168 V. WALFRID EKMAN. 



in the surface of resistance that the body of the pendulum offers 

 to the current in different positions. 



Let M be the moment of the mass of the pendulum with 

 respect to its point of suspension, but with a deduction corres- 

 ponding to the volume of the water displaced, and multiplied by 

 the acceleration of gravity, g. Further let a be the length of 

 the pendulum down to the centre of the bob, and a the angle 

 of its deviation. The pressure of the current, P, against the 

 bob of the pendulum is then given by the equation 



a P ^= M tan a, 



or, as a is small (<^ 10°), 



p M 

 a 



a = 55 cm.; the length of the penduhmi down to its point 

 is 66 cm., and let r be the displacement of the pendulum, mea- 

 sured in centimetres. Calculating all lengths in centimetres, and 

 forces in grammes (properly 'in g dynes), we have then 



r, M r M . 



^==55-66 = 363Ö-^ ^^"^"^™'' ^ 



or if the sign k be introduced for the coefficient of r, 



P ^= k r grammes. 



As the shding weight in water weighs 136 gr., then 



M = 13Q d, B 



where d denotes the distance in centimetres of the sliding weight 

 below its zero-point, i. e. below the position it must assume in 

 order that the pendulum shall be completely released from the 

 influence of gravity. 



If the additional weight, which weighs 556 gr. in water, 

 be added, we obtain 



M = 69^ d B' 



