Floods on the River Bamvon. 89 



two propositions are not strictly true unless the changes from 

 point to point are very gradual; but they sometimes form the 

 only means of arriving at even an approximate result. An 

 additional loss of head, beyond what the regular calculations 

 give, has been allowed, according to circumstances, when a 

 sudden reduction of velocity takes place; since, in irregular 

 channels where side currents and eddies are formed, such 

 loss always takes place. The loss of head at each con- 

 traction is shown on the diagram ; the fall appears as a step 

 where the contraction is great and sudden, as a wave or 

 double carve where the contraction is gradual. The fall or 

 loss of head increases as the difference of velocity increases 

 at any given point. The formulae adopted for the calcula- 

 tions were those ordinarily used in hydraulic investigations. 

 Their application in the manner above described explains 

 some of the difficulties of this case ; while the neglect of 

 such calculations appears to have led more than one 

 professional witness to erroneous conclusions. 



16. One great difficulty in the case was the following : — The 

 actual level of the flood at one point below the embank- 

 ment was about 3 feet above the level of the floor of one of 

 the mills, and yet engineers gave evidence to the effect that 

 the flood would have risen a few inches only on the floor of 

 the mill, had the railway embankment not been in existence. 

 A jury might well be excused for preferring the fact to the 

 theory; still the paradox is capable of explanation, though it 

 must needs be a somewhat lengthy one. Omitting the influence 

 of wind in an open channel or reservoir, water is motionless so 

 long as the surface remains level, but so soon as a difference 

 of level takes place, motion commences, the water flowing 

 from the place of higher to that of lower level. The greater 

 the difference of level, the more rapid the motion; or, in other 

 words, the greater the velocity of flow; and conversely, the 

 greater the velocity, the greater the difference of level must 

 necessarily be. Now, in any channel of given width, the 

 depth of water and the slope of its surface adjust them- 

 selves to the volume of water flowing down it. If the 

 width of the channel be reduced at any part, it is necessary 

 in order that the same quantity of w r ater may pass through 

 the contracted part, that both the depth and velocity should 

 be increased in one of two ways — (1) if the contracted part 

 be uniform in section and slope for such a length that the 

 depth of water would remain uniform, the increased velocity 

 would be obtained by the increase of depth alone ; but (2) 



