YALUE OF AUSTRALIAN LONGITUDES. 
187 
already given) when possible or advisable. These are shown in Table 
I. The “ mean error” was adopted in preference to the “ probable 
error” in order to preserve uniformity with the first portion of the 
chain. The latter can be readily derived by multiplying the mean 
error by 0*6745. 
It must be remembered that this theoretical error is only a 
measure of the agreement of the observations upon which a result 
depends, and therefore only a 'part of the absolute amount of 
uncertainty attached to that result. 
In the next place, it was necessary to scrutinise the accounts in 
order to learn all the facts connected with the operations which might 
increase or decrease the reliability of the given results, such as instru- 
ments used, methods oi: recording the observations, conveniences in 
exchanging galvanic signals, quality of these signals, personal equation 
of observers, stability of stations, agreement of independent results 
where more than one measurement was made, &c., &c. 
These circumstances will be here summarised and arranged for 
comprehensive inspection. There can be no definite rule to serve as a 
guide in their interpretation, nor can they be submitted to mathe- 
matical treatment. Their effect may be variously estimated by different 
investigators, and may sometimes be even misleading; but their 
influence upon conclusions found in regard to the degree of accuracy 
of results will nevertheless be easily recognised as being very great. 
At first I thought to take my start from Aden, since up to this 
point the longitudes have been thoroughly discussed and concluded by 
Dr. Auwers and Dr. Gill (7) ; but I find that the merits and defects of 
this part of the work, and all the separate results belonging to it, must 
be shown, in order to exhibit the complete chain from one point of 
view, so as to be able, and enable others, to weigh it as a whole, with 
the convenience of not having to refer to so many publications ; and 
more especially because on the operations between Greenwich and 
Aden probably rest elements of doubt of a more serious character 
than in the more eastern portions, for, quoting Dr. Gill — (7) page 62 
— u Neither of the two series of operations on which the longitude of 
Aden depends was executed with such refinements or precautions as 
are necessary for the determination of fundamental longitudes.” It 
must be mentioned, however, that these operations were chiefly 
undertaken in connection with the Transit of Venus observations, for 
which purpose their accuracy was sufficient. 
I shall therefore commence at the beginning — viz., the prime 
meridian. The values of intervals, as given in Appendix, Table I., 
will be referred to by the letters respectively attached to them. 
Longitude of Alexandria. — Six different values — viz., ( a ), (6), (c), 
(d) } (c), and \ (f -f f,) — may be combined, giving three values for this 
longitude, two of which are quite independent. 
00 Oreenivich-JKoJcattam . — This was determined by exchange of 
galvanic signals between Greenwich and Portheurno ; Porthcurno and 
Alexandria (by joining the five lengths of cable, Porthcurno, Vigo, 
Lisbon, Gibraltar, Malta, Alexandria) ; and finally, between Alexandria 
and Mokattam. Time observations were made with transit instru- 
ments at Greenwich, Alexandria, and Mokattam, but those at 
Alexandria were not used for this interval. The observers were 
Mr. Criswick at Greenwich, Mr. Ellis at Porthcurno, Mr. S. Hunter 
