252 REPORT— 1870, 



water to be guided in each case to and onwhrd past the orifice by an infinite 

 number of infinitely small frictionless yiiide-tubes arratufed side by side, like 

 the cells of a honeycomb, and having their walls or septums * of no thiclness — 

 and if, in the different vessels, these guide-tubes be, one set to another, similar 

 in form, though they may he of quite different forms from the forms ivhich the 

 stream-lines wotdd themselves assume if the fioivs were unguided — and if, at 

 the homologous terminations of the guide-tubes, fiuid pressures be anyhow main- 

 tained 2iroportioaal, per honiologous areas, to the cube of any homologous linear 

 dimension, or, what is the same, if pressures be maintained proportional, 

 per unit of area, to the homologous linear dimension, — then the velocity of 

 the water at homologous places will be proportional to the square root of the 

 homologous linear dimension, and the pressure of the ivater at homologous 

 places on homologous areas ivill be proportional to the cube of the homologous 

 linear dimension ; and the ivater will press, at homologous places, on homo- 

 logous areas of the septums, tvith a force on one side in excess of that on the 

 other, which tvill he proportiorud. to the cube of the homologouslinear dimension. 



Note. — For brevity in what follows, pressures at homologous places on 

 homologous areas will be called homologous pressures, and pressures per unit 

 of area will be called unital pressures ; and any difference of the fluid pres- 

 sures on the opposite sides of any small portion or element of a septum will 

 be called a differential pressure. 



The demonstration of the proposition will be aided bj fii'st noticing the 

 following relation in respect to two small solid masses in motion. It' two 

 similar small solid bodies of masses m and m', having their homologous linear 

 dimensions as 1 to n, are guided to move along similar curves, having likewise 

 their homologous linear dimensions as 1 to n (fig. 6), and if the velocities of 

 the bodies at homologous points in their paths be as 1 to Vn , then — 



First. Their gravities are as 1 to n^, evidently. 



Second. Their "centrifugal forces "f applied by them in the plane of 

 curvature and normally to the guide are also as 1 to n^. 



Let r and r be put to denote the radii of curvature of the paths at homo- 



logous places. Then centrifugal forces are as 



r 



But 



mv m V ■ 



m'^n^m, 



v'=^n . V, 

 r z=yir. 



* The English form for the plural of septum, when septum is used as an English word, 

 is here purposely preferred to the Latin sepfa. 



t The name " centrifugal force" is here adopted in the sense in which it is commonly 

 used. I fully agree with the opinion now sometimes strongly urged to the effect that 

 this name is not a very happily chosen one ; for two reasons : — first, because the name 

 centrifugal would be better applied to a moticm of flying from the centre, than to a force 

 acting outwards along the radius ; and secondly, because the body really receives no out- 

 ward force, no force in the direction from the centre, but receives a centreward force which, 

 being unbalanced, acts against the inertia of the body, and diverts the body from the straight 

 line of its instantaneous motion. The centreward force actually received by the body, and 

 which is the force acting on it normal to its path, maybe called the devia five force received 

 by the body. This is equal and opposite to the outward force called "centrifugal force" 

 which is not received by the body, but is exerted outwards by it against whatever is 

 compelling it to deviate from the straight line of its instantaneous motion. The name 

 "centrifugal force," however, although objected to, is in too general use tlu-oughout the 

 world to allow of its immediate abandonment. 



