent variables, and the simultaneous determination of their 

 singular solutions, where such exist. 



2. The examination of the general theory commonly attributed to 

 Laplace. 



3. The indication of certain desiderata. 



February 4, 1858. 

 The LORD WROTTESLEY, President, in the Chair. 



The following communications were read : 



I. " On the daily Fall of the Barometer at Toronto." By 

 THOMAS HOPKINS, Esq. Communicated by WILLIAM 

 FAIRBAIRN, Esq. Received December 19, 1857. 



(Abstract.) 



In this paper the writer exhibited tables of the movements of 

 meteorological instruments registered at Toronto in 1846, in the 

 months of January and July, as specimens of the changes which 

 take place in the atmosphere in winter and summer. The principal 

 object was to find the cause of the fall of the barometer in the middle 

 of the day. The author endeavours to show that the vapour, which 

 in the early part of the day was produced by solar heat at the surface, 

 by its expansive power, bore that heat to the upper regions of the 

 air, where it was condensed by the cold of the gases in that situation, 

 when the heat of elasticity was set at liberty to warm and expand 

 the gases, and that it was this expansion which reduced atmospheric 

 pressure in the locality and caused a fall of the barometer. 



