VOL XLI.j PHILOSOPHICAL TRANSACTIONS. 1Q\ 



Corol. — When q is given, v is as v, that is, as v'a. 



Prob. VII. — Supposing the water issuing into the air, and neglecting the acce- 

 leration of the water without the hole, proceeding from gravity; when any two of 

 the following are given, it is pioposed to determine the third, viz. the measure of 

 the effluent water, its velocity in the axis of the contracted vein, and the diameter 

 of the same vein. 



When the water issues through the hole into a vacuum, it is shown, in the 

 solution of prob. 3, that the velocity of the particles of water is the same in the 

 whole section of the contracted vein ; but now, when the vein passes through 

 the air, the velocity is no longer equal in all parts of the section: for the outer 

 parts of the vein put the surrounding air into motion, and are retarded by it, 

 so that they cannot acquire the same velocity as the rest. But the outer parts, 

 when they are retarded by the air, retard the inner contiguous parts, and these 

 the next ; and so by this means every outer particle is carried slower than the 

 contiguous inner one, so that the velocity is greatest in the axis of the vein, 

 and least at the circumference. For which reason it is. Dr. Jurin thinks, that 

 the middle parts of the water in fountains rise much higher in the open air than 

 they would rise in vacuo. 



Also, those parts of the air that are contiguous to the vein of water, when 

 they are put into motion by this fluid, they put the adjacent ones into motion, 

 that lie near them on the outside, and these the next outer ones, and these 

 again the next, and so on successively to some distance without the circumfe- 

 rence of the vein. 



But the velocity of the particles of water must necessarily so decrease, from 

 the axis of the vein to its circumference, that the relative velocity of every par- 

 ticle, wherever placed, must be every where the same, with respect to the par- 

 ticle lying on the outside. For if any particle had a greater relative velocity 

 than the rest, it would find a greater resistance from the attrition of the adja- 

 cent outer particles, and thus would be reduced to an equal relative velocity with 

 the rest. In like manner, every particle of the surrounding air, which is put 

 into motion, will have all the same relative velocity with respect to the adjacent 

 particles of the air outwards. 



But the relative velocity of the particles of water among themselves, is very 

 different from the relative velocity of the particles of air; as may be conceived 

 in this manner. Any particle of water in the outer part of the vein, is solicited 

 by the next particle inwards, to accelerate its motion; and is also retarded by 

 the next particle of air; and when that outer particle has acquired the due velo- 

 city, these two contrary forces must needs be equal, one of which retards the 

 particle, and the other accelerates it. But that cannot be done, unless the pro- 



p p 2 



