at ae 
TRANSACTIONS OF SECTION E. 1122 
2. Account of the Levelling Operations of the Great Trigonometrical Survey of 
India, By Major A. W. Bano, R.L., F.R.S. 
From the origin of the Great Trigonometrical Survey of India until the year 
1858 all determinations of relative height were effected by the measurement of 
reciprocal vertical angles, a method which is based on the assumption that the back 
and forward angles are equally refracted, in which case the difference of height 
deduced from them should be exact. But when rays of light passing between two 
mutually observing stations traverse the lower strata of the atmosphere and graze 
the surface of the ground, the refraction is rarely identical at both stations even at 
the same moment of time, and is liable to vary greatly at different hours of the day 
and at the same hour on different days. ‘Thus determinations of the relative 
height of stations situated on extensive plains by this method are liable to con- 
siderable inaccuracies ; and as a belt of plains of great extent—in places several 
hundred miles broad—intervenes between the hill ranges of Lower and Central 
India and those of Upper India, and every principal chain of triangles has had to 
be taken over these plains for a greater or less distance, lines of spirit-levels 
were initiated, to be carried across them from sea to sea, as a check on the trigono- 
metrical determinations of height. The opportunity was availed of to connect and 
reduce to a common datum the levels executed in all parts of India for irrigation, 
railway, and other purposes. Subsequently, when systematic tidal observations 
came to be undertaken at various points on the coast, lines of level were carried 
between the tidal stations, to serve as a check on the spirit levelling, and also to 
connect the tidal stations together. 
Every line is gone over by two surveyors working independently of each other, 
with separate instruments and staves, and comparing results from time to time. 
The staves have two faces, both graduated in feet and tenths, but one with black 
divisions on a white ground reading from 0 to 10, the other with white divisions 
on a black ground reading from 5°55 to 15°55, which gives a useful check against 
accidental gross errors of reading, as the observer has no bias to repeat on the 
second face an error made in reading the first. The bulbs of the levels are fitted 
with graduated scales; the readings of the ends of the bubble are recorded, and 
corrections are applied for dislevelment, as with astronomical instruments. As 
there isa tendency to an accumulation of minute constant error in all levelling 
operations, such tendency is guarded against as far as practicable by alternating 
the order of the back and forward stafl’ readings at successive stations, aud also 
alternating the direction of operation on successive days or in successive sections 
of each line. 
The rate of progress is not, of course, as rapid as in levelling operations executed 
with less care and precision, but an average of four miles daily may generally be 
relied on. Up to the present time 9,680 miles of rigorously executed double line 
have been completed, and about 300 miles of single line to connect collateral and 
subsidiary bench marks. 
The first five lines which were executed to connect tidal stations indicated, in 
every instance, that the sea level was apparently higher at the southern than at 
the northern station. It is quite possible that the level of the surface of the sea 
may be disturbed under the influence of local attractions, and be higher at some 
points of a coast-line than at others; but the actual difference of level is only 
ascertainable approximatively by calculations based on various assumptions regard- 
ing the constitution of the earth’s crust and the surrounding elements of attraction. 
Tt cannot be measured, because the attractions have the same influence on the fluid 
in the bulbs of the levelling instruments as on the waters of the ocean, when both 
are equally exposed to their influence ; thus, when working along a line of open coast 
the instrumental would coincide with the ocean level, and a large deviation from 
the normal level of the ocean might exist without any possibility of measuring it. 
Thus it seemed that the apparent raising of the southern ends of these lines of level 
must be due not to actual variations in the height of the mean sea, but to some 
error in the levelling operations. They had been conducted with scrupulous care, 
and with every conceivable precaution to guard against either accidental gross 
4c2 
