1883.] 



On the Motion of Water. 



93' 



Taking a metre as the unit;, TJ S the critical velocity, and D the 

 diameter of the tube, the law of the critical point is completely- 

 expressed by the formula 



IT- 1 P 



where B,= 43'7 



This is a complete answer to question 5. 



During the experiments many things were noticed which cannot be 

 mentioned here, but two circumstances should be mentioned as 

 emphasizing the negative answer to question 6. In the first place, 

 the critical velocity was much higher than had been expected in pipes 

 of such magnitude, resistance varying as the square of the velocity 

 had been found at very much smaller velocities than those at which 

 the eddies appeared when the water in the tank was steady. And in 

 the second place it was observed that the critical velocity was very 

 sensitive to disturbance in the water before entering the tubes, and it 

 was only by the greatest care as to the uniformity of the temperature 

 of the tank and the stillness of the water that consistent results were 

 obtained. This showed that the steady motion was unstable for 

 large disturbances long before the critical velocity was reached, a fact 

 which agreed with the full blown manner in which the eddies 

 appeared. 



12. Experiments with two Streams in Opposite Directions in the same 

 Tube. — A glass tube 5 feet long and 1*2 inch in diameter, having its 

 ends slightly bent up as shown in fig 6, was half filled with bisulphide 



Fig. 6. 



of carbon, and then filled up with water and both ends corked. The 

 bisulphide was chosen as being a limpid liquid, but little heavier than 

 w^ater and completely insoluble, the surface between the two liquids 

 being clearly distinguishable. When the tube was placed in a 

 horizontal direction, the weight of the bisulphide caused it to spread 

 along the lower half of the tube, and the surface of separation of the 

 two liquids extended along the axis of the tube. 



On one end of the tube being slightly raised the water would flow 

 to the upper end, and the bisulphide fall to the lower, causing opposite 

 currents along the upper and lower halves of the tube, while in the 

 middle of the tube the level of the surface of separation remained 

 unaltered. 



