55) 
first journey to Mecca. But of however much value this long series 
is for the investigation of the watches and of the observations them- 
selves, it cannot be of any immediate use for the derivation of the 
longitude. The longer the periods that are discussed the greater does 
the uncertainty become in the calculated rates and corrections of 
the watches, and soon its influence surpasses that of the errors of 
the observation. The great difficulty lying here in the answer to the 
question at what distance from the journey determinations of time 
may still be used to advantage, this will certainly not be the case 
for the observations in January. Finally only the observations of 
Febr. 6-—12 have been used as a first group. 
In the following we shall indicate Leroy’s watches with the 
numbers they have in the Dutch Navy. 
a. Chronometer Dent 2527. 
This was taken by Mr. Sarim on all his journeys to Mecca and 
we have therefore at our disposal 4 groups of observations at 
Jidda, each including 4 nights, and between these 3 groups at Mecca 
with resp. 3, 3 and 6 determinations of time. Hence the discussion 
of the results obtained with this chronometer offers the best oppor- 
tunity for comparing the different methods that may be followed 
for the deduction of the difference of longitude. 
This deduction must be based on the comparison of observed 
chronometer-corrections at one place with interpolated corrections 
with regard to the local time of the other, whether that interpolation 
is made directly or in such a way, that we represent the corrections 
found for both stations by formulae differing only in the value of 
the constant term 
An exhaustive criticism of these methods of calculation has been 
given by W. Srruve on the occasion of his discussion of the results 
of the chronometer-expeditions *) executed between Pulkowa and 
Altona. He arrived at the conclusion that for observations made 
during a long period with a great number of journeys in both 
directions, as in his case, the representation by one formula, which 
must then contain a rather great number of powers of the time, 
would be unpractical. Our case, however, is somewhat different. 
The number of journeys and the duration of each was much less, 
and, whereas our determinations of time were much less accurate, 
we had attempted to make up for this inferiority by observing on 
several nights each time at each station. 
1) F. G. W. Srruve. Expéditions chronométrigues entre Poulkova et Altona, 
St-Pétersbourg 1844, p. 117—128. 
