0. E. SCHI0TZ. [NORW. POL. EXP. 



V\ V\ L __ \ 



where r = for p even, and =^5 for p odd. The sign p indicates the 



Z 



number of observations in each of the two series that are taken, and n the 

 number of coincidences between the times, a, and b q , of two corresponding 

 observations in the two series. The second term on the right will generally 

 be exceedingly small in proportion to the first, if n is not too small ; this term 

 can therefore be left out of consideration, and notice is only taken of it in 

 two or three observations made in Christiania (added as "Corr." in the last 

 column of the following tables). On one or two occasions during the expe- 

 dition, three series of observations were taken, the following formula, in 

 which the correction terms are left out of consideration, being employed for 

 their calculation: 



p [m* + H* + (m n) 2 -f (p 2 1)] c = 



a g , 6 5 , c q , are corresponding observations in the 3 series; n is the number 

 of coincidences between the first and the second series, m between the first 

 and the third. If m = 2n, the formula is reduced to 



c = - Y] (c a), 

 pm ^-< v 



so that the second series will be of no importance. 



The constants necessary for the reduction of the observed periods of 

 oscillation, have been determined, as already mentioned, by Colonel VON 

 STERNECK. Expressed in units of the 7th decimal place of the period of os- 

 cillation (in mean time), the correction for the temperature, T, is 44'23 for 

 every degree Celsius, and the correction for the resistance of the atmosphere, J, 

 5*53 for every per cent of the relative density, the density of the atmosphere 

 at zero, and a pressure of 76 cm. being taken as unity. If the rate of the 



