212 LECTURE XXIII. 



cury 1 inch high, would produce the same effect as a reservoir of water 

 more than thirteen times as high, and the force of the air confined in a 

 closed bottle under the receiver of the air pump, will cause a jet to rise to 

 the same height as a column of mercury which measures the difference of 

 the elasticities of the air in the bottle and in the receiver. 



But these calculations are only confirmed by experiment in cases when 

 the ajutage through which the fluid runs is particularly constructed ; that 

 is, when it is formed by a short tube, of which the sides are so curved that 

 the particles of the fluid may glide along them for some distance, and es- 

 cape in a direction parallel to the axis of the stream. A short cylindrical 

 pipe is found to answer this purpose in some measure ; but the end may be 

 more completely obtained by a tube nearly conical, but with its sides a 

 little convex inwards, so as to imitate the shape which a stream or vein of 

 water spontaneously assumes when it runs through an orifice in a thin 

 plate : for in such cases the stream contracts itself, after it has passed the 

 orifice, for the distance of about half its diameter, so that at this point its 

 thickness is only four fifths as great as at its passage ; and the quantity 

 discharged is only five eighths as great as that which the whole orifice 

 would furnish, according to the preceding calculation : instead, therefore, 

 of multiplying the square root of the height by 8, we may employ the 

 multiplier 5 for determining the actual discharge. But the velocity, where 

 the stream is most contracted, is only one thirtieth less than that which is 

 due to the whole height ; and when the jet is discharged in a direction 

 nearly perpendicular, it rises almost as high as the surface of the fluid in 

 the reservoir. 



This contraction of the stream, and the consequent diminution of the 

 discharge, is unquestionably owing to the interference of the particles of the 

 fluid coming from the parts on each side of the orifice, with those which 

 are moving directly towards it ; and the effect is more perceptible when 

 the orifice is made by a pipe projecting within the reservoir, so that some 

 of the particles approaching it must acquire in their path a motion contrary 

 to that of the stream. It would be possible to obtain an approximate cal- 

 culation of the magnitude of this contraction, from the equilibrium which 

 must subsist between the centrifugal forces of the particles, as they pass 

 out of the orifice, describing various curves, according to their various 

 situations, and the pressure required for the contraction of the internal 

 parts of the stream, which obliges the particles to move more rapidly as 

 they proceed, and which must be proportional to the height required for 

 producing this acceleration. (Plate XX. Fig. 255.) 



When a short cylindrical tube is added to the orifice, it is probable that 

 the motion of the fluid within the tube is still in some measure similar : 

 but the vessel must now be supposed to be prolonged, and to have a new 

 orifice at the end of the tube, at which the particles cannot arrive by any 

 lateral motions, and which will, therefore, not be liable to a second con- 

 traction : the discharge may, therefore, be estimated nearly according to 

 the true measure of this orifice ; the original pressure of the fluid continuing 

 to act until the stream escapes. 



The effect of a short pipe in increasing the discharge, ceases when the 



