The measurement of Everest was a result of a larger interest in map...
Mount Everest was given its moniker in honor of Sir George Everest ...
Geodetic operations are a set of mathematical and scientific techni...
Atmospheric refraction along the sightline is one of the principal ...
This sentence roughly translates to:
> "In the practice of geodesy...
This sentence translates to:
> "It is therefore true to say that...
This translates to:
> "Delambre noticed in France that it [the coe...
This translates to:
> "We will assume it [the coefficient of refr...
The Great Arc of triangulation refers to the network of survey line...
This translates to:
> "meteorological elements which are indispens...
*The six measurement stations...
James Thomas Walker was the Surveyor General of India.
*New observation points*
VARIOUS DETERMINATIONS OVER A
CENTURY OF THE HEIGHT OF
MOUNT EVEREST
J. de GRAAFF-HUNTER
To appreciate the problem of the height of Everest, now brought a long stage
nearer to finality by recent observation work of the Survey of India, 4 it is
necessary to look back over a century of effort under circumstances of progressively
lessening difficulty.
It was in the mid-nineteenth century that Himalayan snow peaks first came
under serious observation for height determination; and when first the problem of
terrestrial refraction was encountered on an unprecedented scale. With noteworthy
vision Sir Andrew Waugh, successor to Sir George Everest, wrote in 1845?as
quoted by Mr. Gulatee?"The lofty snow peaks situated north of Nepal are the
most stupendous pinnacles of the globe. Their heights and relative positions
should form permanent objects in the geodetical operations.'' Within the next ten
years a large crop of observations was reaped and came up for computation.
Just how much was known by Waugh about refraction on terrestrial rays over
100 miles long from plains to peaks?or by anyone else at that time?is uncertain.
Waugh had probably read Puissant J whose work had been published in 1842.
Therein one may read, paragraph 214, sub-paragraph 3: "Dans le pratique de la
geodesie, la trajectoire lumineuse est une courbe toujours assez peu etendue pour
pouvoir etre confondue avec son cercle osculateur_"
And in the next sub-paragraph: "II est done vrai de dire que la refraction terrestre
est proportionelle a l'angle forme par les verticales des extremites de la courbe de
refraction, et qu'elle est sensiblement la meme, a une epoque donnee, aux deux
stations comparees, si toutefois leur difference de niveau est trespetite."
In both the above the usual idea of the coefficient of refraction, k, is still in
general use; but there are wise limitations which have often been forgotten. In
the penultimate sub-paragraph Puissant continues: "Delambre a remarque en
France que n a environ pour valeur moyenne 0-07876, ou simplement 0-08 . . .
par des temps brumeux 0-15 . . . 0-06 a 0-08 en ete, et 0-08 a o-io en hiver. . . .
D'autres observateurs ont meme trouve 0-5 par les temps de pluie. . . ." Later on
in paragraph 217 Puissant develops a theoretical expression varying as air pressure
and as inverse square of absolute temperature of air; and with a factor involving
the Lapse Rate of which he says: ". . . et nous la supposerons constante, quoique
en realite elle varie d'un lieu a un autre, et peut-etre aussi dans un meme lieu en
differentes saisons."
Puissant says nothing about diurnal variation of refraction (nor of minimum
refraction) though this is the most important variation in the case of rays in the
lower atmosphere. Certainly it had been well known to Colonel Everest at least
ten years earlier, for in his reconnaissance for the Great Are of triangulation at the
crossing of the featureless plains north of Agra he was making use of maximum
refraction. He wrote instructions l6 to Boileau: "The extent of view at time of
maximum refraction-, this varies from midnight to sunrise and is generally about
3 o'clock. . . ."
22 VARIOUS DETERMINATIONS OVER A CENTURY OF THE HEIGHT OF MOUNT EVEREST
Returning to Puissant, at end of paragraph 216, he says:
"... elements miteorologiques qu'il est indispensable de recueillir en meme
temps que les distances zenithales." Unfortunately this last counsel has seldom
been followed; and no temperatures were recorded with the vertical angles to
Everest about 1850. In spite of the theory, there seemed then, and even much
later, a curious tendency to assign values to k appropriate to sea level, though it is
quite certain that it should be smaller at considerable elevations. In Europe, 0-08
was much in favour and A. R. Clarke proposed .075 for rays over land for Great
Britain without allowance for height.
Now long rays to high snow peaks are fugitive things, often interrupted by clouds,
particularly as the day wears on. Waugh accordingly ordered his observers to be
ready to begin such observations at first light, so that no opportunity be lost.
Fortunately observations at early afternoon hours were secured in most cases.
Waugh had results of observations of vertical angles to Mount Everest from six
stations in the Bengal plains, at average height 230 feet, of lengths ranging from
108 to 119 miles. Closer approach had been denied by the Maharaja in spite of
Waugh's repeated urgent requests to enter Nepal?an embargo which lasted
during British administration in India. On his own system Waugh derived values
for k ranging from 0-0727 to 0-0753; and thence he obtained individual values of
the peak height ranging over 36 feet, with the world-renowned mean value of
29,002 feet. At that time there were not the spirit-levelling connections which later
reduced the station heights by an average amount of 8 feet.
These values of k used by Waugh are 15 per cent. too large. A proper value is
about 0-064 (not ?'?5 as stated by Mr. Gulatee at p. 2 of his paper). But at that
time it appears that there was more confidence in empirical than in formula values,
even though the former were based on low-lying rays?not comparable with rays
attaining a height of 29,000 feet. Indeed, it would have not been surprising if Waugh
had used 0-08. I cannot think that criticism can rightly be directed against him
about refraction. Rather let us admire his drive in getting these observations made
and computed.
About a score of years later General J. T. Walker was investigating refraction
in the Punjab plains 5 where extreme and even negative refraction was encountered
?diurnal variation of refraction of the kind that makes the observer feel as though
in a saucer at dawn, later on seeing objects sinking below the horizon as receding
ships at sea! It remained to Sir Sidney Burrard 7 to re-open the question of
Himalayan heights about 1905. He was very conscious of the refraction difficulty
and soon set Mr. H. G. Shaw I0 observing vertical angles in the neighbourhood of
Dehra Dun between stations Nojli (887 feet), Mussoorie (6930 feet), Nag Tiba
(9915 feet) and thence to peaks of the snowy range distant about 100, 60 and 50
miles respectively. Since Waugh's time, Everest had been observed from six stations
in the Darjeeling Hills, of average height 10,600 feet, lying on an average 95 miles
from the peak. For k Burrard used 0-0645 f?r ravs fr?m tne Bengal plains and 0-05
for those from the Darjeeling Hills; and his computed heights for Everest ranged
over 43 feet with average 29,141. It will be seen below that these values of k were
very proper.
The formulae for heights in triangulation from vertical angles do not imply
either of the "drastic assumptions" imputed by Mr. Gulatee (p. 5). When there
are reciprocal angles, as between stations, the height increment derived (apart from
refraction errors) refers to the circle to which the terminal verticals are normal and
which touches the horizontal plane at one of the stations. When observations are
VARIOUS DETERMINATIONS OVER A CENTURY OF THE HEIGHT OF MOUNT EVEREST 23
made to an unvisited point the radius of the circle is at choice. A wrong choice will
lead to a faulty estimate of the curvature effect.
When observations at several stations are to be associated the problem is com?
plicated if there are significant difTerential deflections at these stations. Spheroidal
heights may be obtained after due correction of observed geoidal vertical angles
and geoidal station heights to their spheroidal counterparts. In the vast majority
of practical cases no such treatment is needed; the Everest case was exceptional, as
sensible geoidal differences exist between the observation stations, and the effects
were aggravated by the extreme length of all the rays.
Burrard was very conscious of the deflections of the vertical, a subject which
he brought into prominence by two important papers 2, 9 He held, however, that
the deflection data available were too scant for tracing the geoid. Indeed the era of
the geoid had not yet arrived. Practically any derived height, other than those from
spirit-levelling, had reference to a locally positioned spheroid with the dimensions
of the Everest spheroid. A few years later, about 1910, I began studying refraction,
finding a mine of material to work on in Mr. Shaw's observations I0 of 1905-9,
which Burrard's foresight had provided. Results were published in 1913 ". In a
lecture before the Indian Science Congress at Madras in February 1922 12, I gave
the local spheroidal height of Everest as 29,149 feet. This was derived, taking
account of all then known deflection data (see above); the computations being made
in the Dehra Dun Computing Office, where they may still be found. The geoidal
data had been somewhat increased from what Burrard had but were still scanty.
Refraction was derived by formula for which temperature had to be assessed from
nearby meteorological reporting stations at corresponding season and hour, as it
had not been recorded?as Puissant had laid down (see above). I estimated the
geoidal rise from the Bengal plains to Everest at 70 feet, and gave with diffidence
the geoidal height 29,080 feet. Some years later Bomford x5 proposed to increase
the geoidal rise by 30 feet and so to reduce the mountain height to 29,050. This
figure is also given in a note which I wrote for Sir Sidney Burrard in 8 at
p. 62.
The study of refraction enabled me to publish in z3 a table, numbered 5 Sur.,
giving standard horizontal refraction coefficient, and the rule, stated by Mr.
Gulatee at end of his paragraph 2,4 for using the value at height one-third of the
way along a sloping ray. For this a lapse rate of 30 F./iooo feet was used. Applied
to the Everest observations, with standard conditions of temperature and pressure,
one finds for the rays from the Bengal plains 0-063 > anc* for those from the Darjeel-
ing Hills 0-053. These may be compared with Burrard's 0-0645 and 0-05. The
small differences could be due to departures from standard conditions of 40 and
8? F. respectively. With no exaggeration one may say that the refraction problem
for these long rays to Everest had been solved. The only outstanding difficulty
was the geoidal shape, for which many more observations were required. These
have been provided now by the 1952-54 observations.4
In the late nineteen-forties the political barrier to entry to Nepal was removed.
The Survey of India, for the first time free to do so and now concerned with con?
trol of new irrigation schemes, executed some good topographical triangulation in
Nepal and this passed within 40 miles of Everest. A meridian connection reached
from the Ladnia-Harpur side of the old geodetic triangulation to Namche Bazar
only 17-5 miles from Everest. The stage was set for new observations for the
height of Everest, with the difficulty of geoidal rise reduced ten-fold. The short-
sided triangulation brought up what were practically geoidal heights and, apart
24 VARIOUS DETERMINATIONS OVER A CENTURY OF THE HEIGHT OF MOUNT EVEREST
from ordinary triangulation operations, only the change of geoidal slope between
it and the peak needed assessment.
Provided with this great opportunity Mr. Gulatee planned observations on a
broader basis than would be necessary for the sole object of Everest height?for
which he is to be commended?and valuable extra geodetic information has been
obtained. The circuit formed by the loop of new topo triangulation and the old
triangulation between the sides Ladnia-Harpur and Sandakphu-Phallut was now
provided with four Laplace points and three extra bases (quality not stated). The
upshot was circuit-closing errors of 2 seconds in azimuth, 1/40,000 in scale and
12 feet in position, in a distance of 300 miles. He added extension triangulation of
eight stations, flanking the topo triangulation. These extra stations lay at elevations
from 8670 to 14,762 feet and at distances from 29 to 47 miles from Everest. At all
of them, as at several of the meridian portion, Ladnia-Namche Bazar, and on the
eastern branch to Darjeeling, he provided deflections in both components, from
astrolabe observations. To the spirit-levelling connections at Darjeeling and the
next station to Harpur was added a new connection at Chatra h.s., some 35 miles
south of Mayam, the nearest of the eight extra stations from which Everest was to
be observed. One may regret that longitudes were not observed with an impersonal
instrument.
In all this Mr. Gulatee had for guidance the experience gained in some 8000
miles of geoidal sections, observed in India 1932-39, along which astrolabe obser?
vations were made at intervals 10-20 miles. Admittedly the Nepal terrain was
difficult. The observers deserve full praise.
From three of the extra stations, horizontal angles were taken to Everest?the
largest subtended angle being about 420. These led to a fix some 40 feet S. and
40 feet W. of the old accepted position. Fixation of a snow peak offers difficulties
in that there is no precise mark to intersect. What may appear the highest point
viewed in one azimuth by a ray inclined some 50 will not be so regarded on another
azimuth. Moreover the snow itself is mobile with wind and time. The new fix
brings Everest some 56 feet closer to the new observing stations, and thus lessens
the computed height by some 5 feet.
Section 5 of Mr. Gulatee's paper is headed "Outline of the New Method";
then three main sources of uncertainty in "the older determinations" are stated and
an illustrative diagram follows. There is, however, nothing new in the method. This
with the handicap of scanty deflection data, was used for my 1922 lecture.1* The
diagram shows no new concept not included in one to be found in an Appendix 6
of Burrard's, written in 1910.
What is new is the great simplification in the problem due to the withdrawal
of the embargo on entering Nepal and accordingly the observations which it has
recently been possible to make. There is nothing new in the type of these
observations.
With the resulting deflections it is a straightforward matter to trace the geoidal
rise, as in section 7 of.4 Now only extrapolation beyond Namche Bazar for 17-5
miles is uncertain?compared with 90 miles formerly?and in this short distance
an error as much as 10 seconds in deflection at Everest would change geoidal level by
only 2 feet. Mr. Gulatee has gone to the trouble, of debatable value, of computing
Hayford deflections at a number of points to assist inter- and extra-polation of
additional deflections. Of these he says that they "produce greater sinuosity in
the deflection curves"; and these cancel out almost entirely in the integrated height
effect. Later, in the last two sub-paragraphs of this section 7, he gives computed
VARIOUS DETERMINATIONS OVER A CENTURY OF THE HEIGHT OF MOUNT EVEREST 25
results of geoidal elevations at Everest?due to simple topography 333 feet; to
compensated topography 31 feet; the actual value derived from multiple deflections
being 92 feet.
From the observed and the interpolated deflections he obtains the geoidal rises
between each of the observing stations and the peak, and these range from 30 to
52 feet. He also finds the rise between Ladnia and Everest to be 109 feet. A chart
of geoidal contours at 5-foot intervals covering region 260 to 280 lat. and 850 to
88? long. is given.
Section 2 of Mr. Gulatee's paper is headed "Refraction." In this is set out
an account of refraction in which there is no advance on what can be found in
Survey of India publications prior to 1930, e.g. pp. 109-14 of.H Mr. Gulatee
quotes a formula from Bomford's 'Geodesy,' which is the essential basis of the
refraction table 5 Sur. of x3; but he has elected to use a lapse rate of 3?-2 F./iooo
feet rather than the 3?.o mentioned by Bomford and used for 5 Sur. The effect
of this is to reduce k by 1-3 per cent.; and on the longest of the new rays to
Everest, that from Mayam h.s., this increases the computed height by 2 feet. One
can hardly fail to notice that a change in the other sense to 2?*7/iooo feet (which
would agree with the density law given by Brunt in his 'Physics of the Atmos?
phere') would reduce the scatter of the new height determinations from 16 feet to
11 feet.
In his section 9, Mr. Gulatee adopts the role of critic of some of his pre-
decessors in the Survey of India, especially of Burrard. Burrard opened up new
fields in geodesy and he most certainly knew very well the significance of the height
29,141 feet which he had determined for Mount Everest. Burrard was not talking
about geoidal heights, nor was anyone else at that time. Any thinking person knew
what was meant and also recognized that there was no practical alternative until
extensive geoidal observations had been made and computed. Burrard did more
than anyone to bring deflections into the geodetic picture and laid foundations for
the geoidal determinations which were initiated in the Survey of India prior to
Mr. Gulatee's recruitment.
The 1952-54 observations have given a value of 109 feet for the geoidal rise
between Ladnia and Mount Everest. When this is subtracted from Burrard's
spheroidal height the result is 29,032; which accords closely with Mr. Gulatee's
value 29,028, said to be for time of minimum snow. This latter height is smaller
by 5 feet on account of the new position assigned to Mount Everest (see above). All
this confirms the opinion, held since 1925, that the only outstanding difficulty was
assessment of geoidal rise. And yet Mr. Gulatee tells us "the estimation of geoidal
rise between the stations of observation and Mount Everest involves an extra step
but it has to be done." This point was brought out strongly in I2 and again in 3
and estimates of geoidal rise were made using the scanty available deflection data.
Mr. Gulatee has had just the same opportunities of doing this as anyone else for
over twenty-five years, and did nothing until all serious difficulties were removed
by access to Nepal being allowed.
Mr. Gulatee now earns the thanks of geodesists for providing adequate deflection
data penetrating the Himalaya 100 miles. It is indeed unfortunate that in present-
ing the results of important work, he has signally failed to acknowledge how very
essentially he has depended on earlier workers. He has also been guilty of
plagiarism. His criticisms of that most distinguished geodesist, the late Sir Sidney
Burrard, can most kindly be attributed to ignorance.
It is agreeable in conclusion to accord hearty praise to the triangulators and
26 VARIOUS DETERMINATIONS OVER A CENTURY OF THE HEIGHT OF MOUNT EVEREST
astrolabe observers whose work has rendered possible the closer approach to the
true geoidal height of the "world's most stupendous pinnacle." The height
observations were made in months December to March, at which season precise
work at altitudes approaching 15,000 feet must involve physical hardship.
Summary of altitude results
(a) Waugh's value, 29,002 feet, is a spheroidal height. It is too low owing to
over-correction for refraction.
(b) Burrard's value, 29,141 feet, is a good spheroidal height. The corresponding
geoidal height, 109 feet lower, is 2g,032 feet.
(c) The present writer's 29,080 feet12, 3, was the first attempt at a geoidal
height. The reductions took account of any known deflections and the correction,
? 69 feet, was the geoidal rise inferred from the geoid in meridians 780 and 88?
and, more recently 75 ?. With the recently found value, - 109 feet, 4 it reduces
to 29,040 feet geoidal height.
(d) Mr. Gulatee's 2Q,028 feet is a geoidal height, at season of minimum snow,
in years 1952-54.
It is not to be expected that the height of a snow peak will be invariable over
different years and seasons.
REFERENCES
1 L. Puissant, 'Traits de g^odesie* (3me. edition), Torne premier. Paris. 1842.
2 S. G. Burrard, "On the intensity and direction of gravity in India." Proc. roy. Soc. Ser. A.
76 (1905) 313-15, and Phil. Trans. Ser. A. 205 (1905) 28, 318.
3 J. de Graaff-Hunter, "Heights and names of Mount Everest and other peaks." Occ. Notes
R. Astr. Soc. 3 (1953) 15-
Survey of India Publications
4 B. L. Gulatee, "The height of Mount Everest: a new determination (1952-54)." Technical
Paper No. 8, 1954.
5 J. T. Walker, Appendix 3 of 'Account of the Great Trigonometrical Survey of India."
Vol. II, 1879.
6 S. G. Burrard, Appendix 8 of 'Account of the Great Trigonometrical Survey of India.'
Vol. XIX, 1910.
7 S. G. Burrard and H. H. Hayden, *A sketch of the geography and geology of the Himalayan
mountains and Tibet.' Delhi, 1907-8.
8 S. G. Burrard and A. M. Heron, Revision of the above. Delhi, 1932-33.
9 S. G. Burrard, "The attraction of the Himalayan mountains upon the plumbline in India."
Prof. Pap. Surv. India No. 5 (1901).
10 H. G. Shaw, "Observations of atmospheric refraction 1905-9." Prof. Pap. Surv. India
No. ii (1911).
11 J. de Graaff-Hunter, "Formulae for atmospheric refraction and their application to
terrestrial refraction and geodesy." Prof. Pap. Surv. India No. 14(1913).
? J. de Graaff-Hunter, "The height of Mount Everest and other peaks." Lecture before the
Indian Science Congress, Madras, 1922. Reprinted in Geod. Rep. Surv. India, 1 (1924).
J3 J. de Graaff-Hunter, 'Auxiliary Tables.' Part II (Fifth edition) reprinted, Dehra Dun,
1928.
x4 J. de Graaff-Hunter, "Geodesy." Dep. Pap. Surv. India No. 12 (1929)*
*5 Guy Bomford, Geod. Rep. Surv. India, 3 (1929) i33~35-
16 R. H. Phillimore, Historical Records of the Survey of India. Vol. IV, 'George Everest,
1830-43" (in proof stage, December, 1954).
The measurement of Everest was a result of a larger interest in mapping India. This was driven by the British desire to define the boundaries and geographic features of the subcontinent for both political and commercial reasons. The maps created by the Survey of India were crucial establish the British notion of India and helped to turn this idea into a tangible reality.
Atmospheric refraction along the sightline is one of the principal factors that affects the accuracy in computing the height of a mountain peak.
When a line of sight is directed from the observer to a mountain top, the light must pass through different layers of the atmosphere with varying densities and temperatures. As a result, the light is refracted, or bent, along its path. This bending causes the apparent position of the mountain top to change.
Geodetic operations are a set of mathematical and scientific techniques used to accurately measure and represent the Earth's surface and shape. In the 19th century these operations were crucial for creating maps and determining precise locations on the Earth's surface. Common geodetic operations involved measuring angles and distances between points on the Earth's surface to determine their positions relative to each other. These techniques were essential for the creation of accurate maps, particularly in the context of territorial claims, and laid the foundation for modern surveying.
This sentence roughly translates to:
> "In the practice of geodesy, the light path is always a curve that is sufficiently small to be equivalent to its osculating circle."
*The six measurement stations (all in Indian territory)*
The Great Arc of triangulation refers to the network of survey lines (pictured below) that was established across India to map the country.
This translates to:
> "meteorological elements which are indispensable to collect at the same time as the zenith distances."
James Thomas Walker was the Surveyor General of India.
*General JT Walker*
This sentence translates to:
> "It is therefore true to say that terrestrial refraction is proportional to the angle formed by the verticals at the ends of the refraction curve, and that it is substantially the same, at a given time, for the two compared stations, provided their difference in level is small."
The reason for this is related to the way that light is refracted as it passes through Earth's atmosphere. When light enters a medium with a different refractive index, such as the different layers in the Earth's atmosphere, it is bent, or refracted. The amount of refraction that occurs depends on the angle at which the light enters the medium and the difference in refractive index between the two media. The greater the angle at which the light enters the atmosphere and the greater the difference in refractive index, the greater the amount of refraction.
In the context of measuring the height of a mountain, the angle formed by the verticals at the ends of the refraction curve represents the angle at which the light enters the atmosphere, so the greater this angle, the greater the amount of refraction and the greater the error in the height measurement.
This translates to:
> "Delambre noticed in France that it [the coefficient of refraction] has an average value of about 0.07876, or simply 0.08, during foggy times 0.15, 0.06 to 0.08 in summer, and 0.08 to 0.10 in winter. Other observers have even found 0.5 during rainy times."
This translates to:
> "We will assume it [the coefficient of refraction - k] to be constant, although in reality it varies from one place to another, and perhaps also in the same place in different seasons."
Puissant understands that by assuming that the value of atmospheric refraction is constant, the calculations and measurements made in geodesy can be simplified.
Spheroidal height refers to the height of a point above an oblate spheroid, which is a mathematical representation of the Earth's surface that takes into account its equatorial bulge and polar flattening. It is used in geodesy and surveying to accurately determine the three-dimensional location of points on the Earth's surface.
A lapse rate is simply the rate of decrease of air temperature with increasing height above the Earth's surface.
Differential deflections are the difference in the magnitude of the deviation of a ray of light due to atmospheric refraction at two or more observation stations. In triangulation, when observations are made at several stations to determine the height of an object, significant differential deflections can complicate the problem and lead to a faulty estimate of the curvature effect.
*New observation points*
A geoid is the Earth's surface that represents a level surface that would be obtained by a sea level extended under the force of gravity and undisturbed by tides, winds, or other influences. It is used as a reference surface for determining the heights of objects, including heights of terrain and objects above the sea level. In other words, a geoid is a mathematical representation of the Earth's irregular shape and its uneven distribution of mass.
Mount Everest was given its moniker in honor of Sir George Everest - British Surveyor General of India (1830 to 1843).
In 1849, the British survey team aimed to preserve local names for the various peaks, but the task proved difficult as they were unable to locate a commonly used local name for the highest mountain. As a result, Andrew Waugh, the then-British Surveyor General of India, chose to name the peak after Sir George Everest (his predecessor as Surveyor General of India).
Despite Sir George's objections, as he believed the name couldn't be written in Hindi or pronounced by those in India, Waugh's suggested name was accepted and in 1865, the Royal Geographical Society officially recognized Mount Everest as the name for the tallest mountain on Earth.
*Sir George Everest*