252 



NATURE 



\_7uly 14, 1 88 1 



ieiiiibly reduce the velocity registered, and accordingly raise 

 the coefficient which Dr. Robinson denotes by m, the ratio, 

 namely, of the velocity of the wind to the velocity of tlie 

 centres of the cups. It may be noticed that the percentages col- 

 lected in the above table are very distinctly lower for the moderate 

 velocities than for the high velocities. Such an effect would be 

 produced by friction ; but how far the result would be modified 

 if the extra friction due to the centrifugal force were got rid of, 

 and the whirled anemometer thus assimilated to a fixed anemo- 

 meter, I have not the means of judging, nor again how far the 

 percentages would be still further raised if friction were got rid 

 of altogether. 



Perhaps the best way of diminishing friction in the suppport of 

 an anemometer is that devised and employed by Dr. Robinson, 

 in which the anemomeser is su| ported near the top on a set of 

 spheres of gun-metal contained in a box with a horizontal bottom 

 and vertical side which supports and confines them. For vertical 

 support this seems to leave nothing to be desired, but when a 

 strong lateral pressuie has to be supported as well as the weight 

 of the instrnment, it seems to me that a slight modification of 

 the mode of support of the balls might be adopted with advan- 

 tage. When a ball presses on the bottom and vertical side of its 

 box, and is at the same lime pressed down by the horizontal 

 disk attached to the shaft of the anemometer which rests on the 

 balls, it revolves so that the instantaneous axis is the line joining 

 the points of coi t ct v\i[h the fixed bcx. But if the lateral force 

 of the wind presses the shaft against the ball the ball cannot 

 simply roll as the anemometer turns ronnd, but there is a slight 

 amount of rubbing. 



This however may be obviated by giving the surfaces where 

 the ball is in contact other than vertical or horizontal direction. 



Let A B be a portion of the cylindrical shaft 01 an anemometer ; 

 c D the axis of the shaft ; E F G H i a section of the fixed box or 

 cup containing the balls ; l M N a section of a conical surface 

 fixed to the shaft by which the anemc meter rests on its balls ; 

 F I K M a section of one of the balls ; F, i, the points of contac 



of the ball with the box ; M the point of contact with the sup- 

 porting cone ; K the point of contact, or all but contact, of the 

 b:ill with the shaft. The tall is supposed to be of such size that 

 when the anemometer simply rests on the balls by its own weight, 

 being turned perhaps by a gtntle wind, there are contacts at the 

 points M, F, I, while at K the ball and shaft are separated by a 

 space which may be deemed infinitesimal. Lateral pressure 

 from a stronger wind will now bring the shaft into contact with 

 the ball at the point K also, so that the box on the one hand and 

 the shaft with its appendage on the other will bear on the ball 

 at four points. The surface of the box, as well as that on the 

 cone L N, being supposed to be one of revolution round C D, 

 those four points will be situated in a plane thn ugh c D, which 

 will pass of course through the centre of the ball. 



If the ball rolls without rubbing at any one of the four points 

 F, I, K, M as the anemometer turns round, its instantaneous axis 

 must be the line joining the points of contact F, I, with the fixed 

 box. But as at M and K likewise there is nothing but rolling, 

 the instantaneous motion of the ball may be thought of as one 

 in which it moves as if it were rigidly connected with the shaft 

 and its appendage, combined with a rotation over LNAB sup- 

 posed fixed. For the two latter motions the instantaneous axes 

 are CD, M K respectively. Let M K produced cut c D in o. Then 

 since the instantaneous motion is compounded of rotations round 

 two axes passing through o, the instantaneous axis must pass 

 through o. But this axis b F i. Therefore F 1 must pass through 

 O. Hence the two lines F i, M K must intersect the axis of the 



shaft in the same point, which is the condition to be satisfied in 

 order that the ball may roll without rubbing, even though im- 

 pelled laterally by a force sufficient to cause the side of the shaft 

 to bear on it. The size of the balls and the inclinations of the 

 surfaces admit of considerable latitude subject to the above con- 

 dition. The arrangement might suitably be chosen something 

 like that in the figure. It seems to me that a ring of bal's 

 constructed on the above principle would form a very effective 

 upper support for an anemometer whirled \\\\h its axis vertical. 

 Possibly the balls might get crowded together on the outer side 

 by the effect of centrifugal force. This objection, should it be 

 practically found to be an objection, would not of course apply 

 to the proposed sys'.em of mounting in the case of a fixed 

 anemometer. Below, the shaft would only require to be pro- 

 tected from lateral motion, which could be done either by friction 

 wheels or by a ring of balls constructed in the usual manner, as 

 there would be only three points of contact, 



2. Influence on the Anemometer of its own Wahe.—'Zy 'CaS.'i I 

 do not mean the influence which one cup experiences from the 

 wake of its predecessor, for this occurs in the whirling in almost 

 exactly the same way as in the normal use of the instnmrent, but 

 the motion of the air which remains at any point of the course of 

 the anemometer in consequence of the disturbance of the air by 

 the anemometei w'hen it was in that neighbourhood in the next 

 preceding and the still earlier revolutions of the whirling 

 instrument. 



It seems to me that in the open air, where the air impelled by 

 the cups is free to move into the expanse of the atmosphere, 

 instead of being confined by the walls of a building, this must 

 be but small, more especially as the wake would tend to be 

 carried away by what little wind there might be at the time. On 

 making some inquiries from Mr. Whipple as to a possible vorti- 

 cose movement created in the air through which the anemometer 

 passed, he wiote as follows : — " I feel confident that under the 

 circumstances the tangential motion of the air at the level of the 

 cups was so small as not to need consideration in the discussion 

 of the results. As in one or two points of its revolution the 

 anemometer fassed close by some small trees in fnll leaf, we 

 should have observed any eddies or artificial wind had it existed, 

 but I am sure we did not." 



3. Influence of the Variation of the ]Viml ; first, as regards 

 Variations which are not Rapid. — Duiing the twenty or thirty 

 minutes that an experiment lasted there would of course be 

 numerous fluctuations in the velocity of the wind, the mean result 

 of which is alone recorded. The period of the changes (by 

 which expression it is not intended to assert that they were in 

 any sense regularly periodic), might be a good deal greater than 

 that of the merry, or might be comparatively short. In the 

 high velocities-, at any rate, in which one revolution took 

 only three or four seconds, the supposition that the period of 

 the changes was large compared with one revolution is probably 

 a good deal nearer the truth than the supposition that it is small. 



On the former supposuion the correction for the wind during 

 two or three revolutions of the meriy would be given by the 

 formulce already employed, taking for W its value at the time. 

 Consequently the total correction will be given by the formulze 

 already used if we substitute the mean of W- for the square of 

 mean W. The former is necessarily greater than the latter, but 

 how much we cannot tell without knowing the actual variations. 

 We should probably make an outside estimate of the effect of the 

 variations if we supposed the velocity of the wind twice the 

 mean velocity during half the duration of the experiment, and 

 nothing at all during the remainder. On this supposition the 

 mean of W- would be twice the square of mean \V, and the 

 correction for the wind would be doubled. At the high velocit'es 

 of revolution, the whole correction for the wind is so very small 

 that the uncertainty arising from variation as above explained is 

 of liitle importance, and even for the moderate velocities it is not 

 serious. 



4. Influence of Rapid Variations of the ;^z'«(/.— Variations of 

 which the period is a good deal less than that of the revolutions 

 of the whirling instrument act in a very different manner. The 

 smallness of the corrections for the wind hitherto empl yed 

 depends on the circumstance that with uniform wind, or even 

 with variable wind, when the period of variation is a good deal 

 greater than that of revolution of the merry, the terms depending 

 on the first power of \v, which letter is here used to denote the 

 momentary velocity of the wind, disappear in the mean of a 

 revolution. This is not the case when a particular velocity of 

 wind belongs only to a particular part of the circle described by 



