559 
rate of the watch. If e.g. a daily acceleration of 03.10 takes place, 
then a linear interpolation in the middle between two time-determinations 
with an interval of 12 days will yield a result that is 15.8 in error 
and from a journey Ji-—Me—Ji the difference of longitude will be 
found so much too great. 
Now it appears, however, that the change of rate of N°. 80 was 
more complicated. When it was transported after a period of rest, 
it showed a considerable acceleration and then it continued for some 
time to show this accelerated rate unaltered. In such a case the error 
committed by linear interpolation will be much smaller, but it will 
not be easy to account for. Finally 1 have deduced results by 
means of quadratic formulae as well as by linear interpolation. 
We thus found : 
1st Journey. 
a. By interpolation between the last preceding and the next 
following observations at Jidda 
Febr. 14 + 2™ 35575 
15 35.85 
16 35.48 
Mean + 2m 3569 
b. By linear formulae + 2m 37:85 (+ 1:63) 
c. By quadratic formulae + 2m 35805 (+ 0°72) 
As the linear formulae represent the observations very unsatisfactorily, 
the result thus obtained was rejected and we adopted as the result 
yielded by the 1st journey the mean of the results a and c 
+ 2" 358,37. 
3d Journey. 
a. By interpolation between the nearest ubservations at Jidda 
March 11 + 2™ 34°51 
12 34.51 
14 35.49 
15 35.80 
16 35.44 
d 7, 35.33 
Mean + 2m 3518 
b. By linear formulae + 2m 35569 (= 0°59) 
c. By quadratic formulae -+ 2m 33592 (+ 049) 
