Prof. Magnus's Hydraulic Researches. 101 



thereby the surface produced from the whole strata becomes con- 

 cave on the side of the jet with the greater velocity. 



35. Since the phsenomena which jets of different velocities 

 presentj when they proceed from apertures of different magni- 

 tudes, and meet at different angles, are of minor importance for 

 the following considerations, and may be all explained in a similar 

 mannei', it would not be worth while to enter upon them further 

 at present. 



Experiments on the form of Jets ivhich issue from apertures 

 in thin plates. 



36. I turn now to the description of experiments on the form 

 of jets pi'oduced when water issues from apertures in thin plates. 



In these experiments the apertures were made in the bottom 

 of the vessel, because the form of jets issuing from such aper- 

 tures are more regular than those issuing from the side. It is 

 an indispensable condition for the regular form of a jet, that the 

 water should flow towards the aperture from all sides with equal 

 velocity. This is not to be attained with apertures which are in 

 the side of a vessel. By using very high columns of water during 

 the efflux, the influence of the unequal pressures which are exer- 

 cised at the upper and under sides of a vertical aperture may be 

 made as small as possible, so that those differences of pressure 

 appear infinitely small ; but the pressures cannot be made so 

 equal as in the case of apertures in the bottom of a vessel. But 

 in order to obtain a regular afflux from all sides, it is not suffi- 

 cient to make the apertures in the bottom of the vessel. First of 

 all, it is necessary that the bottom should be horizontal and quite 

 plane; next, that the vessel should be so regular and of such 

 dimensions that the side walls do not hinder the motion of the 

 water; and finally, that no external influence whatever should 

 produce any motion in the water. 



37. And even if all these conditions are fulfilled, the afflux 

 will always be irregular for a short time after the efflux has begun ; 

 for there results a rotatory motion in the liquid, which after 

 some time not only communicates itself to the greater part of 

 the lower strata, but also to the higher strata of the liquid. Such 

 a motion results whenever all the particles of water in one plane, 

 for instance those at the bottom of the liquid, have no common 

 resultant. No rotation takes place if the directions of motion 

 of all the particles at the bottom goes through one point, the 

 centre of the aperture ; but if by any disturbing influence, such 

 as an obstruction at the bottom, or a motion communicated to 

 the water by external agency, the directions of the individual 

 particles are altered, then a rotatory motion of the liquid must 

 eusuc, for all the directions do not pass through the same point. 



