24 - 
vestigation. Its sides are inclined at a slope of one-fourth 
horizontal to one vertical. 
The most complete experimental investigation of the 
flow of water over weirs has been made by Americans, and 
the adopted formula is due to one of them. To^ the careful 
experiments of the late Jas. B. Francis, Past President Amer¬ 
ican Society Civil Engineer, Honorary Member American 
Society Irrigation Engineers, of Lowell, Mass., is due the ordi¬ 
nary form of the equation of the weir, and to his careful work 
hydraulic science owes much. At Lowell were located a num¬ 
ber of manufacturing enterprises drawing their water from 
the Merrimac river. Their combined capital was over thir¬ 
teen millions of dollars. It became necessary to determine a 
more definite measurement of the water, and Francis’ exper¬ 
iments were instituted for this purpose. Carried on with all 
the appliances and conveniences which the capital interested 
would warrant, the experiments were performed with such 
care and with such attention to minute sources of error, that 
they are above criticism. 
One difficulty in such experiments is to obtain a suitable 
basin in which to measure the water. In this case, P'rancis 
was fortunate in having one suitable in the Lower Locks, 
into which the water could be deflected at will after passing 
the weir. The lock was carefully prepared. Cracks were 
filled, leaks stopped, even the depressions about nail heads 
filled up. The remaining leakage was ascertained by exper- 
Figure 6. 
iment. The slight increase in capacity due to bulging when 
full was ascertained. The total capacity of the basin when 
feet deep was over 12,000 cubic feet. 
A preliminary set of experiments was made for determ¬ 
ining the proper form of the equation of the weir and after 
this was determined, the main experiments were devoted to 
finding the numerical value of the coefficient of the formula. 
The formula indicated by his experiments has since been 
standard within the limits indicated*by him. If one observes 
the flow of water through an orifice he will notice that the 
stream becomes narrower at the opening or is subject to lat¬ 
eral contraction. If over a weir, the sheet of water becomes 
thinner immediately below the crest, as in Fig. 6, or is sub¬ 
ject to a vertical contraction. By taking separate account of 
