8 EXPERIMENTS IN" AERODYNAMICS 



or model which is the subject of experiment, shall not disturb or vitiate the 

 quantitative data which arc sought to be obtained. 



On the other hand, the effects of circular motion, as regards the behavior of 



the air in its enforced circulation, are only to be obtained, as I believe, empir- 

 ically, and by very elaborate experiments; the formula' that arc likely to 

 present themselves to the reader's mind for this computation, largely involving 

 the very errors of fact which the experiments here described are meant to 

 correct. This class of Correct inns is, then, only approximately calculable, and 

 we have to diminish their importance by the use of so large a circle that the 

 motion can be treated as (for our purpose) linear. To show that these corrections 

 are negligible in relation to such degree of accuracy as we seek, we may advan- 

 tageously consider such a numerical example as will present the maximum error 

 of this sort that obtains under the most unfavorable circumstances. 



Let this example be the use of a plane of the greatest length hereafter 

 described in these experiments, viz., 30 inches, and let us suppose its center to be' 

 at the end of a revolving arm 30 feet in length, which was that employed. 



Let us suppose the plane to be so disposed as to cause the effect of the 

 inequality of air resistance arising from the circular motion to lie a maximum, 

 which will presumably be the case if it is placed parallel to the arm of the whirling 

 table, so that there is also presumably the greatest possible difference between the 

 pressure on the outer and the inner half. Under these circumstances it is assumed 

 in the experiments detailed in the following chapters, that the whole plane may 

 lie treated as moving with the linear velocity of its center, and it will be now 

 Shown that this assumption is permissible. The portions of the plane as we pro- 

 ceed outward from the center, are exposed, on the whole, to a greater pressure, 

 and as we proceed inward to the center to a less. Using, in the absence of 

 any wholly satisfactory assumption, the well-known one implicitly given by New- 

 ton in the Principia, that the pressure of the air at every point of the plane is 

 strictly proportional to the square of the velocity with which it is moving (thereby 

 neglecting the secondary effect of the mutual action of the stream lines on each 

 other), the pressure at the inner end of the plane is proportional to (281 )' 826.6 ; 

 at the outer end to (31i)' 2 = 97<'>.f>, and at the center to (30)- = 900. The mean of 

 these pressures at the inner and outer ends, viz., 1)01. G, differs from the pressure 

 at the center by L.6, or less than one-fifth of one per cent., and a fortiori the inte- 

 grated pressure over the whole area in this and still smaller planes, differs from 

 the pressure computed with the velocity at the center, by less than the same amount. 

 The example will, it is hoped, make it sufficiently clear that such disturbing 

 effects of air-pressure arising from circular motion, are for our purposes negligible, 

 and the precautions taken against other detrimental effects, will be evident from a 

 consideration of the disposition of the apparatus employed in each case. 



