bar: REPORT—1885. 
base-lines measured with the Colby apparatus of compensation bars and microscopes. 
This prodigious amount of field-work furnishes an enormous mass of interdependent 
angular and linear measures; and each of these is fallible in some degree, for, great 
as was the accuracy and care with which they had severally been executed, perfect 
accuracy of measurement is as yet beyond human achievement ; thus every circuit 
of triangles, every chain closing on a base-line, and even every single triangle, 
presented discrepancies the magnitude of which was greater or less according as 
derived from a combination of many, or only of a few, of the fallible facts of obser- 
vation. Thus, when the field operations were approaching their termination, the 
question arose as to how these facts were to be harmonised and rendered consistent 
throughout, which was a very serious matter considering their great number. The 
strict application of mathematical theory to a problem of this nature requires the 
adjustment to he effected by the application of a correction to every fact of obser- 
vation, not arbitrarily, but in such a manner as to give it its proper weight, neither 
more nor less, in the final investigation, and in this the whole of the facts must be 
treated simultaneously. That would have involved the simultaneous solution of 
upwards of 4,000 equations between 9,280 unknown quantities, by what is called 
the method of minimum squares, and I need scarcely say that it is practically 
impossible to solye such a number of equations between so many unknown quan- 
tities by any method at all. Thus a compromise had to be made between the 
theoretically desirable and the practically possible. It would be out of place here 
to attempt to describe the method of treatment which was eventually adopted, after 
much thought and deliberation ; I willmerely say that the bulk of the triangulation 
was divided into five sections, each of which was treated in succession with as close 
approximation to the mathematically rigorous method as was practically possible ; 
but even then the mass of simultaneous interdependent calculation to be performed 
in each instance was enormous, I believe greatly exceeding anything of the kind as 
yet attempted in any other survey. But the happy result of all this labour was 
that the final corrections of the angles were for the most part very minute, less than 
the theoretical probable errors of the angles, and thus fairly applicable without 
taking any liberties with the facts of observation. If the attribute of beauty may 
ever be bestowed on such things as small numerical quantities, it may surely be 
accorded to these notable results of very laborious calculations, which, while in 
themselves so small, were so admirably effective in introducing harmony and precision 
throughout the entire triangulation. 
If now we turn once more to what Lambton calls ‘ the sublime science of geodesy,’ 
which was held in such high regard by both him and Everest, we shall find that 
the great meridional are between Cape Comorin and the Himalayas, on which they 
laboured with so much energy and devotion, is not the only contribution to that 
science to which the Indian triangulation is subservient, but every chain of triangles 
—teridional, longitudinal, or oblique—may be made to throw light either on 
geodesy, the science of the figure of the earth, or on geognosy, the science of the 
earth’s interior structure, when combined with corresponding astronomical ares of 
amplitude. Thus each of the several meridional chains of triangles may be utilised 
in this way, as their prototype has been, by having latitude observations taken at 
certain of their stations to give meridional arcs; and the several longitudinal 
chains of triangles may also be utilised—in combination with the main lines of 
telegraph—hby electro-telegraphic determinations of differential longitudes to give 
arcs of parallel. When the stations of the triangulation which are resorted to for 
the astronomical observations are situated in localities where the normal to the 
surface ‘coincides fairly with the corresponding normal to the earth’s figure, the 
result is yaluable as a contribution to geodesy ; when the normal to the surface is 
sensibly deflected by local attraction, the result gives a measure of the deflection 
which is valuable as a contribution to geognosy. 
Having regard to these circumstances, I moved the Government to supply the 
Trigonometrical Survey with the necessary instruments for the measurement of the 
supplemental astronomical arcs; and as officers became available on the gradual 
completion of the successive chains of triangles, [ employed some of them in the 
required determinations of latitude and differential longitude. It so happened that 
