282 PHILOSOPHICAL TRANSACTIONS. [aNNO 1739- 



shall first propose the more simple cases, and then proceed to those which are 

 more compound, but nearer to the true state of things. Thus, in the first 

 Problem, that the solution may be the more simple, we suppose the water to 

 run out of the hole into a vacuum, and the particles of water, while they 

 descend towards the hole, to be without any resistance arising from a defect of 

 lubricity. 



In the 2d and 3d Problems, the efflux of the water is still supposed to be 

 in vacuo, but we conceive the particles of water, while they descend towards 

 the hole, to meet with some resistance for want of lubricity, but so small, that 

 the decrease of the motion of the water running out of the hole, thus occa- 

 sioned, is to be accounted as nothing. 



In the 4th and 5th we still retain the supposition of the vacuum ; but the 

 decrease of the motion of the effluent water, for want of lubricity, is supposed 

 to be sensible. 



Lastly, in the 6th and following Problems, we consider the thing as it really 

 is, when it is transacted in the air, so that the particles of water suffer a sensi- 

 ble resistance, not only from each other for want of lubricity, within the vessel, 

 but also after their going out of the vessel, from the attrition of the am- 

 bient air. 



Pkob. 1 . To determine the Motion, Measure, and Velocity of IVater running 

 into a Vacuum, through a Hole in the Bottom of a Vessel, where the Par-' 

 tides of IVater meet with no Resistance for want of Lubricity. — So long as 

 the hole is stopped, the stopper sustains the weight of a column of water 

 lying perpendicularly over it. On removing the stopper, the column of water, 

 which lies perpendicularly over it, being no longer sustained, by its pressure 

 causes the water to run out through the hole, and after having brought it to 

 its due velocity, keeps the velocity of the effluent water constant, by its con- 

 stant pressure. 



, It must be conceived indeed, that the motion of the water running out of 

 the hole is derived, not only from the weight of the perpendicular column, but 

 partly from the pressure of this column, and partly from the pressure of the 

 surrounding water. But this makes the motion of the effluent water neither 

 greater nor less, than if it arose from the pressure only of the perpendicular 

 column : not less, because the pressure of the perpendicular column, if it is 

 obstructed, will generate a motion proportionable to itself, and it can only be 

 hindered so far as the surrounding fluid urges the effluent water : not greater, 

 because the pressure of the surrounding fluid can add nothing to the motion 

 of the effluent water, unless it takes away as much from the pressure of the 

 perpendicular column. 



. 1 A ' ', 



