456 



FOURTH REPORT — 1834. 



In the years 1/89 and 1790, Brunnings undertook an exten- 

 sive series of experiments for the purpose of determining the 

 relation between the superficial and mean velocities of the Rhine 

 and Waal rivers which traverse Holland. For this purpose he 

 constructed an ingenious tachometer upon the principle of ex- 

 posing a disc of wood or metal of any given magnitude to the 

 direct action of the current at different depths, so that by the 

 pressure of the disc against a lever placed above, the pressure 

 and consequent velocitj'^ was indicated very nearly. 



The results are shown in the following Table : 



Admitting, however, the accuracy of these experiments, it is 

 difficult to come to any other conclusion than that of a gradual 

 though feeble diminution of the velocity (about j-^^h) between 

 the superficial and mean velocity. 



Woltmann regarded the diminution according to the ordinates 

 of a parabola reversed. 



Funk substituted the logarithmic scale, namely, whilst the 

 depth increases in an arithmetical progression, the velocity de- 

 creases in a geometrical progression. 



Eytelwein, finding that no constant law could be discovered 

 by his experiments, finished by admitting, by way of approxima- 

 tion, a decrease of velocity in an arithmetical progression, and a 



