( 831 ) 



ill tlie slate of rest, and l»y ^ -f- i' the energy in the state of motion, 

 Avc have l\v the formnlae of this paper, up to tlie terms of the 

 second order, 



2 to'' 

 U' = U, 



an expression, agreeing in order of magnitude \\'ith tlie value used 



bv Trolton for estimating the etTect. 



U' 

 The intensity of the sudden jerk or impulse will therefore be — . 



Now, supposing tiie apparatus to be initially at rest, we may 

 compare tlie deflexion a, produced by this iin[)ulse, to the deflexion 

 a' which may be given to the torsion-balance by means of a constant 

 couple K, acting during half the vibration time. We may also 

 consider the case in which a swinging motion has already been set 

 up ; then the impulse, applied at the moment in which the apparatus 

 passes through the i)Osition of equilibrium, will alter the amplitude 

 by a certain amount ,? and a similar effect ;>' may be caused by 

 letting the couple K act during the swing from one extreme position 

 to the other. Let T be the period of swinging and / the distance 

 from the condenser to the thread of the torsion-balance. Then it is 

 easily found that 



a 3 :i: U' I 



-=-=: (39) 



According to Trouton's statements (" amounted to one or tAvo 

 ergs, and the smallest couple by Avhich a sensible deflexion could be 

 produced was estimated at 7,5 C. G. S. -units. If we substitute this 

 value for K and take into account that the velocity of the Earth's 

 motion is 3 X iO* c.M. per sec, we immediately see that (39) must 

 lia\e been a very small fraction. 



Mathematics. — " (Jhsi'rvatlon on tlw jMfper communicated on 

 Fehr. 2 7 1*' 1904 hji Mr. Brouwer: ''On a deco m position of th<3 

 continuous motion about a point of S^ into tu^o continuous 

 motions about of Sy's." By Dr. E. Jahnke. (Communicated 

 by Prof. D. J. Korte weg.) 



The above mentioned paj)er is connected with investigations of 

 Ferd. Caspary and with works pnblislie<l by me hi the years 

 1896 — 1901. Mr. Broiwkh not referring to these, T take the liberty 

 to remark llie following : Problems of the theory of the thetafunc- 

 tioiis on one hand and of ineciianics on the other hand have led 



