288 Transactions. —Miscellaneous. 
Thus both theory and practice agree in allotting to triangulated sides 
_of twelve to fifteen miles, with eight or ten inch theodolites, a minimum 
error of four inches per mile, progressing to a maximum of one foot per 
mile, when extended for sixty miles or so; and to triangulated sides of three 
miles, with five-inch theodolites, a minimum error of two feet per mile, 
progressing to a maximum of six feet per mile, when similarly extended. 
In this latter case, however, it should be remarked that, on the theory of 
accumulating errors increasing in proportion to the number of stations 
triangulated, the maximum error becomes reached by minor triangulation 
when it has passed over fifteen miles or so. The average error may, there- 
fore, be quoted at four feet per mile or six links, and as this may take 
either a positive or negative direction, a double error of twelve links per 
mile might become exhibited by crucial tests. Practical instances might 
be instanced bearing this out, either when triangulation of this class has 
been carried on from one measured base line to another about fifteen miles 
apart, or when the test of secondary triangulation has been applied to it. 
Instances have, I am told, occurred, where closing meridian circuits in 
Otago have exhibited no greater errors than two links per mile; such an 
accordance, however, cannot be received as conclusive evidence of the con- 
sistent accuracy of the measures throughout the circuit, on the ground 
before stated with regard to five-inch theodolites, namely, the want of 
sufficient measuring power in its operations. It is only when a higher 
order of triangulation is placed over it that we should become sensible that 
the stations of a meridian circuit are more or less dislocated from their 
assumed positions, by the larger amount of error above quoted. 
The practical question to discuss, therefore, resolves itself into this, 
what limit of error is it desirable not to exceed in the triangulation neces- 
sary for checking sectional surveys, the errors of these latter being admitted 
to far exceed any assigned limit to the triangulation? From the foregoing 
statements, if the assigned limit of error is to be four feet per mile, with a 
possible double error of eight feet per mile attached to it, minor triangula- 
tion meets the case; if it is to be one foot per mile, involving a double error 
of two feet per mile, secondary triangulation should be had recourse to in 
addition; butif greater aecuracy is desired, then we must revert to primary 
triangulation. With regard to the adaptability of minor triangulation with 
measured bases at intervals twelve miles apart for New Zealand generally, 
it may be asked how are such operations to be carried on in vast wooded 
tracts, such as those which occur in many parts of the North Island, such, 
for example, as the Forty-mile Bush and the Manawatu districts in the 
Provincial district of Wellington, and others of still greater extent in that 
of Taranaki? Itis clear that in these localities a larger system of triangu- 
