32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62 



The equation of motion then is : 



But AIq = Ms by the initial condition of equihbrium. Let 

 then 



The sokition of this equation is well known to be : 



^ = C^ 2/ cos j tj (K-cm') 4 - -/^ +« } ' 



where C and a are arbitrary constants. If time be counted when the 

 amplitude of swing is a maximum, then cos^ f"=i> si^<i ^ = ^0- the 

 initial displacement. Also if the number of beats be counted by 

 observing- the times for succeeding maxima, a plot of amplitude on 

 time will have for its equation the simple form : 



fit 



The coefficient /x is the logarithmic decrement of the oscillation and 

 must be numerically positive to insure that the oscillation dies out 

 with time. 



The apparatus was fitted with a small reflecting prism by which a 

 pencil of light was deflected toward a ground glass plate set in the 

 roof of the tunnel. Nine lines spaced 0.2 inch were ruled on this plate. 

 With the model at rest the beam of light was brought to a sharp focus 

 on the line marked zero. By means of a trigger the observer started 

 an oscillation of the model, and the spot of light was observed to 

 oscillate across the scale. The time t was observed in which an 

 oscillation was damped from an amplitude of 9 to an amplitude of i, 

 for example. 



Then : log, '' = ^ ^ = log, Q, and knowing / and t, u. is calculated. 



Preliminary tests showed that the same value of ^ was obtained 

 whether the timing stopped at ^=5, 4, 3, 2, or i. 



Oscillation tests were made at five wind velocities varying from 5 

 to 35 miles per hour. The coefficient /,(. appeared to vary approxi- 

 mately as the first power of the velocity. 



Similar tests were made with the model for no wind to determine 

 fiQ, which may be said to be due almost wholly to friction and very 

 slightly to the damping of ap})aratus and model moving through 

 the air. 



