DYNAMIC METEOROLOGY. 



359 



cal siiuilarity. The resistance to llu^ How of water in clianiiels and con. 

 (Inits nsually depends mainly on (lie Ibrmation of eddies, and though 

 we can not deteruiiue inathematieally the actual resistance, yet the ap- 

 plicatiou of the above proposition leads to a formula for the flow in 

 which there is a fuost material reduction in the number of constants, 

 for the determination of which we are obliged to have recourse to ex- 

 periment." 



(7) Hagen. — No experimental work has been done on the absolute re- 

 sistance of the air to bodies moving- through it superior to that of the 

 eminent hydraulician H. Hagen, of Berlin ; a translation of whose mem- 

 oir will be given in the series previously referred to, because of the fre- 

 quent inquiries that are made of me as to his results. 



But in applying Hagen's observed pressures to other surfaces, or other 

 angles of incidence than those used by him, great mistakes are liable to 

 be made, and the student should consult the chapter on anenometers 

 and wind pressure in the " Treatise on Meteorologial Apparatus," Ee- 

 port of the Chief Signal Officer for 1887, part ii, or the excellent mem- 

 oir of St. Tenant, quoted below, if he would avoid serious errors. 



(8) Kummer. — Allied to the problem of resistance, treated of by 

 Hagen, for plates normal to the wind, is that of plates inclined to the 

 wind, which is one that is specially important in problems relating to 

 gunnery, sailing, flying, and the construction of windmills. On this 

 matter Kummer has made a serious of experimental determinations of 

 the center of pressure for a thin flat plate when struck by tlie wind at 

 special angles of incidence. 



Although his revised results were published in 1876 in the Berlin 

 Abhandlungeu yet they seem unknown in America, and I have therefore 

 re-arranged them in the following table. Kummer's final measurements 

 were made on six stifl:' glass plates of the following shapes and dimen- 

 sions : 



The center of pressure is the point at which the jdate must be sup- 

 ported in order to remain <pi!etly balanced wiien the wind is blowing 

 upon it at a given inclination. These points are always in front of 

 the center of figure, or between it and the windward edge. 



The distance between the two centers is given in the column C; the 

 angle between the wind and the plate is given in the column a. At 

 first thought one would be inclined to convert the r, as given in milli- 



