414 Mr. Challis on the general Equations 



.031 of an inch. As this interval is diminished, it is fonnd that 

 the pressure attains a maximum before the stream leaves the 

 disc. This must be owing to causes which the theory does not 

 take into account: probably it is due to friction, the effect of 

 which will become more sensible as the passage for the stream 

 is contracted. Whatever be the force which occasions this con- 

 densation, let us call it P. Then by the equation (K), 



«' hyp. log. ^ = fPdr -'l=fPdr-^,; 



from which , -—r-- = P+ -r-^ + — r-r • -r- ; 



par rp- r>^ dr 



and if /) be a maximum, P = — 



c^ 



T^p- r ' 



This shews that the greater P is, the nearer the maximum pres- 

 sure is to the centre ; and the experiments confirm this result ; 

 for when the interval between the disc and orifice was diminished, 

 the circle of maximum pressure was drawn towards the centre. 

 Upon the whole then, there will be a maximum of condensa- 

 tion neai' the centre of the disc, because the particles there, not 

 being in the direct course of the stream, will move but .slowly, 

 and consequently by reason of the equation 



2a' hyp. log. ^ = - -', 



p will be nearly n -. next there will be a sudden rarefaction on 

 account of the confluence of the stream, as it enters between 

 the disc and the plane surface : afterwards, the theory shew.s, 

 tliere would be a continual increase of density up to the edge 

 of the disc, were it not for some cause, very probably friction. 



