VOL. XXX.] PHILOSOPHICAL TRANSACTIONS. 341 



Cor. 3. — Having given the length of the pipe, and the velocity of the water 

 in any section, the motion of the water will be in the ratio of that section. 



Cor. A. — Having given the motion of the water and any section, the length 

 of the pipe will be in the inverse ratio of the velocity. 



Cor. 5. — Having given the motion of the water and the length of the pipe, 

 any section will be reciprocally as the velocity. 



Cor. 6. — Having given the velocity in any section, and the motion of the 

 water, that section will be in a reciprocal ratio of the length. 



Cor. 7. — Given the length of the pipe, and the bulk of water running out 

 in any determinate time, the motion of the water will be reciprocally at that 

 time. 



Cor. 8. — Given the length of the pipe, and the time, the motion of the 

 water will be as the effluent mass. 



Cor. g. — Given the time and the mass of effluent water, the motion of the 

 water will be as the length of the pipe. 



Cor. 10. — Given the motion of the water, and the length of the pipe, the 

 effluent mass is in the ratio of the time. 



Cor. 11. — Given the motion of the water, and the effluent mass, the time 

 will be as the length of the pipe. 



Cor. 12. — Given the time and motion of the water, the effluent mass will be 

 reciprocally as the length of the pipe. 



Cor. 13. — If two masses of water, having a contrary motion, meet each 

 other directly, and if both the superfices with which they impinge, as also the 

 velocities, with which these superficies move towards each other, be equal ; 

 and should one of the masses be equal to a small drop of water, and the other 

 be the whole quantity of water contained in the ocean, or even an infinite 

 quantity of water ; it is possible, for this small drop of water not only to sus- 

 tain the whole quantity of water in the ocean, or an infinite quantity of water, 

 but after concourse, to proceed in its motion in the same direction, and with 

 the same velocity as before, and even repel the other towards the contrary part. 

 Which is a surprising paradox in hydraulics. 



Cor. 14. — If a certain mass of water run from a wider into a narrower tube, 

 through a pipe consisting of two cylindrical tubes of unequal diameters, and if 

 the motion of the water be neither diminished nor increased in its course ; as 

 soon as the first part of the water enters the beginning of the less tube, it will 

 immediately begin to run slower, and by its continual efflux from the wider into 

 the narrower tube, the water will gradually be more and more retarded in the 

 narrower tube, till the whole come into that tube. But the contrary will hap- 

 pen, when water runs from a narrower into a wider tube. Which is another 



