8 O. E. SCHIOTZ. [NORW. POL. EXP. 
P 
ele ay, ee Oh Os) 
C= qo) +o a pay 
1 1 
x b (p—24-+1) [0,41 — 0) + (@yo41— a) - 2 —* 9D} 0, — «a 
where r == for p even, and =” = : for p odd. The sign p indicates the 
number of observations in each of the two series that are taken, and » the 
number of coincidences between the times, a, and b,, 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 2 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: 
plm? +n? +(m—n)? +4 (pb? —Dlo= 
(ty, by, C, are corresponding observations in the 3 series; ” is the number 
of coincidences between the first and the second series, a between the first 
and the third. If m—=2n, the formula is reduced to 
1 Pp 
Cc “pm 2 (¢y— Ay); 
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 
Srerneck. Expressed in units of the 7th decimal place of the period of os- 
cillation (in mean time), the correction for the temperature, z, is 4423 for 
every degree Celsius, and the correction for the resistance of the atmosphere, 4, 
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 
