NO. 8.] PENDULUM OBSERVATIONS. 61 



sider that the irregular movements which could be imparted to the ship, through 

 her drifting with the ice, would cause an increase in the observed value for 

 the acceleration at each separate place, we may conclude from the above re- 

 sults, that the force of gravity over the polar basin cannot be greater than 

 the normal. On account of the close agreement between the observed and 

 the calculated values, it seems to me reasonable to assume that the force of 

 gravity over the polar basin is normal. The circumstance that on January 

 16th, 1894, the acceleration was found too small, will be more fully dis- 

 cussed later on. 



At the two stations on the 14th and 23rd November, separate pendulums 

 were fortunately employed ; and as the stations are only about 26 km. distant 

 from one another, and very nearly in the same latitude, we may consider a 

 combination of these two observations to be equal to a complete observation 

 with both pendulums at the same station. As the latitude is not far off 86, 

 the period of the oscillation may be reduced so as to apply to that latitude. 

 The reduction-formula that may be employed is 



,6 sin 2o> sinl' 



where <p and q> are the latitude at the two places, and 6 the constant in 

 the formula 



g = k (1 + 6 sin 2 gr>). 



As the gravity may be considered normal, we may take for 6 the 

 value in Helmert's formula, and put & = 0'00531. 



By this means we find that the correction to a latitude of 86 



for the period of pendulum 33, Nov. 14, = 3X10' 

 34, Nov. 23, = - 7 X 10-'; 



and the period in a latitude of 86 thus becomes, 



for pendulum 33, 5,,, = 0-505601 1 ) 



} Mean, 0'5057268. 

 34, ,, = 0-5058524 J 



If the observations of the 29th and 30th April, 1896, are reduced in a 

 similar way to one latitude, namely 84, the reduction 



for April 29th, = + 12 X 10 " 7 

 , 30th, = + 10X10~ 7 



