AND ON A PHiENOMENON OF ROTATING BODIES. 215 



if the breadth of the current be less than the cylinder's diameter. 

 The motion of the air along the cylinder's surface, therefore, 

 does not produce an increase of pressure against it, but rather 

 a decrease, and that in a direction perpendicular to the current ; 

 and further, this decrease is greater the greater the velocity of 

 the air in the current. 



How such a decrease of pressure is caused, is explained in 

 the above-mentioned essay, § 35 *. 



* I will here give the explanation there furnished, in a somewhat different 

 form. 



If a liquid or gaseous body issues through an orifice into a space filled with 

 a mass of similar nature, but in a state of rest, the moving mass expands itself, 

 so that its transverse sections have a greater area the greater their distance from 

 the orifice. If the influx proceed with a constant velocity, then, after some 

 time, the velocity of the moving mass at any particular place is constant, at 

 the same time, however, the velocity in different transverse sections decreases 

 the greater the distance of the latter from the orifice. If we suppose that all 

 particles of the fluid, passing simultaneously through the same transverse 

 section, whose area may be P, have an equal velocity C, then, considering the 

 fluid's density equal to unity, the mass which passes through this transverse 

 section in the unit of time will be PC ; and if P^ be the area of a more distant, 

 and consequently greater transverse section, and Cj the velocity present in the 

 same, then the mass which passes through this section in the unit of time 

 will be PjCj. The moving force, or quantity of motion in any transverse sec- 

 tion, is represented, however, by the product of the mass which moves through 

 the same in the unit of time, into the velocity, i. e. PC^ and PiCj^. 



These values must be eqiral to each other, for there is no reason why the 

 quantity of motion should vary. In each following transverse section, it is 

 true, the motion will be extended to a greater number of particles of the fluid 

 than in the preceding, and on that account the velocity of the same will be 

 less; nevertheless, as all particles are perfectly moveable, the quantity of 

 motion, disregarding the influence of friction, will suffer no essential dimi- 

 nution. Hence must 



PiCi2=:PC2, 

 but as Cj < C ; so also 



PjCi > PC, 

 i. e. the mass which passes through a more distant transverse section in the 

 unit of time is greater than that which in the same time passes through a 

 transverse section nearer to the orifice. 



To render this possible, a part of the fluid mass at r^st on each side must 

 enter the moving mass. The above-mentioned memoir contains (§33) the expe- 

 rimental proof, that in liquids the mass at rest on each side permeates even to 

 the centre of the moving mass ; without doubt this takes place in gaseous bodies 

 also, in an exactly similar manner, and thence arises, in both, a decrease of pres- 

 sure perpendicular to the direction in which the original motion was propagated. 



