July 14, 1 88 1 J 



NATURE 



253 



i 



the anemometer in one revolution. In this case there will in 

 general be an outstanding effect depending on the first power of 

 W, which will be considerably larger than that depending on 

 W-. Thus suppose the velocity of whirling to be thirty miles an 

 hour, and the average velocity of the wind three miles an hour, 

 the correction for (he wind supposed uniform, or if variable, 

 then with not very rapid variations, will be comparable with 

 I per cent, of the whole ; whereas, with rapid variations, the 

 effect in any one revolution may be comparable with 10 per 

 cent. There i-, however, this important difference between the 

 two ; that whereas the correction depending on the square leaves 

 a positive residue, however many experiments be made, the 

 correction depending on the first pow-er tends ultimately to dis- 

 appear, unless there be some cause tending to make the average 

 velocity of t)ie wind different for one azimuth of the whirling 

 instrument from what it is for another. This leads to the con- 

 sideration of the following conceivable source of error. 



S. Influence oj Partial Shelter of the Whirling, Itistrtwient. — 

 On visiting the meriygo-round at the Crystal Palace, I found it 

 mostly surrounded by trees coming pretty near it, but in one 

 direction it w'as approached by a broad open walk. The conse- 

 quence is that the anemometer may have been unequally shel- 

 tered in different parts of its circular course, and the circum- 

 stances of partial shelter may have varied according to the 

 direction of the wind. This would be liable to leave an 

 uncompensated effect depending on the first power of W. I do 

 not think it probable that any large error was thus introduced, 

 but it seemed necessaiy to point out that an error of the kind 

 may have existed. 



The effect in question would be eliminated in the long run if 

 the whirling instrument were capable of reversion, and the 

 experiments were made alternately with the revolution in one 

 direction, and the reverse. For then, at any particular point of 

 the course at which the anemometer was more exposed to wind 

 than on the average, the wind would tend to incre.ase the velocity 

 of rotation of the anemometer for one direction of revolution of 

 the whirling instrument just as much, uldmately, as to diminish 

 it for the other. Mere reversion of the cups has no tendency to 

 eliminate the error arising from unequal exposure in different 

 ]iarts of the course. And even when the whirling instrument is 

 capable of reversion it is only very slowly that the error arising 

 from partial shelter is eliminated compared with that of irregu- 

 larities in the wind ; of those irregularities, that is to say, which 

 depend on the first power of W. For these irregularities go 

 through their changes a very great number of times in the cour.se 

 of an experiment la-ting perhaps half an hour, whereas the effect 

 of partial shelter acts the same way all through one experiment. 

 It is very desirable therefore that in any whirling experiments 

 carried on in the open air, the condition of the whirling instru 

 men! as to exposure or shelter sliould be the same all round. 



The trees, though taller than the merry when I visited the 

 place last year, were but young, and must have been a good deal 

 lower at the time that the experiments were made. Mr. Whipple 

 does not think that any serious error is to be apprehended from 

 exposure of the anemometer during one part of its course and 

 shelter during another. 



From a discussion of the foregoing experiments it seems to me 

 that the following conclusions may be drawn : — 



1. That, at least for high winds, the method of obtaining the 

 factor for an anenometer, which consists in whirling the instru- 

 ment in the open air, is capable, with proper precautions, of 

 \ielding very good results. 



2. That the factor varies materially with the pattern of the 

 anemometer. Among those tried, the anemometers with the 

 larger cups registered the most wind, or in other words required 

 the lowest factors to give a correct result. 



3. That with the large Kew- pattern, which is the one adopted 

 by the Meteorological Office, the register gives about 120 per 

 cent, of the truth, requiring a factor of about 2"5, instead of 3. 

 Even 2'5 is probably a litth too high, as friction would be intro- 

 duced by the centrifugal force, beyond what occurs in the normal 

 use of the instrnment. 



4. That the factor is probably higher for moderate than for 

 high velocities ; but whether this is solely due to friction the 

 experiments do not allow us to decide. 



Qualitatively considered, these results agree well with those of 

 other experimentalists. As the factor depends so much on the 

 pattern of the anemometer it is not easy to find other results with 

 which to compare the actual numbers obtained, except in the case 

 the Kew standard. The results obtained by Dr. Kobinson, by 



rotating an anemometer of this pattern without friction purposely 

 applied are given at pp. 797 and 799 of the Phil. Trans, for 

 187S. The mean of a few taken with velocities of about 27 

 miles an hour in still air gave a factor 2 -36, instead of 2-50, as got 

 from Mr. Jeffery's experiments. As special anti-friction appliances 

 w ere used by Dr. Robinson, the friction in Mr. leffery's experi- 

 ments was probably a little higher. If such were the case the 

 factor ought to come out a little higher than in Dr. Robinson's 

 experiments, which is just what it does. As the circumstances 

 of the experiments were widely different with respect to the 

 vorticose motion of the air produced by the action of the anemo- 

 meler in it, we may, 1 think, conclude that no verj' serious error 

 is to be apjirehended on this account. 



In a later paper (/%//. Trans, for iSSo, p. 1055), Dr. Robin- 

 son has determined the factor for an anemometer (among others) 

 of the Kew pattern by a totally different method, and has 

 obtained values considerably larger than those given by the 

 former method. Thus the limiting value of the factor w 

 corresponding to very high ve!oci:ie,s, is given at p. 1063 as 

 2 '826, whereas the limiting value obtained by the former method 

 was only 2-286. Dr. Kobinson has expressed a preference for 

 the later results. I confess I have always been disposed to 

 place greater reliance on the results of the Dublin experiments, 

 which were carried out by a far more direct method, in which I 

 cannot see any flaw likely to account for so great a difference. 

 It would be interesting to try the second method in a more 

 favourable locality. 



I take this opportunity of putting out some considerations 

 respecting the general formula of the anemometer, which may 

 perhaps not be devoid of interest. 



The problem of the anemometer may be stated to be as 

 follows : — Let a uniform wind wiih velocity V act on a cup 

 anemometer of given pattern, causing the cups to revolve with 

 a velocity v, referred to the centre of the cups, the motion of 

 the cups being retarded by a force of friction F ; it is required to 

 determine f as a function of V and F, F having any value from 

 o, corresponding to the ideal case of a frictionless anemometer, 

 to some limit F,, which is just sutficient to keep the cups from 

 turning. I will refer to my appendix to the former of Dr. 

 Robinson's papers [Phil. Trans, for 1S78, p. 81S), for the 

 reasons for concluding that F is equal to V-, multiplied by a 

 function of V/z/. Let 



VA. = |, F/V==„, 



then if we regard | and i\ as rectangular coordinates we have to 

 determine the form of the curve, lying within the positive 

 quadrant {or;, wh'ch is defined by those co-ordinates. 



We may regard the problem as included in the -more general 

 prolilem of determining v as a function of V and F, where V is 

 positive, but F may be of any magnitude and sign, and there- 

 fore t' also.' Negative values of F mean, of course, that the 

 cups, instead of being retarded by friction, are acted on by an 

 impelling force making them go faster than in a frictioilless 

 anemometer, and values greater than F, imply a force sufficient 

 to send them round with the concave sides foremost. 



* Of course v must be supposed not to be .so large as to be comparable 

 with the velocity of sound, since then the resistance to a body impelled 

 through air, or having air impinging on it, no longer varies as the square of 

 the velocity. 



