74 ELEMENTS OF SCIENCE 



of water, in issuing from an orifice of a vessel (at the 

 bottom), do not, as Newton has shown, pass perpendicu- 

 larly to and through ifc. Many of them converge towards 

 it from every side so that after passing out of the orifice 

 they form a stream of diminished breadth, which he 

 called the Vena contracta. As the liquid issues forth, 

 there forms on its surface (immediately over the orifice) 

 a hollow depression which deepens till it forms a conical 

 space, the apex of which is at the orifice towards which 

 the liquid flows, while a rotary movement can be very 

 easily given to, or transmitted through, its particles. 

 This movement must also augment in velocity as the 

 liquid escapes (and so diminishes the extent of the 

 circling waves) through the inertia of the particles, 

 which tend to preserve whatever velocity they may have 

 gained, and therefore, as they approach towards the 

 centre of the rotating mass, their speed must increase 

 as the circles they form become smaller. If the orifice 

 be closed, then the conical depression will wander 

 over the surface of the liquid, gradually becoming 

 shallower and shallower, till it disappears. The quan- 

 tities which thus flow out, in successive, equal intervals, 

 from the bottom of a vessel with vertical sides, are as 

 the diminishing series of odd numbers 9, 7, 5, 3, i 

 which correspond inversely with the spaces described in 

 equnl intervals by a falling body.* 



The passage of liquids through pipes is greatly retarded 

 by friction within, and by the resistance experienced 

 when bends take place. The retardation may be 

 diminished, however, by giving particular forms to the 

 commencement and termination of a pipe without 

 otherwise changing its capacity. Thus a 4-inch pipe 



* See ante, pp. 61 and 62. 



