MOVING FORCE. 
171 
line surface de merae etendue et direcle, est sensiblement cgal ( a>r?‘ ot diffi- 
, . cully 111 tlio 
au produit de cette surface, par la hauteur due a la vitesse. ,ioctrines of 
L’inteusitc du choc depend ncanmoiiis eu panic de la liberie 
plus au moins grande que les filets ont de se dcvier aux ap- 
proches de cette surface j mais si la vcine rencontre une sur- 
face plus grande qu’elle, qui I’oblige i changer en entier la di- 
rection de tons ses filets, la vitesse perdue, ctaut par 1^ augmen- 
t6e, la resistance devient beaucoup plus grande*.” 
Rut in these cxpetiments, a part only of the vein stiikes the 
surface opposed to it, and the force of that part appears lobe 
equal to the force assigned by the theory to ihe whole vein. 
Of all theoretical propositions, that which was first dcnion- 
Btrated by Daniel Bernouilli, in his Hydrodynamics, page 'iQO, 
and afterwards more fully by the same author in the Comment. 
Petropol. vol. 8, page 120, appears to be tlie most applicable 
to Mr. Smeaton’s cases, and comes the nearest to his results. 
It is, that when the force of an insulated vein of water is di- 
rected perpendicularly against a plane indefinitely large, its 
pressure against the plane is equal to the wciglu of a column 
of water, of which tlie base is equal to the area of the seetion 
of the vein, and the height equal to twice the height due to the 
velocity of the vein. But the circumstances of this case are 
loot quite the same as those of Mr. Smeaton, and he found the 
pressure against the plane to be still greater than the weight of 
II column of twice the height due to the relative velocity of the 
‘Water and the wheel. , 
The most important conclusions drawn by Mr. Smeaton 
from his experiments are (as I have already noticed) not in his 
maxims ; but they are to be found, 1 apprehend, in the two 
! following observations, which I shall quote in his own words : 
1. “It is somewhat remarkable,” he says, “ that though the 
'Velocity of the wheel in relation to the water, turns out greater 
! :han one-third of the velocity of the water, yet the impulse of 
I'the water, in the case of a maximum, is more than double of 
'■what is assigned by the iheoryt. 
* I’rincipcs (i’liyilraul. vol. C, p. IjO. 
t Pliil. Trans. 1739, p. 130. 
2. “ We 
