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RoBiNsox — On the Cup Anemometer. 427 



XXXIX. — OiT THE Theory of the Cup Anemometer, and the 

 Determination oe its Constants. By the E,ev. T. E.. E-obinson, 

 D.D., M.E.I.A., P.E.S., &c. 



[Read December 13, 1875.] 



I HAVE described this instrument in a paper which the Academy did 

 me the honour to publish in their "Transactions,"* and I endeavoured 

 to approximate to its theory by applying to it Borda's Theorem for 

 Undershot Wheels, and adcling terms for the resistance due to the 

 motion of the cups in quiescent air, and to friction. In respect of 

 the coefficients, I determined in actual wind the ratio of the pres- 

 sures on the concave and convex surfaces of the cups at perpendicular 

 incidence, and measured the diiference of these pressures, by a spring- 

 balance connected with the axle of my Anemometer (12-inch cups 

 with arms of 24) for velocities of wind given by a smaller instrument, 

 of known relation to the large one. The resistance due to the rotation 

 was measured by the forces required to make the cups revolve with 

 given velocities, and the friction similarly measured. These data 

 enabled me to compute the ratio of the wind's velocity to that of the 

 Anemometer, supposing friction null, which I found =2-999, and to 

 make corrections for that element of resistance. There were in this 

 three doubtful assumptions; that the mean ratio of the antagonist 

 pressures was the same as that at a perpendicular incidence ; that 

 Borda's formula is strictly applicable to curved surfaces moving in a 

 free current ; and that the resistance in quiescent air is the only one 

 to be considered in that term of the equation which includes v^. I 

 therefore had very little confidence in this theory. However, I tested 

 it by experiment. A small Anemometer was fixed to a whirling 

 machine which carried it through the air with velocities varying from 



II "69 miles an hour to 3'93. And 33 such observations gave for the 

 ratio 3-004. In water it gave 3-020, the results with 2, 3, and 4 cups 

 being almost identical. I tried to ascertain the agreement of this 

 instrument with the large one, by comparing their simultaneous read- 

 ings, but the irregularity of the wind, even at a few feet distance, 

 made the trial ineffectual. However, the agreement of the two 

 ratios given above seemed satisfactory, and I pursued the investigation 

 no farther, till my attention was recently recalled to it by a memoirf 

 byM.Dohrandt, of the Petersburgh Meteorological Observatory, which 

 appeared in the " Eepertorium flir Meteorologie," containing an 

 elaborate series of experiments made chiefly to determine the relation 

 between the rotation- velocity of the Cup Anemometer and that of the 

 wind. 



* Transactions, Vol. xxii., Part I., Science, p. 1.5.5. 

 t Roportoiinin fur Metooroloo-io, Bandiv., 1874. 



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