578 PROCEEDINGS OF THE AMERICAN ACADEMY. 



When 

 <=-,^ = -^and^=— f -e -^ co827r^ + e « -^sin27r-J (2) 



T 



The light being cut oil when < = — - , the equation of motion becomes 



57 + ^^57--^^ (^) 



the solution of which is 6 = Ae "^ cos ( 2 tt-^. + a 1 where A and a can 



( 2 7r— + a j 



be determined by the conditions imposed by equation (2). Neglecting 

 very small quantities, the value of the amplitude A is expressed by the 

 equation 



where r is the ratio of successive amplitudes of the damped vibrations. 

 If r = 1, that is if the motion is undamped, ^ = -^ \/2. In the partial 



vacuum used in the experiments (16 mms. of mercury, a value chosen 

 from the curves in Fig. 5), r was found to be equal to 0.783 ; conse- 

 quently A = 1.357 — . (5) 



From this it is seen that the total angle of deflection of the torsion 

 balance in the ballistic measurements is equal to 1.357 times the augle 

 at which the moment of the torsion of the fibre balances the moment of 

 the radiation pressure. 



The duration of exposure was always six seconds without appreciable 

 error, but the period of the balance on account of slight accidental shift- 

 ing of small additional masses upon the counterpoise weight Wg (Fig. 2), 

 differed from twenty-four seconds sometimes by one per cent. It is 

 necessary therefore to find the error in the deflection due to this variation 



T 



in the period. This is done by making t =-—-{- S in equation (2) and 



in introducing the new conditions in equation (3). But it is simpler and 

 sufficiently accurate to assume the motion as undamped. For this condi- 

 tion, the amplitude 



J = ||2 + 2 sin2;r|,|^ = ^^1 ^1 + ^|,^ nearly. 



