294 
ENGINEERING: E. B. WILSON 
Conclusions. — 1. The stars of class B show systematic differences in 
the proper motions in the two regions of the Milky Way at right an- 
gles to the direction of solar motion. 
2. The solar velocities derived from the B stars in the northern and 
southern hemispheres separately differ, that from the northern stars 
being the smaller. 
3. These conditions appear to be best explained by a general motion 
of rotation of the system of stars in a retrograde direction about an axis 
perpendicular to the Milky Way. 
The details of these preliminary investigations will be published else- 
where. 
THEORY OF AN AEROPLANE ENCOUNTERING GUSTS 
By Edwin Bidwell Wilson 
DEPARTMENT OF MATHEMATICS. MASSACHUSETTS INSTITUTE OF TECHNOLOGY 
Received by the Academy. April 10, 1916 
A number of references to the theory of the stability of aeroplanes may 
be given/ but on their behavior in gusts little has been printed,^ though 
much is probably known and held secret by foreign governments. Last 
summer I was asked to develop a theory of the effect of gusts upon 
(symmetric) aeroplanes, in particular upon a definite machine of which 
the aerodynamical coefficients were furnished me by Mr. Hunsaker. 
Two questions were to be answered: First, what is the effect of a gust 
upon the longitudinal motion in the uncontrolled machine; second, what 
is the effect when the machine is so constrained by an automatic device 
as to maintain its axis horizontal? My report, submitted to our National 
Advisory Committee for Aeronautics, will appear as a part of the Report 
of the National Advisory Committee for Aeronautics, 1915 (Senate Docu- 
ment No. 268, 64th Congress, 1st Session). By the courtesy of the Com- 
mittee I am permitted to give here a brief account of this work. 
In treating the motion of an aeroplane the machine is referred to a set 
of moving axes x, y, z fixed in the body, and directed backward, to the 
left, and upward in normal horizontal flight with velocity — U. De- 
partures from this standard condition of flight are treated by the method 
of small oscillations. 11 U u, v, w, p, q, r be the linear and angular 
velocities in the disturbed motion and if Ui, Vi, Wi, pi, qi, r\ be the linear 
and rotational velocities of the gusts (taken with the proper sign), the 
aerodynamic forces acting upon the machine will vary from those acting 
in the standard conditions by amounts which may be determined by the 
eighteen aerodynamic constants Xu, Xw, Xq, Zu, Zw, Zq, Mu, Mw, Mq, 
