( 719 ) 
fuch manner, that the latter becomes infinitely gr^t in 
proportion to the former, then the Parameter of the 
mixt Motion muft become equal to that of the fimplc 
Motion. 
Fetirthly, That, if the Depth of the dead Water be- 
come infinitely great in comparifon of the Oepth of the 
running Water, the Parameter of the mixt Motion va- 
nifhes, or becomes equal to nothing. 
The Rule, therefore, which is to be found, ought 
to agree with all thefe Obfervations, and befides mufl: 
produce the fame Quantities of Water by Calculation, 
as were found by Experiment to anfwer to‘ the feveral 
Depths of running and dead Water, in the above mc*n- 
tion’d Tryals. 
Upon this Foundation the Learned Author proceeds, 
in a tentative Method, to find his Rule, and having 
difeover’d it, he fhews by Calculation, that it anfwers 
all the Conditions before requir’d. 
This Rule is expreft in a pretty high Equation, which, 
befides other Operations, requires the extracting the 
Root of the fixth Power 
From this Equation is derived another, ferving to 
find either the C^antity of Water difeharg’d, the Depth 
of the running, or that of the dead Water, the other 
two of them being given ; as likewife a third Equation, 
to find the mean Velocity. 
Our Author goes on to fliew the Ufefulnefs and Ne» 
ceffity of confidering the Doctrine of mixt Motion, in 
all Queftions relating to the Courfe of Rivers, the Quan- 
tities of Water which they difeharge, the enlarging or 
narrowing their Outlets, the fcouring and deepening 
their Channels, and ^ the Motion of the Tides in Har- 
bours. Thefe he illuftrates by feveral Deductions from 
the Equations above mention’d; to render which of grea- 
ter Evidence, it were to be wifiit, that thofe Equations 
A a a a a a z were 
