280 LECTURE XXIII. 



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 j and the quantity discharged is only five eighths as 

 great as that which the whole orifice would furnish, according to the preced- 

 ing 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 dis- 

 charged in a direction nearly perpendicular, it rises almost as high as the sur- 

 face 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 eifect 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 calculation of the 

 magnitude of this contraction, from the equilibrium which must subsist be- 

 tween the centrifugal forces of the particles, as they pass out of the orifice, 

 describing various curves, according to their various situations, and the pres- 

 sure 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 contraction: 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 



