VOL. LXXXV.] PHILOSOPHICAL TRANSACTIONS. 471 



entirely on experiment. But if the pipe decrease, having its orifice rs equal to 

 that of a cylindrical pipe of the same length, the velocity through the former 

 appears, from the experiment I made, to be greater than through the latter in 

 the ratio of J 4 to 11. 



If the pipe mr (fig. 13) be inserted horizontally into the side of a vessel, the 

 velocity at the orifice rs, by theory, is always in proportion to the square root of 

 the altitude cd, the orifice being still supposed to be very small compared with 

 the bottom of the vessel. By trying the experiment with pipes of different 

 lengths and of the same diameter, beginning with the shortest and increasing 

 them, it appears that the velocity first increases and then decreases; a circum- 

 stance which has been before observed. If rs be greater than cm, the quantity 

 of fluid which flows out in a given time, the vessel being kept full, appears to 

 be increased in proportion to the increase of rs, as long as the expelling force is 

 able to keep the pipe full; but at what magnitude of rs this effect ceases must be 

 determined by experiment. If rs be less than cm, the quantity which flows out 

 is greater than if the pipe were cylindrical, and of the same diameter as rs. 



The velocities of fluids spouting upwards through an orifice or pipe has not 

 been considered by Bernouilli; but the following experiments will show the 

 effects in this case. Let abcdef (fig. 14) be a vessel filled with a fluid, r an 

 orifice, x, y, z, three pipes each an inch long, having their tops on an hori- 

 zontal line with the orifice; x is cylindrical, of the same diameter as that of the 

 orifice; y is conical, increasing upwards, of the same diameter at the bottom as 

 the orifice; z decreases upwards, of the same diameter at the top as the orifice. 

 In 12", the quantities which ran out through the orifice and pipes, x, y, z, the 

 vessel being kept full, were found to be in the ratio of 7, 9.4, 11.2 and 10.7. 

 Hence the ratio of the velocities through the orifice and pipe x appears to be 

 very nearly in the ratio of 3 to 4, agreeable to what was found to take place for 

 an orifice and short pipe at the bottom. The quantity which ran out of the 

 pipe y increased by increasing the diameter at the top, in proportion to that area 

 as nearly as could be ascertained, as long as the expelling force could keep it full; 

 and a greater quantity ran out of the pipe z than through the orifice. All this 

 is agreeable to what was found to take place under similar circumstances when 

 the orifice and pipes were inserted at the bottom. So far therefore as the theory 

 can be applied when the fluid descends perpendicularly, it appears to be appli- 

 cable also to the case when it spouts upwards. 



At the bottom of the vessel abcd (fig. 15) having an orifice rs, was inserted a 

 pipe axyzwv conical at the top and cylindrical downwards from it, having the 

 diameter of the cylindrical part equal to that of the orifice, and directly under 

 it. I then stopped the orifice sr within, and filled the vessel, and expected, that 

 as there was now no pipe immediately connected with the orifice, the fluid would 

 form the vena contracta as if there was no pipe, and that the velocity at the 



