434 



Proceedings of the Royal Irish Academy. 



Notwithstanding these defects in M. Dohrandt's experiments, I 

 think they show the necessity of further investigation ; and as I am 

 convinced of the advantages which this instrument possesses as a 

 recorder of the wind's velocity, I think it may be useful to point out 

 the processes by which, as it seems to me, a closer approximation to its 

 theory may be obtained, and the co-efficients of the resulting equation 

 deduced with sufficient certainty. If in doing this I seem to go too 

 minutely into details, I must plead in excuse the great complexity of 

 the inquiry, and my desire to omit nothing of importance. 



Considering a single cup of an Anemometer exposed to a current 

 of air of velocity F", making an angle with its arm, and incident on 

 its concave surface ; its pressure on that sur- 

 face = SV~ X a; a being a co-efficient depending 

 on 6, and on the figure of the cup, and S the 

 area of its mouth : the power of this pressure to 

 make the cup revolve is SaV^ x sin 6. But 

 suppose the cup in motion with the velocity v, 

 and convex foremost, this motion lessens the 

 effect of V, and instead of V, we must use the 

 resultant of it and v. This resultant also makes 

 with the arm an angle <^, difi^erent from ; let 

 AR be the arm, AV a. line proportional to V. 

 AB X to AR, as v ; the diagonal BV oi the 

 parallelogram under them = R the resultant 

 when Fand v are in the same direction ; CA = R' 

 that when they are in opposite ones. Drawing 

 BB II to AR, VBB = <^. It is obvious that R~ = V^~-i- v"" + 2Vv sin 6, and 



Fsin 6 + V 

 R or R' ' 



Fcos^ 

 R or R" 



the lower signs belonging to the case R'. Hence for Sa V^ sin 6 we 

 must use SaR^ sin cji = Sa {F^+v'^ + 2Vv sin ^) x sin <^. <;^ is best found 

 by the equation — 



4. . ^. a secants . V 



tan G) = tan a + , m being = — . 



m V 



It will be shown (V.) that m, though changing with v, varies 

 little ; and taking its mean value, no important error will arise from 

 assuming it constant. 



This is the positive or impelling pressure. (1.) 



When sin 6-^„ it should vanish ; but in fact I found that one cup 

 exposed to the wind has a positive pressure far beyond this point, not 

 resting till 210°. I could not determine the opposite point of rest, 

 because the least eddy of the wind set the cup in rotation. I do not 

 know whether this curious fact arises from the wind eddying into the 



