1878.] Dr Pearson, On a new hind of self-acting weir. 143 



If we next endeavour to estimate the value of the forces arising 

 (1) from the water on the lower side ; (2) the weight of the upper 

 section of the valve ; (3) that of the lower do. ; (4) the friction ; 

 (5) the vis viva of the current, we find that, 



1. The pressure of the lower water assists in producing the 

 rotatory motion, but this pressure is destroyed by slightly raising 

 the height of the axis, i.e. an inch or two. 



2, 3. It is best to weight the lower section of the valve, to 

 balance the weight of that part of the upper section not within 

 the water. 



4, The friction on the trunnions of the axis is very small 

 compared with the forces acting on the valve ; and an increase of 

 ■8 to 1'2 in. in the depth of the overflow is sufficient to neutralize 

 it. 



5. The effect of the vis viva of the current is very small when 

 the river is not high, and the depth of the overflow not more than 

 4 inches, but it will increase rapidly when the stream of itself is 

 deep enough to submerge the axis of rotation {i.e. is considerably 

 above the etiageY; and when the overflow amounts to or exceeds 

 six inches : and generally it will increase with the rapidity of the 

 stream, which is itself affected by secondary causes, e.g. by opening 

 a part of the navigable pass. For example, it has been ascertained, 

 from oscillations observed in the valves of the navigable pass, that 

 the forces acting on the upper and lower sections of the valve are 

 literally in equilibrium when the overflow approaches to six inches 

 in depth, (the water in the river, and consequently that also below 

 the weir, being otherwise decidedly high), but that two or three 

 valves in the pass lost their equilibrium as soon as some adjoining 

 ones were lowered by the men in charge, in consequence of -the 

 increased velocity of the current. 



It will be found by calculation, with a valve 10 ft. high by 

 four feet broad, that the value of this force, or vis viva, the current 

 being 1 metre (= about 2^ miles an hour) is represented pretty 

 nearly by a force of 176 lbs. av. on the centre of the upper 

 section, or volee, of the valve, in a direction at right angles to its 

 surface. 



The valves of a navigable pass were not designed by the in- 

 ventor to be actually self-acting, for floating substances will pile 

 themselves up against the upright staunchions, and be entangled 

 between them and the lower parts of the valves when the latter 

 are lying flat on the apron of the weir : and so make them project 



1 Etiage is a word of common occurrence in the papers dealing with the 

 subject : I believe it means the normal level at which the stream would maintain 

 itself, if there were no weir or sluice. It is said to be derived from cestiraticinn, 

 i.e. the summer level. For example, on the Kilometer, it would be the zero of 

 the scale. 



