Prof. Magnus on the Motion of Fluids. 17 



unit of time. According as this mass expands in a direction 

 perpendicular to the axis of the jet, its dimension in the direction 

 of the jet must decrease in like proportion. If at the same time 

 the velocity decreases, so that both velocity and thickness are in- 

 versely proportional to the cross section, then this mass will pass 

 through all planes perpendicular to the axis of the jet in the 

 same space of time. But in order to fulfill these conditions, the 

 force which imparts motion to the water must decrease as the 

 velocity decreases. 



It is easy, however, to see that this cannot be the case. For, 

 setting aside the loss of force arising from the friction of the 

 fluid particles, the vessel, as already remarked, being so large 

 that the sides thereof present no resistance to the motion, — if 

 the surface during the motion remain horizontal, and if, in the 

 next place, it be assumed that the pressure due to every portion 

 is the same during the motion as during a state of rest, — then 

 there is no force present which acts in a direction opposite to 

 the motion, and hence no part of the moving force will be de- 

 stroyed. 



The jet, indeed, expands itself on account of the resistance 

 presented by the water mass which it enters ; but as this resist- 

 ance is offered by perfectly mobile particles, or, in other words, 

 is due to inei'tia alone, the moving force in the direction of the 

 axis remains unaltered ; and hence as soon as the motion has 

 become permanent, the same amount of force is exerted during 

 the unit of time in all planes perpendicular to the axis of the jet. 



Did the widening of the jet consist merely in a change of 

 shape undergone by the mass in question during its progressive 

 motion, so that it simply assumes a greater cross section, the 

 velocity in this case being unchanged, the time occupied by the 

 mass in passing throi^gh the diflFerent cross sections in its course 

 would be less and less according as its width increased. For 

 this reason the successive layers of the jet must either separate, 

 or an altei'ation of density must take place. In those cases 

 where care is taken that no addition is made to the mass, but 

 that the same mass alone expands, a decrease of pressure in the 

 case of liquids, where a change of density is impossible, and an 

 actual change of density in the case of gaseous bodies, can be 

 experimentally established, as has already been done in § 14. 

 This decrease of pressure has been demonstrated theoretically. 

 (See D. Bernovdli, Hydrodynamica Sectio 12, § 9, ]). 262; and 

 Poisson, Traite de Mecanique, 2"^'"^ edit. ii. p. 730.) In such 

 cases, however, as the present, where the jet moves in a fluid 

 similar to itself, there occurs a lateral motion of the fluid towards 

 the jet by which the mass of the latter is increased. 



This increase of mass, however, is accompanied by a diminu- 

 Phil. Mac,, S. 4. Vol, 1. No. 1. Jan, 1851. C 



