64 Mr. C. Chree on the Theory of 



from the " Kew " or standard pattern. It is pretty generally 

 suspected * that a lower value for the constant would give 

 more accurate results. Formulae involving two or three con- 

 stants have also been proposed and applied in experimental 

 investigations by Robinson, Dohrandt (I. c), Stellingf, 

 Dubinsky J, and others, but they have not come into general 

 use, at least in this country. 



Experiments involving comparisons of different anemo- 

 meters have been fairly numerous. An account of the principal 

 ones prior to 1887 is given by Professor Cleveland Abbe in 

 the ' Report of the Chief Signal Officer of the Army to the 

 Secretary of War/ part ii., Washington 1887, and a biblio- 

 graphy of the subject has been given more recently by 

 Mr. Dines on pp. 36-37 of vol. xvi. of the ' Quarterly Journal 

 of the Royal Meteorological Society.' More recent investiga- 

 tions have been carried out by Mr. Dines himself in papers 

 printed in the ( Proceedings ' of- the Royal Society and the 

 ' Quarterly Journal § of the Royal Meteorological Society/ 



A study of some of the literature of the subject has led me 

 to think that a critical examination into certain theoretical 

 aspects of the Robinson cup- anemometer may be of service. 



Nature of the Problem. 



§ 2. For a final treatment we require in the first instance 

 an exact determination of the physical conditions. This in- 

 volves a knowledge of the true values of the normal and 

 tangential forces experienced by the Robinson cups and arms 

 during slow or rapid motion through the air, and also of the 

 frictional forces which arise during the relative motion of the 

 variously lubricated metal surfaces. 



The cups, be it remembered, are not travelling in straight 

 lines inclined at a constant angle to the wind's direction, but 

 rotate round an axis whose distance from the centres of the 

 cups is not a very large multiple of their diameters. Thus 

 at any given instant the relative velocity of the wind to a 

 cup's surface varies appreciably over the cup, and even when 

 the wind is steady the relative velocity at any one point on 

 the surface is continually changing. 



The superficial area of the arms and the accompanying 

 stays is usually small relative to that of the cups, but in a 



* See for instance p. 27 of a paper by Dohrandt in Repertorium fiir 

 Meteorologie, Bd. vi. Heft i. ; also " Report of Wind Force Committee," 

 drawn up by Mr. Dines, • Quarterly Journal Iioy. Met. Soc' vol. xvi. 

 pp. 26 et seq. 



t Rep. filr Meteoroloyie, Bd. ix. t Ibid- Bd. xi. 



§ See specially vol. xviii. p. 105. 



