204 
PLOCEEDIN G-S OE SECTION A. 
In justification of such procedure, it is simply submitted that one 
of the two measures ( A T ) and (B r ) of the intervals Sydney to Boundary 
Pier ana Melbourne to Boundary Pier is probably in error to the extent 
of about half a second of time ; that the value (B r ) of the one is 
corroborated by the geodetic difference of longitude Melbourne to 
Mount Buskin, and by the assumption that the marked boundary 
between South Australia and Victoria is a true meridian ; and, finally, 
that the less reliability of the value (A 1 ) of the other was recognised at 
the time of its determination, which appears all the more reasonable in 
view of the probable causes of uncertainty already pointed out in these 
pages. 
I shall therefore deduce the longitudes of the eastern boundaries 
of South Australia by adopting the last course. AV e have then — 
Adopted longitude of the marked boundary between 
South Australia aud A 7 ictoria — 
i*{(XV.) + (XXI.)} ... 9 hr. 23 min. 51‘67 sec. = 140° 57' 55*0" 
Adopted longitude of the boundary between South 
Australia and New South Wales, as fixed by 
Mr. C. Todd in 1868 9 hr. 24min. 01-01 sec. = 141° 00' 15-1" 
At the Murray Stiver- — 
The boundary between South Australia and Victoria is 10,535 feet 
west of the 141st meridian of east longitude from Greenwich ; 
The boundary between South Australia and New South Wales is 
1,273 feet east of the 141st meridian of east longitude from 
Greenwich. 
PROBABLE AMOUNT OE UNCERTAINTY OE THE AUSTRALIAN 
LONGITUDES. 
It remains now to be seen with what degree of confidence the 
given results may be taken. 
The theoretical errors attached to the longitudes of Adelaide, 
Melbourne, and Sydney, found above, are respectively ± 0‘ 157 sec., 
+ 0-158 sec., aud ±0*182 sec. It has already been stated that these 
errors represent only that part of the probable uncertainty due to the 
disagreement of separate results of the same measure derived from 
each night’s work, when compared with their mean value. It would 
appear then that the really and purely accidental errors incurred in 
each single night of the period upon which a longitude result depends 
are fairly measured by the theoretical errors; or, if this measure is 
not quite satisfactory, is at least the best that can be obtained. But 
there may he involved systematic errors common to all the nights of 
that period, some of which are beyond the reach of investigation, and 
others that might possibly be discovered only by delicate and con- 
tinued experiments in fixed institutions, but not in the temporarily 
arranged longitude observatories. 
Altered personal equations at each new place of observation, 
instrumental changes, flexure, physical peculiarities of the localities, 
and many other known and unknown causes may bring in systematic 
errors not easily discovered. The theoretical error has no concern in 
these matters, and gives no help. It is when new instruments and 
new observers are employed in different years, so as to make the 
redeterminations entirely independent, that the existence of these 
