Travers.—Thomson's System of Survey from a Legal Point of View. 287 
result in actually showing discrepancies of ten seconds between the single 
observations, because in this latter case we have approached more closely 
the limits of our measuring powers, and have therefore become sensible of 
the discrepancies of the observations. Here, however, the discrepancies 
themselves are prima facie evidence of the angle observed being subject to 
‘an error of ten seconds only, whereas in that taken with the five-inch 
theodolite the amount of error could not be relied upon as being within one 
minute. In both instances they may be called errors produced from 
constant causes. 
The inference from these remarks is that the ratio of error of work 
performed by the two classes of instruments is as six links to one link per 
mile. I am informed, that remarkably enough, in praetice the errors 
disclosed by the two class of triangulations bear out this theory. That 
taking, for example, the partial check afforded by the sides of triangles 
which eombine into polygonal figures and comparing common sides, it is 
found that the computations derived from the eight or ten inch theodolite 
give consistent results with an average accuracy of a half link per mile, 
while those due to five-inch theodolites average three links. 
The above figures cannot, however, be taken as representing the actual 
errors committed by each class of instrument. They serve only to show 
that the ratio of error is in the proportion of six links to one link per mile. 
The actual error of triangulation with eight or ten-inch theodolites, as 
exhibited by closing its sides on measured verification bases at intervals 
of 60 miles or so, amounts, I am told, to one foot per mile, and this 
large increase may easily be accounted for from various causes, such 
as errors arising from tremors of the telescope produced by wind, 
from anomalous changes in the atmosphere, from anomalous con- 
traction and expansion of the parts of the instrument used, and from an 
accumulating tendeney to error in the triangulation itself. Indeed, an 
accumulating tendency to error is obvious, and must proceed in arithme- 
tieal progression aecording to the number of triangles extended from the 
measured baseline. It therefore follows that the risk of an accumulat- 
ing tendency to error increases as the extent of country to be triangulated 
over without check. . It was in order to avoid this that the engineers who 
conducted the great trigonometrical operations of Great Britain and India 
inaugurated the now received principles of primary, secondary, and minor 
triangulations, the superior order serving as a check upon the inferior. 
Thus by carrying each principal series of triangles in a direct course 
from one measured base line to another in as small a number of stations 
as possible, the accumulating tendency to error becomes reduced to a 
minimum, 
