553 
It therefore was difficult for us to decide whether the different 
journeys would have to be discussed each by itself, or whether it 
would be preferable to take two or three together. And so finally 
it seemed best to follow both ways or rather try a number of 
different methods of calculation. 
As the smallest group of observations discussed together we have 
always taken those obtained during the stay at one station combined 
with those from the preceding and the following visit to the other 
station. Then only a real interpolation is possible, and there is besides 
another circumstance demanding this. The rate of a chronometer may 
not only be subject to chance perturbations during the transport, 
but there may also take place a systematic retardation or acceleration, 
which continues thronghout the duration of the transport. So a 
chronometer-correction calculated by means of extrapolation would be 
subject to systematic errors. On the other hand it is easy to see 
that in the calculation of a chronometer-correction for instance 
during a stay at Mecca from preceding and following observations 
at Jidda, the above mentioned error will be altogether eliminated 
for a moment exactly between those of the observations and that it 
would be small for other moments. 
In this respect therefore such a group of observations can yield 
accurate results. A uniform retardation or acceleration, however, 
cannot be taken account of in this way but very imperfectly. This 
will become clear when we represent the chronometer-corrections 
by formulae. These will then contain terms with the square of the 
time, and it will be easily seen that in a combination Jidda—Mecca— 
Jidda the influence of such a term and that of an error in the 
difference of longitude will not differ greatly. If, however, a com- 
bination Mecca—Jidda—Mecca is also discussed then the influence 
of a quadratic term on the difference of longitude will have the 
reverse sign. Hence it will be possible to eliminate that influence 
by forming combinations of the two kinds and taking the mean of 
their results. This approaches already the calculation of a quadratic 
formula from a longer period. 
I shall now communicate the numerical results obtained by means 
of Dent 2527 using the different methods of calculation. 
1. Results from the separate journeys. 
Journeys to Mecca (J.—M.—1J.). Determinations of time in Mecca 
compared with interpolated values between the observations at Jidda 
immediately before and after the journey. 
