THE MEASUREMENT OF THE RESISTANCES EXPERIENCED BY PLANE 

 PLATES WHEN THEY ARE MOVED THROUGH THE AIR IN A DIRECTION 

 NORMAL TO THEIR PLANES.* 



By Professor G. H. L. Hagen. 



Sometime since I submitted to the Academy the results of a series 

 of observations that I had instituted upon the motions of air and of 

 water when the uniform flow of these fluids is interrupted by means of 

 interposed planes.t By means of small bits of paper or tin foil floating 

 from the tips of needles the direction of the motion could be perceived 

 at every point. The velocities were indeed too feeble to be capable of 

 direct measurement, but the disposition of particles of pulverized am- 

 ber that were strewn over the water showed the limits of the strongest 

 current, and when the coarser particles came to rest before the finer 

 ones it was to be inferred that there was a gradual diminution of ve- 

 locity at such points. 



In general it was concluded that air and water alike swerve in curved 

 paths in front of such obstacles and flow towards the free openings. 

 In the latter and directly adjoining the outer ends of the obstacle the 

 strongest current is formed which here retains its direction unaltered, 

 therefore free from all variations. The deviation in front of the obstacle 

 does not take place at any definite distance from it, but rather extends 

 up to the- obstacle itself and even when the plate faces the current it is 

 seen that a feeble motion still exists immediately adjoining it. 



Behind the obstacle the fluid by no means remains at rest, but rather 

 there is always formed here a counter current whose length is equal to 

 four or five times the distance of the head of the obstacle from the neigh- 

 boring side wall of the channel, which counter current, however, is not 

 only fed at its rear enc, but principally also at two intermediate points 

 by the steadily broadening main current. The latter immediately be- 

 hind the head of the cross-wall meets the outcomiug counter-current 



*Read before the Academy of Sciences, Berlin, January 22. February 16, and April 

 20, 1874. (Translated from The Mathematical Memoirs [ Abhandlungen] of the Royal 

 Academy of Sciences at Berlin for the year 1874, pp. 1 to 31.) 



tSee tbe Monats-Berichte for 1872, p. 861. 



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