Intelligence and Miscellaneous Articles. 239 



ON THE UNIFORM MOTION OF WATER, BOTH IN SMALL CANALS 

 AND TRENCHES AND IN STREAMS AND RIVERS. BY M. HAGEN. 



For the former the observations of Darcy and Bazin on the inlets 

 and outlets of the Bourgogne canal, and for the latter those of 

 Humphreys and Abbott on some of the great rivers of America 

 were taken as a basis. Introducing the simple law 



c= =fc ."«•>* 



where c signifies the mean velocity, a the relative fall, and r the 

 mean radius (that is, the quotient obtained by dividing the area of 

 the cross section by the liquid periphery), and employing the method 

 of least squares, gave, after comparison with various other measure- 

 ments : — 



For trenches, c = 4*9 . r a^ ; 



For rivers, c=6 . t\ a a. 



The numerical coefficient holds in the first case for any measure 

 whatever ; but in the second it holds for English and Rhenish 

 measurement in feet, while for metres it changes into 3*34. 



As soon as r = 1*5 foot or =0-47 metre, both expressions give 

 the same result ; at this point, therefore, there is a transition from 

 the one law to the other. — Monatsberieht der h.jpreussischen Akademie 

 der Wissenschaften zu Berlin, 1876, p. 243. 



A GLASS CIRCLE FOR THE MEASUREMENT OF ANGLES. 

 BY LEWIS M. RUTHERFURD. 



At the summer meeting of the National Academy of Sciences 

 in the year 1866, I described the micrometer which I had con- 

 structed for the measurement of astronomical photographs. It 

 was capable of measuring angles of position, and also distances in 

 directions at right angles to each other. These last measurements 

 were made by aid of screws arranged after the manner of those of 

 an ordinary slide rest : these screws were constructed with great 

 care ; and I had good reason to be satisfied with the smallness of 

 their errors. 



At the spring meeting of the Academy for the year 1870, I ex- 

 plained that I had been obliged to give up the idea of using screws 

 on account of the rapid changes in their errors caused by friction 

 and consequent wear ; and I then stated that I intended to discard 

 the screw and the compressed slide, and substitute for them a 

 divided glass scale, to be read by a micrometer-microscope, and a 

 gravity-slide with one V and one flat slide. This intention I car- 

 ried out during the year, the new form being first used about the 

 month of March 1871. It has been constantly used since that 

 time, and continues to give great satisfaction. The success of this 

 divided glass- scale confirmed me in a determination of long stand- 

 ing, to try the experiment of substituting a glass circle for one of 

 metal in some instrument for the measure of angles of precision. 



Two years' absence in Europe and other occupations conspired i o 

 postpone the execution of this plan until the past winter, during 

 which it has been realized with what seems to me the most pro- 



