Jidy 14, 1 881] 



NATURE 



251 



.shown to be \V74V on the.first supposition, and 3WV4V on the 

 second. 



Three anemometers were tried, namely, one of the old Kew 

 standard pattern, one by Adie, and Kraft's portable anemometer. 

 Their dimensions, &c., were as follows :— 



(a) The Old Kau Standard. — Diameter of arms between 

 centres of cups 48 inches ; diameter of cups g inches. Fixed to 

 machine at 22 3 feet from the axis of revolution. 



((8) Adk's Aticmoiiieter. — Diameter of arms between centres of 

 cups I3'4 inches; diameter of cups 2'5 inches. Fixed to machine 

 at 207 feet from the axis of revolution. 



(y) Kraft's Portable Anemometer. — Diameter of arms between 

 centres of cups 8 '3 inches ; diameter of cups 3 '3 'nches. Fixed 

 to machine at 19 'lo feet from the axis of revolution. 



With each anemometer the experiments were made in three 

 groups, with high, moderate, and low velocities respectively, 

 averaging about 28 miles an hour for the high, 14 for the moderate, 

 and 7 for the low. Each group again was divided into two subor- 

 dinate groups, according as the cups were direct, in which case 

 the directions of rotation of the merry and of the anemometer 

 were opposite, or reversed, in which case the directions of the 

 two rotations were the same. 



The data furnished by each experiment were : the time 

 occupied by the experiment, the number of revolutions of the 

 merry, the number of apparent 'revolutions of the anemometer, 

 given by the difference of readings of the dial at the beginning 

 and end of the experiment, and the space S passed over by the 

 wind, deduced from the difference of readings of the fixed ane- 

 mometer at the beginning and end of the experiment. 



The object of the experiment was of course to compare the 

 mean velocity of the centres of the cups with the mean velocity 

 of the air relatively to the anemometer. It would have saved 

 some numerical calculation to have compared merely the spaces 

 passed througli during the experiment ; but it seemed better to 

 exhibit the velocities in miles per hour, so as to make the 

 experiments more readily comparable with one another, and 

 with those of other experimentalists. In the reductions 1 em- 

 ployed 4-figure logarithms, so that the last decimal in V in the 

 tables cannot quite be trusted, but it is retained to match the 

 correction for \V., which it seemed desirable to exhibit to o'oi 

 mile. 



On reducing the experiments with the low velocities I found 

 the results extremely irregular. I was subsequently informed by 

 Mr. Whipple that the machine could not be regulated at these 

 low velocities, for which it was never intended, and that it some- 

 times went round fast, sometimes very slowly. He considered 

 that the experiments in this group were of little, if any, value, 

 and that they ought to be rejected. They were besides barely 

 half as numerous as those of the moderate group. I have 

 accordingly thought it best to omit them altogether. 



In the complete paper tables are then given containing the 

 reduced results of the individual experiments, and from them 

 the mean results for the high and moderate velocities are col- 

 le;ted in the following table, in which are also inserted the mean 

 errors : — 



anemometer small or large in correcting for the wind. From 

 the mean errors \\e may calculate nearly enougli, by the usual 

 formula;, the probable errors of the \-arious mean percentages 

 for rotations opposite and alike. The probable errors of these 

 mean percentages come out as follows : — 



Kew, fo for high velocities ; 2-7 for moderate velocities. 

 Adie, 1-5 ,, ,, 2-0 ,, ,, 



Kraft, 0-9 ,, „ 1-8 „ ,, 



These probable eiTors are so small that it appears that for the 

 high and even for the moderate velocities the experiments are 

 extremely trustworthy, except in so far as they may be affected 

 by systematic sources of error. 



It may be noticed that the difference of the percentages ac- 

 cording as the directions of rotation of the anemometer and 

 of the merry are opposite or alike is greatest for the Kew, in 

 which the ratio of >- to R is greatest, ;• denoting the radius of 

 the arm of the anemometer, and R the distance of its axis from 

 the axis of revolution of the machine, and appears to be least 

 (when allowance is made for the two anomalous experiments in 

 the group " Adie H + ") for the Kraft, for which ;-/R is least. 

 In the Kraft indeed the differences are roughly equal to the 

 probable errors of the means. In these whirling experiments 

 r/R is always taken small, and we might expect the correction to 

 be made on account of the finiteness of R to be expressible in a 

 rapidly converging series according to powers of WR, say — 



A'^-B-(g.c(0 



The mean errors exhibited in the above table show no great 

 difference acoorrling as we supp"se the mrmrnt cf inprtii of the 



We may in imagination pass from the case of rotations opposite 

 to that of rotations ahke, by supposing R taken larger and larger 

 in successive exieriments, altering the angular velocity of revo- 

 lution so as to preserve the same linear velocity for the anemo- 

 meter, and supposing the increase continued until R changes 

 sign in passing through infinity, and is ultimately reduced in 

 m;ignitude to what it was at first. The ideal case of R = so is 

 what we aim at, in order to represent the motion of a fixed 

 anemometer acted on by perfectly uniform wind by that of an 

 anemometer uniformly impelled in a rectilinear direction in per- 

 fectly still air. We may judge of the magnitude of the leading 

 term in the above correction, provided it be of an odd order, by 

 that of the difference of the results for the two directions of rota- 

 tion. Unless therefore we had reason to believe that A' were O, 

 or at least very small compared with B', we should infer that 

 the w-hole correction for the finiteness of R is very small, and 

 that it is practically eliminated by taking the mean of the results 

 for rotations opposite and rotations alike. 



We may accept, therefore, tlie mean results as not only pretty 

 well freed from casual irregularities which \\ould disappear in 

 the mean of an infinite number of experiment.s, but also, most 

 probably, from the imperfection of the representation of a recti- 

 linear motion of the anemometer by motion in a circle of the 

 magnitude actually employed in the experiments. 



Before discussing further the conclusions to be drawn from 

 the results obtained, it will be well to consider the possible 

 influence of .systematic sources of error. 



I. Friction. — No measure was taken of the amount of friction, 

 nor were any special appliances used to reduce it ; the anemo- 

 meters were mounted in the merry just as they are used in actual 

 registration. Friction arising from the w-eight is guarded against 

 as far as may be in the ordinary mounting, and what remains of it 

 would act alike in the ordinary use of the instrument and in the 

 experiments, and as far as this goes, therefore, the experiments 

 would faithfully represent the instrument as it is in actual use. 

 But the bearings of an anemometer have also to sustain the 

 lateral pressure of the wind, which in a high wind is very con- 

 siderable ; and the construction of the bearing has to be attended 

 to in order that this may not produce too much friction. So far 

 the whirled instrument is in the same condition as the fixed. 

 But besides the friction arising from the pressure of the artificial 

 wind, a pressure w-hich acts in a direction tangential to the 

 circular path of the whirled anemometer, there is the pressure 

 arising from the centrifugal force. The highest velocity in the 

 experiments was about thirty miles an hour, and at this rate the 

 centrifugal force would be ab^ut three times the weight of the 

 anemometer. This pressure would considerably exceed the 

 former, at right angles to which it acts, and the two would 

 compound into one equal to the square root of the sum of their 

 squares. The resulting friction w-ould exceed a good deal that 

 arising from the pressure of the wind in a fixed anemometer with 

 the same velocitv of wi-;d, ratural or artificial, ard would 



