11 PHYSICAL GEOGRAPHY OF 



many observations, and is therefore more to be relied on for every stage of the 

 water, than any single experiment that can possibly be made expressly for a 

 given stage. 



The objects of the research required that we should possess a convenient 

 means of determining the actual discharge of the Ohio river in every condition 

 of its waters, and for every day during a series of years. 



The following table has been constructed for this purpose, from the foregoing 

 formula, modified to express the diurnal instead of the hourly discharge. The 

 table exhibits only the volume due to each foot in height, and of course will 

 require interpolations for the fractions of feet. It is extended from common 

 low water up to a flood of 36 feet — the highest, save one, which has been 

 known in the Ohio, at Wheeling, for the space of a quarter of a century. 



The scientific reader will recognise the utter impracticability of framing an 

 empirical equation, which shall express minutely the volume of water flowing in 

 a channel confined by such rude and irregular surfaces as the bed and borders 

 of a great river. The writer, not wishing to affect a precision incompatible with 

 the nature of the problem, has neglected the smaU decimals in carrying out the 

 calculations for the construction of this table, taking care merely to preserve 

 accuracy to the third place, so as to avoid any error equal to one per cent, of 

 the discharge indicated by the formula for any given stage of the river. 



The following equation, in which d is put for the reduced depth in feet, and 

 D for the diurnal discharge of the river in cubic feet, will represent the volume 

 of water flowing down the Ohio, at Wheeling, in a period of 24 hours, with as 

 much precision as can be desired for any practical purpose. 



26,000,000 (Z^ — 240,000 d"" = D. 



The equation, in this form, is more convenient for apphcation than the pre- 

 ceding. 



In Table IV, the figures in the third column show the number of cubic feet of 

 water flowing past Wheeling, for the depths on the bar, which are given in the 

 first column. 



