SCIENCE. 



[Vol. XIII. No. 32 j 



the winter of 1888-89 the temperature has been decidedly above the 

 normal in the northern United States, and normal or below normal 

 in the Southern States. As a consequence the pressure-gradient 

 in the upper air has been less steep than usual, the movements of 

 the upper-air currents and of storms has been comparatively slow, 

 and the winter over the entire country exceptionally free from sud- 

 den changes. The correlation of these facts seems to the writer to 

 promise much ; for, when the causes governing the distribution of 

 temperature are better understood, it seems evident that the mete- 

 orologist will be able to foretell for considerable intervals the special 

 characteristics of the weather to be expected over large areas. 



I trust these few facts may serve to further stimulate the interest 

 which is now being aroused in more exact and detailed cloud- 

 observations. H. Helm ClaytOn. 



Blue Hill Observatory, Readville, Mass., March 20. 



The Robinson Anemometer Factor. 



This name has been commonly applied to the earliest expression 

 of the law of relation between the velocities of the centres of the 

 cups of the Robinson anemometer and that of the wind which sets 

 them in rotation. Being a simple ratio between the two velocities 



■w 

 in question, or — as expressed in Science (xiii. p. 227), it is not 



V 



surprising that subsequent experiments should show, that not only 

 is the original factor, namely 3, incorrect, but that such a simple 

 relation can by no means be made to express with any reasonable 

 accuracy the anemometer law. It is surprising, however, consider- 

 ing the numerous experiments made by Dohrandt as well as others, 

 that writers and investigators of the present day should still adhere 

 to the use of the old anemometer " factor," and group together in 

 a general mean a large number of experiments at different veloci- 

 ties. 



The writer of the communication referred to above, in a dis- 

 cussion as to just what constitutes the true anemometer factor, has 

 presented the matter in a form that shows at once how futile it is 

 to use the old factor. Following Dohrandt and others, he assumes 

 that the velocity of the wind, w, and the velocity of the cup-centres, 

 V, bear the following relation to each other : — 



w ^ a + bv (l), 

 in which a and b are constants. The anemometer factor then be- 

 comes 



w b 



■w — a 

 We see from this equation, that, when w ^ a, x becomes infinite, 

 which corresponds to the condition when the wind is just too feeble 

 to start the cups. As w increases, x approximates more and more 

 to the value of b ; but, even between the small ranges of velocities 

 that occur in ordinary practice, x is entirely too variable to consider 

 constant, as shown by the values given in the above-mentioned 

 paper, and is too troublesome to use in calculation, especially since 

 the very equation from which it is computed is in much simpler 

 form, and, moreover, gives at once the velocity of the wind from 

 the cup-velocity, which is the quantity observed when the ane- 

 mometer is in use. The facts of the case, however, are not satis- 

 fied with even this degree of complication, and the anemometer 

 factor becomes quite out of the question. Dohrandt's fesults up 

 to 30 miles per hour are only approximately represented by an 

 equation like (i) ; and as in his experiments, owing to the com- 

 parative shortness of the whirling arm, the friction of the ane- 

 mometer at high velocities, from centrifugal action, was very great, 

 it may be shown that the approximation is even closer than it 

 actually should be. In fact, recent anemometer experiments upon 

 a whirling arm 35 feet long are in most cases represented accu- 

 rately by an equation of three terms : thus, 



■w = 225 + 'i-i^v — 0.0362 v^ (2), 

 the numerical values being those computed for an anemometer of 

 the Signal Service pattern, the cups of which are 4 inches in diame- 

 ter on arms 6.7 inches long. 



In view of this discussion, and taking into consideration that the 

 experiments just mentioned were made in a closed court under the 



most favorable circumstances, it would appear that the different 

 conclusions reached by the wind force committee of the Royal Me- 

 teorological Society in their open-air experiments are largely mis- 

 leading and in error, due probably to the serious influence of the 

 outside wind-movement. 



It seems that one effect of this wind-movement, outside of the 

 motion of the arms of the whirling-machine, is not clearly under- 

 stood, or at least receives little attention, and is nevertheless of 

 the greatest importance. 



If a uniform wind blows across the path of the anemometer 

 when being carried upon the whirling-machine, every one sees, 

 that, during one half of its motion, the anemometer is going more 

 or less with the wind, and against it during the remaining half. 

 That these effects do not fully neutralize each other, is clearly 

 shown in a mathematical analysis by which it is not difficult to find 

 the correction that should be applied ; but this is only small in 

 most cases, and is not very serious. A far greater error arises 

 from the effect this extra wind has in causing a very large and rapid 

 variation in the actual wind-movement experienced by the ane- 

 mometer, which, if its axis is being revolved on the whirler at the 

 rate of 15 miles an hour, and an extra wind of 4 miles per hour is 

 blowing, is at one point of its path moving through the air at the 

 rate of 19 miles an hour, and at the opposite point at the rate of 

 only 1 1 miles per hour ; the change, moreover, from the maximum 

 to the minimum being accomplished with great rapidity. The 

 mean velocity of the cups in this case may be shown to be such as 

 corresponds to a wind-velocity of nearly 19 miles per hour, the 

 reason being that the inertia of the cups keeps them spinning after 

 experiencing the maximum velocity ; so that during the minimum 

 velocity they do not slow up as they should, the only tendency to 

 do this being the air resistance to the backs of the cups ; and, as 

 this is considerably less than that felt by the front or concave sides 

 of the cups when the wind tends to increase their velocity, it must 

 follow that the mean velocity of the cups in a variable current is 

 considerably higher than such as would otherwise occur. A more 

 extended statement of this inertia effect, and numerous experiments 

 by which the theory is confirmed, have been already submitted for 

 publication in the American Meteorological Jourjial. 



The large and erratic variations in the results obtained by the 

 wind force committee with anemometers of the Robinson type are 

 to be attributed to this cause ; and the noticeably more uniform re- 

 sults obtained with the helicoid anemometer were due to the fact 

 that this instrument, being driven by the direct pressure of the 

 wind, and not by the difference of several pressures as is the case- 

 with the Robinson anemometer, is not subject to the inertia effect 

 just described. The explanation of this point, given in Science of 

 March 22, p. 227, to the effect that the helicoid anemometer was 

 tested with a vane attached to keep it in the wind, is hardly suffi- 

 cient to account for its seeming better performance. 



It follows from the above, that, if two sets of anemometer cups are 

 fitted up exactly alike except in weight, one having paper cups, for 

 instance, the latter will in the open air, exposed to a variable wind,, 

 give seemingly less wind than the former, both being reduced by 

 the same formula. Formula (2) given above is also only to be used 

 for perfectly uniform currents. 



Some mention was made in a " Note on the Robinson Anemom- 

 eter Constant," in Science of March 15, of the relative merits of the 

 recently invented helicoid anemometer and those of the Robinson 

 type. Judging by the description of the former, its mechanical con- . 

 struction cannot possibly be so simple as that of the latter ; and 

 as to what would happen to it and its delicate self-adjusting vanes 

 when exposed to the sleet and frost of a winter season, is by no- 

 means difficult to tell. The inventor himself considers the instru- 

 ment defective or unsatisfactory, owing to the ease with which the 

 readings are altered by bending the vanes. 



Robinson anemometers, to give the most satisfactory results in 

 the open air, and variable winds, should have very light cups. 



It may be added, in conclusion, that all anemometers acting by 

 direct wind-pressure are subject in much greater degree to varia- 

 tions in their law connected with temperature and pressure changes 

 than are those depending only on difference of pressures. 



C. F. Marvin.. 



Washington, D.C., March 25. 



