OF ARTS AND SCIENCES. 



49 



With our present knowledge, this cannot be done with accuracy ; but 

 from observations, which I will not describe, I am able to present an 

 approximate result which will serve to illustrate one principle. 



Taking, for example, the conditions when the mean velocity of the 

 stream is 8 ft. per sec, I construct the following table : — 



Recurring to the observations when the westerly tube projected 

 0.055 ft. and the paths of some of the particles were found to deviate 

 about ninety degrees, and, passing through a quadrant of an ellipse, 

 again resume a direction parallel with their former course, it would be 

 reasonable to conclude that, with a projection of a few thousandths of 

 a foot, the deviation of the paths would be less than ninety degrees, 

 and the curve would be flattened, and become more like a segment 

 taken nearer the transverse axis. In this case, the lowering of the 

 reservoir would not bear a constant relation to the head which would 

 produce the velocity existing at the end of the pipe, but would be a 

 fraction of this head, increasing with the distance from the side, rapidly 

 at first, and then slower, until reaching a limit would remain constant. 

 This conclusion is confirmed by the results of the table, in which with 

 distances from 0.007 ft. to 0.055 ft., the velocity due a height equal to 

 the lowering of the reservoir increases from 0.38 to 0.67 of the veloc- 

 ity at the end of the pipe, and this increase is in a rapidly decreasing 

 series. 



I have reason to conclude, from experiments made elsewhere, that 

 the lowering of the reservoir depends also upon the thickness of the 

 end of the pipe ; for I found by projecting a pipe 0.02 ft. in diameter, 

 having very little thickness at the end, into water flowing in an iron 

 pipe one foot in diameter, with a mean velocity of 9 ft. per sec, a 

 lowering of the piezometric column greater than that above given ; 

 namely, for the same distances from the side, the velocity due a 

 height equal to the lowering was from seventy to ninety one-hundredths 

 vol. xiv. (n. 8. VI.) 4 



