VALUE OF AUSTRALIAN' LONGITUDES, 
203 
Mean Values. 
By combining (XVI.) and (XIX.) according to their mean errors, 
we have h. m. sec. 
Longitude of Boundary Pier 9 23 50-01 
Longitude of Boundary between South ... 9 24 00 72 
Australia and New South Wales 
Longitude of north end of Marked (XXII.) 9 23 51*37 
Boundary, South Australia and 
Victoria 
The two values (XV.) and (XVIII.) differ by 0'67 sec. — that is, 
they make tho longitudes of the north and south end of the marked 
Victorian boundary line with South Australia differ by that amount. 
If we take instead the mean values (XV.) and (XVII.), the difference 
is reduced to 0*36 sec. ; and if the value (A 1 ) of the interval Sydney to 
Boundary Pier be excluded altogether, using only tho value (B‘) of 
the interval Melbourne to Boundary Pier, the difference is further 
diminished to 0*12 sec. ; a quantity sufficiently small to admit a 
proper adjustment of both ends of the line without vitiating its longi- 
tude. We see then that the introduction of the value (A. 1 ) into the 
final deduction of results would cause the south end of the boundary 
line to appear 500 or 600 feet further east than the northern end. 
The anomaly might be explained in various ways. 
Pirst* by assuming an accumulated error in the Victorian 
triangulation, or some defect in the dimensions of the ellipsoid on 
which its calculations are based, causing the difference of longitude 
Melbourne to Mount Buskin to be some 10 seconds too small. Such 
assumptions, however, are in the present state inadmissible, as the 
records of the survey do not show any such error on the one hand, 
and on the other it may be said that the operations of 1868 at the 
boundary were not sufficiently complete to serve as a test to the 
trustworthiness of geodetic measurements. 
Second, by great carelessness in the marking of the boundary 
line— a supposition which could only be made on the very difficult 
condition of having every other probable source of error clearly and 
absolutely eliminated. 1 have no knowledge as to the means bv which 
the line was marked, but it would require nothing less than direct 
evidence to show that its direction is wrong by 600 feet. 
Third, by considering the value (B 1 ) of the interval Melbourne- 
Boundary too large by over half a second of time. In this case the 
true meridianal direction of the Boundary would be maintained, and 
the adopted value of the difference of longitude Sydney-Melbourne 
would receive further proof of its accuracy; but then the geodetic 
arc (Melbourne to Mount Ruskin) would become affected by a large 
error a condition already refuted ; and, moreover, the superiority of 
the value (B 1 ), as admitted by Mr. Todd in 1868, when he assigned to 
it double the weight of the value (A 1 ) [see (17)], would have to be 
arbitrarily inverted. 
There remains only one way of explaining the discrepancy, and 
only one solution of the difficulty — viz., by taking the value (A‘) of 
the difference of longitude Sydney- Boundary as being considerably 
too large, and to exclude it from the Boundary results, in order to 
produce a general agreement, without fear of vitiating the absolute 
longitudes of the boundaries. 
