66 Mr. C. Chree on the Theory of 



experiment can hardly be absolutely conclusive. The com- 

 parison instituted by Mr. Dines * between the experimental 

 results he has found for a long narrow blade moving in air 

 and the formula established by Lord Rayleigh for an infinitely 

 long rectangular lamina, which a stream of perfect liquid 

 meets normally or obliquely, shows apparently a pretty fair 

 qualitative -\ agreement. But experiments under considerably 

 more varied circumstances would be required to determine 

 how closely the one set of results accorded with the other. 



The application of Lord Rayleigh's formula to ordinary 

 square and rectangular plates, instances of which are recorded 

 by Prof. Cleveland Abbe (I. c. p. 243), is, it need hardly be 

 said, entirely without mathematical warrant. 



The desirability of the solution of some simple three- 

 dimensional problem is increased by some recent contri- 

 butions of Lord Kelvin's to ' Nature ' J, if they are intended, 

 as seems the case, to throw doubt on the views of discontinuity 

 in fluid-motion current since KirchhofFs treatment of the 

 subject. 



While the exact formula for the resultant force experienced 

 by a finite solid moving in a perfect liquid is not known, there 

 is at least a pretty strong h priori probability § that it depends 

 on the square of the relative velocity, so long at least as the 

 velocity is small compared to that of sound in the medium, 

 and the body's course does not cross its own wake. With 

 the Robinson cups in air the former condition is satisfied, the 

 latter perhaps hardly, especially in short-armed instruments. 

 In experiments on whirlers, where the air is naturally at rest 

 and the cups in motion, a very perceptible current has been 

 observed by Robinson ||, DohrandtH, and others. In ordinary 

 use the wind's velocity so much exceeds that of the cups, that 

 if there were only a single cup an appreciable effect of this 

 kind could hardly arise. In the actual case of four cups it 

 can hardly be doubted, however, that during part at least of 

 its course the wind's action on any one cup is modified by the 

 presence of the others, and when the arms are short the 

 neglect of this interference might possibly lead to serious 

 error. 



* Proc. Roy. Soc. vol. xlviii. pp. 254-257. 



t See, however, Lord Kelvin, ■ Nature/ vol. 1. pp. 574-5. 



t Vol. 1. 1894, pp. 524, 549, 573, 597. 



§ Cf. Professor Stokes in Appendix to Dr. Robinson's paper, Phil. 

 Trans, for 1878, p. 819. 

 . || Cf. Dr. Robinson, Phil. Trans. 1878, pp. 783 et seq. 



^[ Repertorium fur Meteorologie, Bd. iv. Heft i. (see p. 32 of paper) & 

 Bd. vi. Heftl. 



