NICHOLS AND HULL. — PRESSURE DUE TO RADIATION, 577 



It was plaiu, therefore, that further elimination of the gas action must 

 be sought in ex230sures so short that the gas action would not have time 

 to reach more than a small fraction of its stationary value. This led to 

 the method of ballistic observations. 



The Ballistic Observations. 



In passing from the static to the ballistic observations it must always 

 be possible to compute the static equivalent of the ballistic swings. 

 Furthermore the exposures should be made as short as possible without 

 reducing the size of the swing below a value which can be accurately 

 measured. 



If the exposure lasts for one-half the period of the balance, the deflec- 

 tion, if the gas action be small and the damping zero, is equal to 2 d, 

 where 6 is the angle at which the torsion of the fibre will balance the 

 moment produced by the radiation pressure. If the duration of the 

 exposure be one-quarter of the period of the balance, the angle of deflec- 

 tion is 6'\/'2. The deflection is thus reduced by 30 per cent, but the 

 effect of the gas action is reduced in greater proportion. It was decided 

 therefore to expose for six seconds, one-quarter of the balance period. 

 Neglecting the gas action, the equation * of motion of the balance is 

 given by 



where k = the moment of inertia of the torsion balance, 

 c = the damping constant, 



G = the moment of torsion of the fibre for 0=1 radian, 

 and L = the moment of the radiation force. 



The solution of this equation is 



L ( -it ,/G e" > 



e=.-^{l-e «cosj/---,.| 



= ^|l-«~^'c082,r|,| (1) 



the constants of integration having been determined from the condition 

 that ^ = ^^ := when t = 0. 



* We are justified in using quantitatively this equation, containing a damping 

 term proportional to the velocity, because the amplitudes of tlie successive swings 

 of the torsion balance, when no energy fell upon the vanes, were found u.xperi- 

 nientally to follow accurately the exponential law. 

 VOL. XXXVIII. — 37 



