484 



SCIENCE 



[N. S. Vol. XXXVII, No. 952 



vance natural sciences, particularly chemis- 

 try. The sum will be about £18,000. 



The four largest courses in Harvard Col- 

 lege last year were government 1 with 479 

 undergraduates, economics 1 with 438, philos- 

 ophy E (elementary psychology) with 373, 

 and chemistry 1 with 333. The other two 

 courses which had over 200 undergraduates 

 were philosophy A, Professor Palmer's course 

 on the Greek philosophy, with 272, and his- 

 tory 1 with 250. 



The vice-chancellor of the University of 

 Cambridge has appointed April 19 for the 

 election to the Plumian professorship of as- 

 tronomy and experimental philosophy, vacant 

 by the death of Sir George Darwin. Candi- 

 dates are requested to send their names to the 

 vice-chancellor on or before April 11. 



Professor Henkel, of Konigsberg, has been 

 appointed director of the institute of pathol- 

 ogy at Breslau, as successor to Professor 

 Ponflck. 



Professor Hoffman, of Prague, has been 

 appointed to succeed Professor L. Hermann 

 as director of the institute of physiology at 

 Konigsberg. 



DISCUSSION AND COBEESPONDENCE 



A SIMPLE FORMULA FOR COMPUTING GYROSCOPIC 



FORCES m AN AEROPLANE 



The recent letter of Mr. James Means, in 

 Science for December 13, 1912, has called re- 

 newed attention to the problem of the gyro- 

 scopic action of a revolving motor as affecting 

 the safety of an aeroplane. The following 

 simple formula for computing the magnitude 

 of this gyroscopic action is offered as a con- 

 tribution toward the symposium suggested by 

 Mr. Means. 



We shall regard the rotating motor as con- 

 sisting essentially of a single wheel or disc, 

 whose axle is supported by two bearings at 

 known distances from the center of the wheel. 



If the aeroplane is compelled by the rudder, 

 or by a sudden gust of wind, to change its di- 

 rection of flight, this compulsion may be 

 thought of as due to the pressure of a flat 

 board against the side of the axle, at a point. 



say, in front of the wheel. As is well known, 

 the axle will resist this pressure on account 

 of the gyroscopic action of the rotating wheel, 

 and will strive to move off at right angles to 

 the impressed force, and in so doing, will 

 strive to carry the whole aeroplane with it. 

 If the wing surface of the aeroplane is large, 

 this motion will be practically entirely pre- 

 vented by the resistance of the air, and the 

 result of the gyroscopic action will be the set- 

 ting up of internal stresses in the framework 

 of the machine. 



The object of the following formula is to 

 provide a simple means of computing the 

 maximum value of these internal stresses in 

 any given case. 



Let a = the distance between the bearings, 

 measured along the axle, in feet, and let P=: 

 the pressure, due to gyroscopic action, on each 

 bearing, in pounds. Then P is given by the 

 following formula : 



Pa= (0.00034 ..■)Wr'Nn, 

 where 



W = weight of the rotating wheel, in pounds, 

 N = angular velocity of the rotating motor, in 



revolutions per minute, 

 n = the angular velocity with which the aero- 

 plane is turning out of its path, measured 

 in revolutions per minute, and 

 r = the radius of gyration of the wheel about its 

 axle, in feet. 



Note 1. — A fair estimate of the radius of 

 gyration can be obtained by a mere inspection 

 of the linear dimensions of the wheel. For ex- 

 ample, if the wheel were a homogeneous disc 

 of radius B, then r^ (0.7)5, approximately; 

 while if all the material were concentrated in 

 the rim, then r=^B; intermediate cases can be 

 judged by the eye. 



Note g.— The coefficient 0.00034 •■• repre- 

 sents the value of '^/%00g, where fif ^ 32 ft. 

 per sec. per sec. If the lengths r and a are 

 measured in centimeters instead of in feet, 

 this coefficient must be replaced by 0.0000112 • • ■. 

 If r and a are measured in inches, the coeffi- 

 cient is 0.000029 •••. 



As an illustrative numerical case, suppose 

 W = 167 lbs. (which is the actual weight of a 

 fifty-horse power Gnome motor), iV = 1,200 



