142 Dr Pearson, On a neiv kind of self-acting weir. [Feb. 25, 



in work, may visit any of the weirs on the upper Seine, or those 

 on the river Meuse between Namur and Dinant; the flow of 

 water in these two rivers is very much the same, and I was in- 

 formed by the men in charge of the weir near Corbeil on the 

 Seine, and also of one near Dinant, that the system was working 

 without the least difficulty, and as well as could possibly be 

 expected. 



I will next endeavour to give a short analysis of the way in 

 which the inventor discusses the question as a hydrostatical 

 problem. He considers separately the different forces which act 

 on a valve upright on its staunchions and partly immersed in the 

 water, and tend, some to make it revolve on its axis, some to 

 prevent its doing so. 



The forces tending to make it revolve are : 



1. The pressure of the upper water on the upper section of 

 the valve. 



2. The pressure of the lower water on the lower section. 

 8. The weight of the upper section itself. 



4. The vis viva residing in the current. 

 The contrary forces are : 



1. The pressure of the upper water on the lower section of 

 the valve. 



2. The pressure of the lower water on a small part of the 

 upper section. 



3. Tlie weight of the lower section. 



The relation of equilibrium between all these forces is neces- 

 sarily somewhat complicated ; but if we observe that the principal 

 forces arise from the pressure of the water, especially the upper 

 water ; and if also, to simplify the question, we consider the valve 

 itself a mathematical plane, and the axis of rotation, a line drawn 

 in this plane, we arrive at the following result : 



1. If the axis of rotation is so placed that the length of the 

 lower section of the valve is half that of the upper section, there 

 will be equilibrium between the pressures exercised by the upper 

 water on the two parts of the valve, supposing the water to be 

 just covering its top. 



2. If the axis of rotation be placed in the middle of the valve, 

 there can be no equilibrium between these pressures, whatever be 

 the height of the water flowing over the upper part of it ; the 

 pressures on the lower section will always be in excess of those 

 acting on the upper one. 



3. From this we .conclude that the axis of rotation ought to 

 be placed at a point situated between J and \ of the height of the 

 valve, reckoning from the bottom, for those which do not act of 

 themselves : and at a point about \ from the bottom for the self- 

 acting valves. 



