TECHNICAL PAPER No. 8
THE HEIGHT OF MOUNT EVEREST
A NEW DETERMINATION ( 1952-54) "
BY
B. L. Gulatee, M.A. (Cantab.). F.R.I.C.S., M.I.S. (India)
Director, Geodetic and Research Branch, Survey of India
PUBLISHED BY ORDER OP
THE SURVEYOR GENERAL OF INDIA
Price Three Rupees or Five Shillings.
TECHNICAL PAPER No. 8
THE HEIGHT OF MOUNT EVEREST
'' A NEW DETERMINATION ( 1952-54 ) "
BY
6. L. Gulatee. M.A. (Cantab.). F.R.I.C.S.. M.I.S. ( India )
Director, Geodetic and Research Branch, Survey of lndla
PUBLISILED BY ORDER OF
THE SURVEYOR GENERAL OF INDIA
Price Three Rupeen or Five S h i l l i ~ g s .
PREFACE
Mount Everest is located on the Nepiil-Tibet border and is the
pride of the Great Himiilayan range. It is about 10,000 feet higher
than ICilimanjaro, Africa's highest mountain, whose height has just
been re-determined precisely1, and even the highest peaks of U.S.A.
would rank as its minor satellites.
The height of Mount Everest accepted by the Survey of India is
29,002 feet ; this has elitlured for over a century ancl the last digit of 2 has
intrigued the expert and the lay-man alike for a long t,ime. Scvcral
other values such as 29,050, 29,080, 29,141 and 29,149 have been quoted
for it from time to t,ime and with the growing enthusiasm regarding all
matters pertaining to Mount Everest, certain half truths keep on getting
printed in the semi-popular and even geographical and scientific literature.
For instance, in the wake of the disastrous Assam earthquake of 1950,
a story found wide circulation in U.S.A. that Mount Everest was pushed
up and that the geologists now consider its height t o be 29,200 feet.
Similarly in t,he London Times ( December 3, 1951 ), a correspondent
asked for the most recently determined height of Mount Everest. He
was told in reply by a wiseacre that 29,140 feet was the latest figure
from revised computations and "Until Mr. Shipton or some other climber
stands gasping on the summit wit'h an aneroid in his hands, this seems
to be the best that science can do".
To dispel such popular erroneous impressions, the author brought out
a paper2 which gave an appraisal of the peculiar difficulties associated
with the determination of the heights of lofty mountain peaks. Cwlculations of such heights is dependent on a number of important factors in
a field which is mainly the preserve of specialists. It was explained in the
above paper that because of lack of proper observational material and
geodetic data the older calculation of the height of Mount Everest was
entirely inadequate and there was urgent need for scientifically planned
observations t,o this peak from mountains in Nepal not far from it.
This papcr describes in detail the work undertaken for this purpose
during the years 1952, 1953 and 1954. Very careful planning was required to ensure an adequate number of ~bservat~ions,
bearing in mind the
difficulties of terrain and lack of transport and communications.
The first desideratum was to carry a triangulation series as close t o
the peak as possible. This is a costly item and would have been unjustifiable if carried out solely for the purpore of detcr~niningthe height of the
peak. Fortunately a chain of minor triangulation was run in Nepal in
the years 1046-47 t o provide control for irrigation projects. 'Phis was
reinforced by 3 measured bases and 3 spirit-levelled connections and
the triangulation was extended to the north in 1952-53, so that its most
northerly stations were a t distances of 30 t o 40 niiles from the peak ( see
Chart I1 ). Mount Everest was observed from 8 stations of this series
ranging in height from 8670 to 14762 feet and great care was taken t o
ensure that the heights of these take off stations were well fixed in
tenns of spirit-levelling.
' The ralculatiorl of the height of Kilitnnlljnro ', l)y 11'. 1.. 1)ickson. Empirr S ~ ~ r v e ~
Review, Jan. 1954, p. 206.
" M O I I I1':verekt-Its
I~
name ant1 height ", by 13. 1,. Gul~tee,Survey of Indin, Technical
Papcr No. 4.
The previous attempts t o fix the height of the peak were also hampered by complete lack of geodetic data. I n 1953-54, a comprehensive
programme of plumb-line deflections and gravity observations was
carried out t o delineate the geoidal rise under Mount Everest. These
observations are unique in many ways and are of great significance for
revealing the mecllanisnl of conlpensation of this interesting region.
Topo triangulation extending west from Darjeeling was carried out
by Messrs. R. S. Chugh, U. D. Mamgain, R. L. Sharma and N. N. Dhawan
during the years 1946-53 ( Chart I1 ) ; the extension triangulation by
Capt. &I.M. Datta ( 1953 ) ; vertical angle observations by Messrs.
M. M. Datta and J. B. Matliur ( 1952-53-54 ) ; the plumb-line deflections
by Shri J. B. Mathur and the gravimeter observations by Shri A. N.
Ramnnathan ( 1954). Much credit is due t o the observers for carrying
the work to a s~zccessfulconclusion under arduous conditions, especially
as t,hey were not well equipped for climbing on high mountains.
The analysis and reductions of the new data have entailed heavy
worlr in which I have received much assistance from Shxi C. B. Madan and
the staff of the Comput,ing Section a t Dehra Dan. These are described
fully in this paper and are compared in detail with the earlier observations.
The new value obtained is 29,028 feet which, it is hoped, is not
likely to be in error by more than 10 feet. It will serve no useful purpose
t o push the accuracy further by more observations as the seasonal
fluctuation of snow on the summit could well be of this order of magnitude.
The older value of 39.002 feet was vague and was computed in a most
incomplete manner, e.g., with a definitely wrong value of refraction and
with no regard t o the datum surface. It has always been suspected
that it erred on the moderate side and some enthusiasts have regarded
the peak t o be some 200 feet higher than the quoted value. They will,
no doubt, be disappointed. The accepted value 29,002 feet has been
critically appraised in para 9 and it will be seen that the implications of
this new figure for height are very different from those of the old one and
the two are really not comparable. The fact that they are so close
together is due to fortuitous cancellation of the effects of certain important
physical factors which had been neglected in the previous computation.
My thanks are due to Brigadier G. Bomfortl for helpful discussions
both orally and by correspondence.
B. L.GULATEE, M.A. ( CANTAB. ),
DEHRA
D ~ :N
Dated 25th Oct. '54.
F.R.I.C.S., M . I . S .
( I N D I A ),
Dirwtor, Geodetic & Research Branch.
CONTENTS
Page
..
Preface
..
..
..
I
Para
2.
Heights of HimPlayan Snow Peaka
..
Refraction
..
3.
Datum
4.
Heights of Observing Stations
..
..
..
..
..
5.
Outline of the New Method
..
..
.
6.
Triangulation and Height Data . .
..
..
7.
Plumb-line Deflections and the Geoid
..
8.
Final Value of Height
..
..
9.
Analysis of the older values of 29,002 feet and 29,141
..
..
..
feet for Mount Everest
1.
10.
Summary
..
..
..
..
..
..
..
..
..
.
..
..
..
Tables
Table 1. Height of Mount Everest from observations from
the plains
Table 2. Height of Mount Everest from observations from
Darjeeling Hills
At end.
Table 3. Deflections and Hayford Anomalies
Table 4. Vertical angles to Mount Everest
Table 5. Height of Mount Everest
Charts and Plates
Pi~go
Air Photograph of Mount Everest from the south-west . . Frontispiece.
Chart I Older Observations to high HirnFilayan Peeka.
.. I
Chart I1 Triangulation, Levelling and Deflection Date in Nepgl.
2
Chart I11 Triangular Misclosures in Height. . .
..
..
9
Chart I V Deviation of the Vertical.
..
..
. . 10
V Geoid in NepLl. . .
..
..
Chart V I Geoidal Section Ladnia-Mt. Everest.
Chart
..
..
..
12
13
3
4
I
I
1
84. -
CHART I
-
I
I
88"
II
9i
P
OLDER
OBSERVATIONS
TO
HIGH HIMALAYAN PEAKS
THE HEIGHT OF MOUNT EVEREST
B. L. GULATEE,M.A. ( CANTAB. ),
F.R.I.C.S.,
M.I.S.
( INDIA )
Heights of Himllayan Snow Peaks.-The
North-East LongiI.
tu&llul Series, covering a linear distarlce of about 740 lnilos from the
Debra Diii~base to Sonakboda base in BihLr, was observed in the year8
18.16 to 1851, with theodolites ranging in size from 16 inches to 3G inches.
It. was oiiginally inteilcled that this series should run along the Nepal
nlountains but inspite of repet~tedattempts the Nepiil Government clid
not accord permission for observations along tllis route and the plan had
to be itltered. After crossing the hills of Garhwsl, the t,riangles were
lilacle to pass through t,lie malarious and unhealthy tracts a t the foot
of the HiiuLlayas. The country being flat, towers about 20 to 35 feet
high were used to secure inter-visibility of stations. Chart I illustrates
how the HimLlayan peaks in NepLl were observed as intersected points
by surveyors in 1849 to 1856 from distant low lying stations of this
series. For comparison, the modern stations from which Mount Everest
has been observed are shown in the inset.
The heights of the Himalayan peaks evoked great interest iu the
Survey of India even in the early days and in a ciroular issued to
the Great Trigoiiometrical Survey parties in the field in 1845, the
Surveyor General Sir Andrew Waugh wrote "The lofty snow peaks
situatecl north of NepLl are the most stupendous pinrlacles of the globe.
Their Ileights and relative positions shoulcl form permanent objects in
the geodetical operations ". His ii~structionsto Nicholson in 1849, when
Ile was observing along the North-East Longituclinal Series, were "You
should be in the observatory before sunrise and all prepared to comnlence
horizolltal a.ngles as soon as i t is light. The verticd angles may be
taken fronl 8 to 10 o'clock a.nr.". It is extremely difficult t o get visibility
in the itftenlooll over such long rays and the lavt sentence was added
to orisure at least some observations being taken a t other times, so that
the opportunity to observe the high peaks was not entirely lost.
When viewed fro111 the plains of Nepiil, Mount Everest, illspite of its
towering personality, does not appear to over-shadow the array of
surrounding peaks. I n fact, some of the peaks, on uccouilt of their
I icanleus, girt: the ill~~sion
of being higher and when observatiolls were
t>akento Mount Everest. there never was the slightest suspicion that
it W ~ L Hthe highest iiiountain in the world. The general belief at the time
was that KBnchenj ungit was the world's loftiest peak. The observers
took an ilnrne~lsenumber of horizontal and vertici~lai~glesto the sn9w
peekn from the pri~lcipalstations of North-Et~stLongitudinal Series.
'l'hey could not, possibly discover inclividnal local llrunes from such
long dista.nc*es and quite u nunlber of peaks were charaoterized by
figures ant1 R,o~llannamernls. Ivlount Everest was simply labelled ' b '
by iir~nstrong,'y ' by Waugh and Lane and ' h ' by Nicholson. This
\vaa changed tto peak XV a t hendq~art~ers
by Hennessey.
X reftarence to some old nluauscriptu hits reveatled that J. W.
t\nnst,rong while observing t'he Gora Meridio~liilSeries had thrown i t
sillgle ray to Mollnt Everest. in 1847 from n distance of nbont 200 miles.
' h e (~bservntio~l
consisted of a single determinntioa of distance and
;I vertical a'ilgle. The vcllae of the height which Iio obtained was
2H,79!) feet,.
It ww later observed from the following aix stations of the N.E.
Longitudinal Series in 1849-50 :-Jarol, Wrz&pur, Janjipati, Lednits,
Harpur, and Minai ( see charts I & I1 ).
These are stations in the plains a t an average height of about 230
feet above mean sea-level and towers ( about 20 to 32 feet high ) had to be
built on them to make them intervisible for triangulation. The stations
were about 110 miles away from the mountain. Once it was known that
this was the world's highest peak, great pains were taken over the
reduction of the data. I n particular, a lot of attention was paid to
refraction which plays a dominant role when the rays are long.
No narrative account giving details of the old height ~oniputation~
of Mount Everest is forthcoming. Table I gives a synopsis of the observations ; the heights calculated from each station are given in column 9, the
mean value being 29,002 feet, which is the figure adopted up to the present
time. This table has been compiled fiom the original computation volumes.
It is on record that Sir Aidrew Waugh took elabori~teobservations
for determining the curvature of the path of a ray of light between a
number of peaks in the outer HhnLlaya and the plains of Bengal by
means of simultaneous reciprocal observations. The coefficients of refraction k were obtained by giving due weight to the number of observations
and the length of the sides. From column 10 of Table 1, we see that the
k's are given to 6 places of decimals and are different for different stations.
The basis for the derivation of so many fictitious digits is nowhere stated
but it is representative of the trends in those days. Actlually,the concept
of k for such long rays is erroneous and although with our present knowledge we can do much better, still for such long rays, the evaluation of
refraction is even now subject to considerable uncertainty. I11 a1137
case, the figures adopted for k ( 07 to - 08 ) were very much s t fault ; t h e j
should have been of t'he order of 0.05. No account was taken of plumbline deflections either, its ideas about them were rather vague in those
times, nor was the necessary information available for fixing t,he datuni
above which the height was reckoned.
In the seasons 1880-83 am1 1902, further. observations were taken
hom statiolis in the Darjeeling hills in the course of the normal survey
programme. ( See Table 2 ). These stations were also too far, being
a t an average distance of 00 miles from Mount Everest, but they had the
;tdvantage of being a t a higher level. Assuming a coefficient of refractio~l
of 0 05, Burrard calculated the height of Mount Everest from these observetiom in 1905 and arrived a t the value of 29,141 feet*. He also recoiiiputetl
t,he olclel* observations and fixed the coo6cients of refraction for the
various rays by trial and error it1 such u way that the mean result came out
to be 29,141 feet. Here again plumb-line deflections were not utilized and
this value is also above an undefined datum. But it has attracted
conRiderahleattention in recent years. The Americans have published it
on their maps and such a11eminent mountaineer as I?. 8. Sniythe in his
book "I\iIountains in co'our" published in 1949 made u definite statement
that the true height of Mount Everest was 29,141 feet. He attributed
the difference from 29,002 feet to be due to the fact that "the mass of
the Himilayas puts the bubble of a, theodolite very slightly out of plumb
to the centre of the earth" which of course in not the true explanation.
Before we describe the new observations, i t would be well to recount
wmo of the factors which have an important boaring on the problem of
the determination of heighbof inaccessible peaks.
__
- __
_
- - __._
_ _ .
-
" A oketch of tho Geography and Geology of the Hirnil8ya Monntains and Tibet," by
Col. 3. O. Uurrerd and H. H. Hnyden, Part I, 1807, p 28.
Chart II
2.
Refraction.-It
was realized even in the earliest days that
refraction was a most potent factor in evaluating the heights of the high
mountain peaks as observed from long distances and much effort was
expended in deriving the appropriate coefficients of refraction. For
rays of 115 miles or so, an error of 10-6 in k produces an error of a
foot or so in height and this is why in the older computations the k's were
taken to 6 places of decimals, because they computed each derivation of
height to one place of decimal. No temperature and pressure observations were taken and it is not known how such a large number of
digits were selected-possibly the ruling consideration was that there
should be a good measure of agreement between the heights derived from
various stations. I n the light of modern knowledge we know now that
the coefficients of refraction adopted in the older computations were
grossly in error and the results from the various stations were quite
heterogeneous being burdened with varying systemat ic
' errors.
The curvature of a ray of light and consequently its refraction
of
depends on temperature T, pressure P and temperature gradient
the atmospheric layers through which a ray passes, and is changing all
the time. To obtain it accurately, observations for air density are
required all along t'he ray at the time of observation. This is never
feasible in practice and certain assumptions have to be made. The
simplest method is to assume a value of coefficient of refraction k for the
ray and get refraction from the formula R = kX, where x is bhe length
of the ray in angular measure. This concept of k is, however, not valid
for long rays with their extremities a t very different elevations. It is
only applicable to an infinitesimal part of a ray, being dependent on the
values of p, P and T prevailing there and these vary throughout the day.
Air being compressible, has a greater density near the earth because
of the greater mass above it. When it rises, it expands and is cooled
without transfer of heat and thus changes of temperature can occur in
an ascending or descending mass of air due to different pressures. Theory
shows that this dynamic cooling of dry air due to expansion is 5.5"P.
per 1,000 feet. This is called the Adiabatic Lapse Rate. The above
figure, however, is for dry air ; the presence of moisture has a considerable retarding effect on the cooling and a good average value is 3 ~ 2 ° F .
per 1,000 feet. Much research (theoretical and practical ) has been
carried out on refraction since the beginning of this century and i t has
been found that the major portion of the variation of refraction is caused
by the large diurnal fluctuations of the temperature gradient. I n the
plains, the lapse rate may change by as much as 200% in the course of
a day and in the layor close to the ground surfacer, the extent of variation can be very considerable. The modern practice to overcome
irregular effects of refraction is by selecting a particular time of observation, called the time of minimum refraction. This happens to be near
mid-day, as it is only a t this time that variations in the temperature
gradient from day-to-day are least. On this account, the normal reciprocal vertical angle observations are confined to this time in t,he
llnual routine of topographical surveys and if tho extremities of t,lle ISny
nre not a t vory different elo~at~ions,
~.ofrscbionis nssnmed to be tho same
at, the two ends.
The snow peaks of tllr Himiilaynu, howevor, present, ono g l r ~ t ,
clifficulty in that reciprocal observations are not possible. Even with our
present knowledge it is not* possible t'o give a theoretical formula for
refraction, which will be eaivrrsnlly applicable for all lrngths ofra,ys, because
int,orvening lapse mtrs nmv he very different. from the accepted onaq.
Experience shows that even for a triangulation series with comparatively
short sides, heights derived from reciprocal observations differ systematically according to the square of the length of the ray, indicating clearly
that the act,ualtemperature gradients are different from the tabulated ones.
The only practical way of overcoming the uncertainty of refraction
in such a case is to observe from high hills close to the peak. The diurnal
variation of lapse rate is comparatively small in this case and it is not
absolutely essential to confine the observations to mid-day. The values
of refraction for the various rays in this paper have been calculated by
using the following formula for the coefficient of refract'ion :k
=
and
50,000
fl
P
-(
T2
0.0187
+ /?), where T is in absolute degrees F
is degrees F/ft.*
has been taken as 3.2"F/1,000 ft.
For steep rays, like the ones to Mount Everest, where the temperature and pressure conditions a t the two ends are very different, it can be
shown t,hat a value of k pertaining to a point 1/3rd up along the ray
gives a very good approximation. It will be shown in a later section
that the resulting error in height, due to probable fluctuaCions in /3 for
the obsel-vations under discussion, is negligible.
3. Datum.-The heights of points on the earth to be comparable
with one another have to be reckoned above the same reference surface.
Several such reference surfaces are available some of which are real
while others are imaginary. Two of the most important' ones are the
reference spheroid of the country on which the triangulation is computed
and the mean sea-level surface ( geoid ). In India, the latitude and
longitude for mapping purposes are computed 011 a true spheroid called
the Everest spheroid. The geoid is, however, not a true mathematical
surface on account of the irregular di~tribut~ion
of land and sea. One
can consistently work on either surface, i.e., one can quote either spheroidal
or geoidal heights provided one does so uiliformly. There are, however,
certain pros and cons regarding the choice of the reference surface which
need clarifying a t the outset. The interacttionbetween these two surfaces
involves some abst,rnse conceptions and even the expert's have fripped
over it in the past,.
The geoid, although irregular, has an actual physical existence and
the surveyor'^ or engineer's level a t each setting sets itself parallel to it.
Starting with the mean sea-level at a given coaetal observatory, i l
geodetic surveyor can trace the geoid in great detail within the limits of
observational and in~trumentalerrors. The reference spheroid, on the
other hand, has a mythical existence and can only be located by means
of the geoid with the help of geodetic and astronomical observation^.
While it is the only suitable surface for reckoning latitudes and longitudes,
it is not MI suitable ag a height datum. I t s adoption would lead to nonuniformity, as different countrie~use verv tlifferent spheroids ;IS trtiei~*
f i p r m of the earth.
O11r predecessors in the laat cent,nry knew levelling and so were
able to obtain gcoiclal heights tthereby. I n the plains by the memuremerit of vertical ;~nglesthey wero also getting geoiclal heights, nlt,hol~gl\
they were o f t ~ n llnnwnro of' it. They were 11ot able to oht nit1
heighk above t,he Everost spheroid, a~ they laoked the inforn~i~Lion
regarding the ~eparationof the geoid from the spheroid. In fact,, t,hoj,
quite often confused the two ~urfnces.
--
-.
--
-
--
" O ~ o r l ~ n vhv
" O Rnmfnrd, p. 169.
-
- --
--
--
I n the plains, the use of geoid EM datum surface for height offers no
difficulty. Levelling with suitable corrections can be made to
give the geoidal height direct. The usual method employed is t h a t of
vertical angles. The heights given by this method ere vague and further
considerations are necessary t o reduce them either to the geoicl or t o the
spheroid. The t,heodolite when levelled, defines the geoidal normal and
angles are really geoidal angle^. The u ~ u aheight
l
so the observed ve~-t'ical
forlnul~employed in triangulation makes two drastic assumptions, viz :,
( a ) that the observed angles are spheroidal, and
( b ) that the geoid is a sphere.
It can be proved that, with conditions :is they exist in nature,
reciprocal vertical angle observations in normal topographical triangulation give good orthometric geoidal heights inspite of the apparently
erroneous assumptions involved in the compu tations. For longer ray8
as are met with in geodetic triang~lat~ion,
the precision of heights becomes
obser~at~ions
are not
less and for high Himiilayan peaks, where recipr~ca~l
feasible, t,he t'rigonometrical method gives poor geoidal heights. Hence,
the older determinations of high HhnBlayan peaks were week. To get
heights of such peaks with any degrec of accuracy requires quite different
considerations as will be seen later. It is important to realize that
spheroidal heights can only be obtained from triangulation if everg
ob~ervedangle is corrected for deflect'ions of t,he plumb-line and t,his has
never been done.
The geoidal height of high mountain peaks can only be derived
via the reference spheroid used and this necessitates that t'he relation
between the two surfaces should be known very accurately.
Tho ftlll specification of a, reference spheroid involves 5 quant,ities
to,No ) a t the datum select,ed a.s the origin of t,riangulation,
where a, b denote the semi-axes, qo, to t'he plumb-line deflections
and No the separation between tIhe geoid and the spheroid. I n India,
t,he axes ( a, b ) of tjhe Everest spheroid which is still in use for mapping,
\\rere determined in 1830 and the datum chosen was KaliBnpur. I n
the 18509s, when observations t o Mount Everest' were taken, ideas about
such concepts as plumb-line deflections and reference spheroids were
rather vague and not much attention was devoted t o qo, to, No. In fact,
t.he measnred base-lines in those days were reduced t o geoid assuming
it t,o coincide witlh spheroid everywhere. As geodetic knowledge progressed, it became imperative to nUocet.e n. valuo t o No. It. was defined
t'o be zero a t KnliZnpur in 1926 using the criterion that this choice made
the mean height of tho geoid above the spheroid under the t.en India,n
bases that, hnd been measured up to t,hat.time to be zero. The yew 1925
1)ronght about t,he advent of the Inte~.n,ztionalspheroid, which is a considcl-a.hleimprovement-,on the Everest spheroid. For all scientific st.udies
of the geoid, thig is t'he spheroid now nsed in India. It was defined tto be
31 feet above the geoid a t KaliZnpur in 1927 and the relation between t,he
:~~bove
two ~pheroidsin India has been sllown graphically by the author'.
It' is only when the concept of such a' reference spheroid is introduced too
serve n's an intermediary t'hxt tthc problem of heights of high Hirnkl~yan
peaks tIalres 011 a coherent form. T l ~ colder fignl.es of 29,002 feet, and
29,141 feet quoted for the lleigllt of Mount Ererest are r.~t,ller
V R ~ I I Cill
tlint, they do not refer t,o any dofilled da8trllnl.
( n, b, qo,
"The sepsrntio~l between diffnrent. ~pheroid~'',by R. L. C1111ntce. Survey of Indin.
flen~letinRixport., 1034, Chnpter VIII.
table below gives the
4. Heights of Observing Stations.-The
heights of the 6 stations from which Mount Everest was observed in
1849-50 :I
I
1
Height
old computations I Height published Difference
St'at'ion of observation
feet
feet
I k -
.Jar01 T.S.
23 1
220
-11
Mirz5pnr T.S.
5 4
245
-
9
Janjipati T.S.
263
255
-
8
Ladnia T.S.
24 2
235
-
7
Harpur T.S.
226
-
7
. --
-
-.
feet
I
219
I
Minai T.S.
I
228
237
- 9
Column 2 gives the heights used in the older computations and column
3, the present accepted heights after adjustment to spirit-level values. I t
will be seen that the mean height of the observing stations has changed
by about 8 feet. As a result of this the height of Mount Everest was
changed to 28,994 feet on the charts of triangulation in the General Reports
for the years 1892 to 1903. I n 1903, the old value of 29,002 was restored
aa it was realized correctly that the change was premature in that any
new value would be burdened by much larger errors*.
The values of the starting stations of 1880 observations have also
undergone changes as a result of later spirit-levelled connections as t'he
following table will show :St'ation
'
1
1
Year of
observation
- _,_
1
Height accepted in Present accepted
values
older computations
I
.
. -- ----
,feet
.feet
-- - -
Suherkum h.s.
1881
1 1,641
..
Tiger Hill h.6.
1880
4.507
..
I
Senchal h.n.
1902
8,599
8,584
I
!
I n order to avoid any uncert.ainby on t'hi8 accollnt, special care we8
taken to provide an adequat,e llilmher of gpirit,-levelled connections in
thc new t r i ~ n g u l a t ~ i owhich
n~
have heen 11.setl bo provide ~t,nt.ionsof'
r ~ h ~ e 1 7 r ~ tfor
i ~ )the
n npw work.
5. Outline of the New Method.. The: three main source8 of' 1111certsinty in tho oltler rleterminatiorl am-( n ) refrrt~t~ion,
( b ) neglect,
of rleflections ant1 ( c ) non-specification of t,he (Iat,um surface.
-
"A
('44.
.
skctrh of the CIrogapl~ynnrl Geology of thc HimBlnvn X l n l ~ n t n i nnnrl
~ Tihrt " l)v
'4. (1. Rnrrnrd, nnrl Jf. H. Hnyrlm. Pnrt 1. 1907, pp 28-27.
The diagram below illuatratea how these have bean overcome in
the new method.
LE dellotes
cross-section of the topography betweell L ~ l n i a
( latitude 26" 25' 50" 32, longitude $6" 37' 15". 04 ), a point i ~ the
l plains
of B i h g ~and Mount Everest; A is it statioii about 12,000 feet high a t
distance of 30 lniles ( say ) froill Everest,. The sections of the geoid,
Internatiollul spheroicl and Elrerest spheroid between these pointts are
ctlso shown in the cliiigritlil.
Our objective is to get EG the height of the peak sbovo the geoid alid
this can bc doile via the inter~uediaryof' the International or Everest.
spheroids. For our ~.eductions,we ha\-c chosen the former. If N1, No
tleliote the geoitiul rises under A and E respectively, we have EG = ACTl
(1 -I
) - ( No - N ) 'I'hc spheroidal height difference ( EI .lI, ) is determined by verticid i~ngleobserl-ations ( corrected for plumbline deflections ) which are burclenccl with ref~act~iol~.
I11 the older
observatioiis AE was of the order of 100 mi1t.s itlid in such a cme refraction
prod~tcesall insuperable dificul tjy. I t is sy bject to large diurnal \.-itri;ttioil
and its coniputation fro111 tlie~ret~icitl
considerntions, c i ~ nbe in error by
considerable nlnounts even if the observations are confined to the time of
minimum refraction. I11 the present work, the vertical angles to Everest,
are taken from a number of high peaks ( typified by A ), ciistant about
35 miles from the peak. Tliese statiolis are connected to the main
G.T.series ( N.E. Longitndin~lSeries ) by a, short -sided triangulation.
Itefritction a t these altitudes, being neither so large nor so erratic rn in
the low lying plains, can be tuclded lnncll more successfully. The oorrection to height due to refraction is only one-tenth of that of the earlier
observations. At S U C ~high levels, the outstsandingitems that have to be
reckoned with are plumb-line clofleot,ions and geoid ; e m m due to refraotion ere secondery,provided there are no grazing rays.
+
It might be mentioned that the height of Mount Kihmanjaro ( 19,340
feet ), the highest mountain in Africa has recently been redetermined'.
I t was possible for the observers to get to the mountain top with their
theodolites and to carry out reciprocal observations. No account was
taken of the plumb-line deflections, as Kilimanjaro is not such a large
mass. It is on account of the gargantuan mass of the Everest producing
exceptionally large deflections and deformation of sea-level and the fact
that no observational work is possible on its summit that so many refinements have to be taken into account.
It can be shown that the ordinary trigononletrical co~upututionsof
reciprocal rays of a short-sided triangulation give a good value of tile
geoidal heights. The geoiclal height AGl of A is thus precisely known.
Tlie carrying out of short-sicled triaiigulwtioil close to the pealr is
tllus an important step forward. Not only does i t do away with tlie
major uncertainty due to refraction but it also gives good geoidal lleight,s
for observation stations without worrying about deflections.
Tlie estimation of ( No - N, ), the anomalous rise of the geoid in the
last 35 miles, has to be baaed on clues provided by deflection and gravity
observations. Deflection observations have been carried up to NZiiiche
Bazgr, a distance of only 18 niiles from Mount Everest.
In the older derivation of heights, neither the deflections nor the
relation between the geoid and the reference spheroids were a~railablc
and the derived heights dicl not pertain to any specific surfacc, as no
;kccount was taken of these important factors.
6. Triangulation and Height Data.-Chart I1 shows the triangulatioil used for deriving the new value of the height of Mount Everest.
The various topographical triangulations emanatring from the stations of
the North-East Longitudinal Series were execut'ed in the years 1946-53 to
provide control for irrigation projects in coniiectioil with the Kosi Dam.
Four Laplace stations and three base-lines were introduced in the circuit
Thakurganj-DumdZilgi-Tonglu-Sandakphu4al~hi4hy.zmtang-TemkeKhamtel -Meenashi - Dungre - CheutZre - Sartulga - Ladnia. This circuit
closed with an error of 1 in the 5th place of log side, 2" in azimuth, -0".07
in latitude and - 0". 1 1 in longitucle, which is very satisfactory.
stations to Mount Everest.
For the purpose of providing ob~ervst~ion
itn extension triangulation was carried out in 1932-53, starting from the
aides MayBm h.a .-L5ori Danda, 1i.s. and AisyBlukharka h.s.-Chhuly81iilr
h,s, of the above work. This extension triarigulstioii provided eight,
stations a t heights railging from 8,670 to 14,762 feet, from whcll
vertical angles were observed to Mount Everest in the years 1052-53 and
1!h53-*54.
( u ) Y o ~ i t i ooft ~J l o ~ t Everest.--The
~t
old podition of Mount E:ve~-cst~
was rather doubtfully fixed. It was observed from seven stations of the
North-East Longitudinal Series, but no two of them were intervisiblc.
The angles had to be deduced through reference station9 other than the
observing station9 with the help of azimuths computed from co-ordinates.
The origind computed values of the position wero :-
Latitude
Longitude
-I
.--
0
1
27
86
69
16:748
58
05.852
--.
-
--- - .- .
-
-- -
Empim S m a y Review, Jan. 1964, No. !)I, Volume XII, p. 206.
Tho co-ordinates wero recomputed in 1005 using the adjusted
co-ordinates of the observing stations as derived from the simultaneous
adjustment of the principal triangulation of India. Tlie longitude WPY
also brought into terms of the latest value of the longitude of tho Madras
Observatory. The co-ordinates adopted were
16". 22
Latitude
27"
59'
Longitude
86
55
39 - 9 1
Although not important from the point of view of height determination, the co-ordinates of Mount Everest have been refixed from three
stations, viz., Bukur h.s., ChhulyBmu 11.s. and Upper Rauje h.s. during
1963.
The results of t,he two triangles are very accordant, the mean value
being
67"
59'
15". 85
Latitude
55
39 -51
86
Longitude
Mount Everest has thus to be shifted by about 40 feet southwards
and westwards from its accepted position.
( 6 ) ~ e i ~ h t s . - - ~ i o ran perusal of Chart 11, it would appear that the
triangulation heights are well vorltrolled by spirit-level connections. The
heights for the computations of the present series take off from Diwanganj
T.S. ( 72 J ), Chatra V.S. ( 72 N ) and Darjeeling Observatory h.s. ( 78 A ).
Thcir spirit-levelled heights are as follows :feel;
Diwanganj T.S.
188-89
378.68
Chatra V.S.
Darjeeling Observatory 1l.s. 7,144.85
Tlie hcights of Maysin h.s. and LLori Dsnda 1l.s. were clerivecl
iiltlepei~dently from 3 routes,-from Ladnin T.S., fronl Cliutr;~V.S. nncl
Irom Di~rjeeling Observatory h.s. respectively. The heiglits derived
froin these three routes have bcen weighted in the pl.oportion of 2, 3 and
1 respectively. The result fi-orn Chatra v.s. has been given the greatest
weight as apt~1.i;fronl being sl~ortest in length, it h i ~ s the sinallest
triangular inisclosures in height. The filially acceptccl values of tho
heights of MayZin h.s. and L5ori Duncla 1l.s. are its follows :Height in feet
AlayLnl h.s.
10,948
Liiori Danda 11.8.
11,877
r i
1llc tri;~ngular lnisclosures in h i g h ts of the iliain ancl ex teiisiol~
~triangulatioils
(see Chart I11 ) arc vcry snlall ranging o d y fi-oni O to 4 feet
; ~ u it
d was not considered worthwllilc to acljust. the extension triungul LI, t'1011
1)y t,he nlethod of least squares.
The final vnlues of the heights of bile Y sti~tionsfroln which Moullt
Evcrest is observed are given below :Height in feet
Height in feet
Mnyalll h.s.
10,948
12,059
Pike Sub. 11.s.
L5ori Danda 11.s.
11,877
Sollung 11.s.
11,658
Ai~yRlultllnrlrnh.s.
8,670
13,357
Lower Rnuje h.s.
Cllhuly,%inu h.s.
10,160
Uppor R'nujc 11s.
11,762
Froiu tllc evidence of llic t r i i t l l q ~ l iinisclosums
~~
i t CiLli bo safely
inferred that thcae are correct to witlllll 2 or 3 feet.
'
7. Plumb-line Deflections and the Geoid.-Tlie rise of the gcoid
under t,he mighty range of tho Hi~nblayttsllits been tho subject of much
spaculation. Uue to Llie paucity of deflection a ~ i dgravity data in this
region, no reliable estimate has so far been possible.
By taking a generalized section of the topography of the Himdayas
and Tibet, Mader* reckoned that N ( height of the geoid ) under
Himslayas would be 377 metres without isostasy and 40.7 metres with
isostasy. He also estimated that the uncompensated geoid would rive by
about 300 feet from the plains to a point under the summit of the
Himslayas and Compensated geoid by 120 feet. Mader was not concerned with Mount Everest in particular and his figures can only be
regarded as indicative of the orders of magnitude.
Deflection observations have been carried out during the last 3 year8
to delineate the geoid in the Mount Everest area. For this purpose, a lot of
preparatory work was necessary for providing a good starting basis. The
existing geoidal section along the foot-hills of tlie Himdayas fro111
Dehra DBn to Darjeeling was very weak on account of the paucity of
prime vertical deflections.
I n 1952, a chain of astrolabe stations ( covering a linear distance of
about 300 miles ) was est,ablished a t about 15-mile interval along tlle
tower stations of the North-East Longitudinal Series. These observations provide a reliable value of the geoidal height a t Ladnia T.S.
( latitude 26" 25' 50"- 32, longitude 86" 37' 15".04 ), a point in the plains
of Bihk. I n 1953, work was extended from this point to NLmche Bazsr
( latitude 27" 48' 46" 5, longitude 86" 43' 12". 0 ) which is distant only
18 miles from Mount Everest. The main effort was directed to establish
stations as far as possible along the meridian of 86' 40'. A number of
other surrounding stations were also observed to extend the knowledge of
the geoid in this virgin region.
On account of the cost of transport, difficulties of rations, lack of
communications and paucity of trigonometrical data to establish positions
of stations by resection, it was not possible to put in as dense a, mesh as
would have been desirable and it was apprehended that the variations of
deflections a t such long intervals might be too ragged to allow of an accurate geoidal section being drawn. But the following will show that the
data obtained is quite adequate for providing reliable geoidal information.
Chart IV shows the resulting deflections vectorially at the stations observed. As expected, these deflections exhibit several points of interest.
I n the plains, a t a distance of 96 miles from Mount Everest, the deflections
are northerly and easterly but are of small magnitudes. The northerly
deflections increase rapidly till the foot of the hills is reached at Chautgro
( height 2,615 feet, distance 70 miles from Mount Everest ). From Chautkre
to the hill station of Meenashi ( 6,3 18 feet ), theie is a decrease of 9" in the
meridional deflection and after that there is a steady increase of about
1" a mile t'ill tlie maximum value of 71" is reached a t Lower Raujc
( height 13,357 feet, distance 30 miles from Mount Everest ), beyond which
there is again a decrease as woultl be expected. The 71" deflection at
Lower Rauje is Lhe largest in the world. This deflection is with respect to
the International spheroid. If Everest spheroid had been chosen as
the reference surface, i t would have been greater.
'l'he section Lndnia-Sarunga-ChsutLra-Dungre-Meena,shlianltclKupiikot- A i s y L l u k h a r k a - P L n g u - K h L r t e - C h a u l m c h e BazLr (see
"amid elovstion due to messes of Himilayw & Tibet ", by Medcr. Qerl. Beit. 1036
Vololne 46.
Chart 11) is about 100 miles long and the average interval between
stations in its hilly portion is 10 to 12 miles. It is not ~ t r i c t l yalong
a meridian, although very nearly so.
The geoidal rise along this section was carefully computed as follows:
Although the curves of observed deflections were fairly smooth, our past
@xperienceshows that 10 miles is too long an interval for mountainous
regions and that it is desirable in such cases to reduce the station interval
by deriving deflections a t some intervening stations from theoretical
considerations. The Hayford deflection anomalies ( 7 - qc, 5 - tC)
were computed for the above stations on the assumption of depth of
compensation of 113.7 kilometres and are shown in Fig. 1 along with
the curves of observed deflections. As expected, the anomaly curves
are much smoother than the ( 7 , 6 ) curves. Deflection anomalies
at 6 intervening stations ( K. 109, K. 108, Dungre h.s., K. 136, S. 130 and
Chattarpu h.s. ) were read from these curves and Hayford deflections were
also computed for them from which values of 7 and 6 were derived. The
values at these stations have been joined by dotted lines and it will be
seen that these values produce greater sinuosity in the deflection
Furves, but they reduce the interval between the stations t,o an average of
6 miles, and it is hoped that their introduction has helped to eliminate,
to a great extent, the systematic errors in the computations of the geoidal
rise. I t should be noted that this device to obtain deflections a t intervening stations is not vitiated by the inaccura-cy of the maps or by the
fact of Hayford's hypothesis not being true to nature.
As has been explained before, a knowledge of the geoid between the
plains and the stations from which Mount Everest has been observed is
really not indispensable for deriving the height of Mount Everest. The
very nature of our method ensures that the trigonometrical heights of our
observations would be geoidal heights even though no account was
t'aken of deflection corrections. This depends on the supposition that the
deflections vary linearly between neighbouring stations and are not
burdened with large random errors. To check this, the difference of
height between Upper Rauje and Rupiikot was computed by two
methods :( n ) utilizing reciprocal observations, dispersing height triangular
errors and ignoring deflecbions altogether ;
( h ) by
correcting observed vertical angles for deflections,
computing spheroidal heights and then applying separation
between geoid and spheroid to get geoidal heights.
The difference of heights between the two methods is only 2 - 6 feet in
A tlifferent~ialheight of 6,237 feet which is very satisfactory and sllows
t,hnt, the deflections are adequately linear. Part of the difference is
ncconnted for by the fact that ( b ) was computed dong one flank only.
while ( n ) was compnted by lising a series of triangles.
We now come t80the important problem of estimating the anomnlol~s
gooicld rim hotween tho observation stations and Mount Everest.
A reference to Fig. 1 shows that the meridional anomaly 7 - qc hns
nearly a constant valne of 16" in the hilly area from Chnutiire to KhLrt'e nnd
tlwindles down to zero a t NLmche Bazkr. This is in accord with what one
would expect. Theory shows that for n depth of compans~tionof 1 13.7
Itms., tho effect of compensntion on the deflection should be pr~ct~icnlly
nil
for distlancos up to 18 nliles frotn the peak and the observed deflection
shonlcl bc nnnrly eqnnl t,o tShct,opogmphionl defl~ot~ion,A t a ciistnnm of
40 miles from the peak, effect of compensation is very material and ia of
course dependent on the type of compensation assumed. Since 7 is
greater than vC, we see that the region is under-compensated, a fact
which is corroborated by the gravity data.
-lO r
P
-50
-yD
-
0
"
Distances in miles
l2.2
I3.zR4 5 . 6 '
'" '
*
a
..........
17.5
+lo;
.-C
o
A
cn
0
I
*
a
a
Fig. 1 .
P
5
Deflection and Deflection Anomalies.
The extrapolation of the ( r ] - r ] , ) and ( f - 6, ) curves up to
Mount Everest can, thus, be carried out with a considerable measure of
certainty. The extrapolated curve is shown by dotted lines and thc
values of r ] - qc, $, - f c for Mount Everest are (
1"~ 2 , 1".9 ). By
computations, the Hayford defle~t~ions
a t Mount Everest are ( - 13",
- 2" ) from which the cleflections cleriveci are ( - 1 1 " . 8, - 0" 1 ) .
These can be utilizod for computing thr, geoidal height of Mount
Evorost. Arr independent method is to integratc, 7-7, ant1 (-[,
hetwoen NLmcho Baziir ancl Mount Everest and to this value add tllc
rise of tho isostatic gooid as clerived from considerations of topography.
Tho final value arrived a t for tho gooidal hoight of Moimt E v o r o ~ th v n
con~idorationof tho two mothods is 9 2 . 3 foot.
+
C
f
tm
a
7
E'
+
Tnblo 3 gives the cleflections a t stations which have been utilizod to
draw :I picture: of thc gcoicl in this nren. The meridionnl components of
thc tlotlr:ction hnvc bccn corrected for t,lle normal curvature of the vertical.
rl'tlo rr*nl~lf
ing geoitl is ~ h o w nin ('hart V and i~ believed to hc of a high
or(1f-r of' ;WCII~:L(:Y.
'rhc clcflcction ~ t a t ~ i o nhnvo
s
becn chosen ; ~nt:tt,ions
t
W
of topographical triangulation and these can be regarded as unlikely to be
in error by more than f 0". 1. The probable error of the astronomical
latitudes is f 0".3. The average interval between the station^ is 6 miles
and the probable error of the geoidal rise N in so far as it depends on the
meridional components of the deflnctions can be reckoned to be f 0 - 3 feet.
The error of personal equation in the oblique portion of the section may
produce an error of a foot or so and so might the neglect of the rigid
curvature correction to meridional deflections. The last lap between
NBmche Baziir and Mount Everedt may furt,her be in error by f 4 foot.
The total probable error of the geoid in the Mount Everest region can,
thus, be reckoned to be of the order of 2 feet.
Chart VI showing the section along the line of greatest change from
Ladnia in the plains of Bihiir to Mount Everest is unique and of very
great interest. The geoid shows an unprecedented rise of 109 feet in a
distance of 109 miles.
Computations show that the topogrctphic geoid due t o visible masses
would produce a rise of 333 feet. The actual geoid displays 1/3rd of thhq
rise indicating a considerable measure of compensation. To get a n idea
of the.magnitude of the compensation, Hayford deflections were computed
for these stations and Hayford anomalies were integrated for the section.
The corresponding geoidal rise of the compensated geoid between the two
points is 3 1 feet.
Both, the natural and compensated geoids follow the topography
and in the higher hills there are indications of a certain amount of undercompensation. Gravity observations have also been taken in this
region and confirm the above conclusion.
angle observations to Mount
8. Final Value of Height.-Vertical
Everest were observed with n Tavistock theodolite in 1952-53 and with
a Geodetic Wild theodolite in 1953-54. An abstract is given in Table 4.
A number of sets were taken a t each station. They were generally very
consistent and the mean of the various sets on each day was used for
calculating the height. Column 6 shows the number of sets from which i t
would appear that a sufficiently large number of observations spread over
three months in two different years have bee11 taken to get a reliable value
of height. As a rule, a t these heights, diurnal variation of refraction is
very small and it is not essential to adhere strictly t o the time of
minimum refraction. However, column 3 will show that in the main,
observations have been taken a t this time. With the data derived in
the previous paragraphs, the ground is now cleared for arriving a t the
final value of height of Mount Everest.
The geoidal heights as derived from each station are given in Table 5.
The various columns in tllis table are self-explanatory. Column 6 gives
the spheroidal height difference between the station of observatio~land
Mount Evercst and colnm~l7 the correspondi~~g
geoidal rise.
The heights, as tabulated in the last column, arc burdened wit,ll the
following errors :( n ) Error in adopted geoidnl height of obscrring s t r a t i ~ ~Thew
~~.
are well tied to spirit-levclled heights and can be in error
by 2 or 3 feet a t the mostf.
( 6 ) Errors in 6N the estimated gcoidal risc lwtwcen t>l~c
stntions
and Mo~lntEverest,. 'l'hiq can atrt0,aill
n rna\-ililnln o f 5 fcct
but sho1,ld be bettor than thh.
( c ) Errors drln to ost,imntccI rc.fi.actio~~.
No observational data for lapse rate exists for the actual stations and the
refraction is computed on the hypothesis of saturated adiabatic lapse
rate of 3 -2"P/1,000 feet. For each ray, the coefficient of refraction is
computed with this lapse rate for temperature and pressure appropriate
to a point one-third the distance along the line. The variations in the
lapse rate have, however, an important effect on the refraction. A
reference to the normal charts of the Meteorological Department shows
that the average lapse rate in the Mount Everest region agrees very
well with the above value. The vertl'cal angle observations were taken
during the months of December to March on sunny days when there
was no possibility of inversion. Variation can occur in this lapse rate
due to changing pressure and other abnormal conditions, but it is believed
that the deviations from this adopted lapse rate are never likely to be
more than 20% in our case as the observations were carried out at the
time of minimum refraction and the lines were well clear of grazes. A
fluctuation of this amount in the lapse rate would introduce an error of
only 3% in the adopted value of k, which would produce an error of 1
foot or so in height over a ray of 35 miles length. The error due to
refraction may be considered as random for different stations and of
very small amount. Considering that we have observations from eight
stations, spread over a period of three months in two years, the effect of
refraction errors on the mean value should be quite negligible.
A perusal of column ( 8 ) shows that the scatter of the derived values
is only 16 feet, which is very satisfactory and is compatible with the above
remarks regarding the errors due to different sources. I n deriving the
fhal result, weights have to be assigned to tho values from the various
stations taking into account the total number of obsorvations, the
number of days on which observations have been made and the length
of tlio rays. It might, however, be pointed out that repeat observations
on the samo day are heavily correlated and even the observations on
~onsocutivedays are correlated to some extent. For instance, it can
happen that succe,~siveobsorvations on four days made during the time
of minimum refraction may contain the same systematic error. These
observations can, thus, bo regarded a9 a general check against grow
ormrs in the vertical angles accepted for computation.
As regards tho length of the rays i t is still open to doubt whether the
weights should be assigned proportional to reciprocal of the length of the
ray or the reciprocal of the square of the length of the ray. Fortunately
the scatter of the observations is such that it does not make much of a
difference whichever form of weighting is adopted.
The woightecl mean value of tho height of Mount Everont workout
This probable
srror is cierivecl from intornal ovidonco alone and is likely to be too small
on account of tho presenco of systematic errors. Boaring in mind the
various possible sources of error, it is considerod that the otids ore 20 to
1 against this vol~lohoing in error by moro than 10 foot.
to ho 29,028 feet with a probable error of f 0 . 8 feet.
The height ha3 been determined during tho months of December to
March. T1li.r is tho period when the smount of snow on the top is likely
to be lewt ctr the north-west wind is in its full stride. There is heavy
j'recipitntion of mow tlr~ringthe monsoon months-June to Septemberand, r ~t lhough t horo is no observational evidence available regarding the
c h n g o o f snow fall a t the ~ i ~ m r n iitt ,i~ likely t,o be well over 10 feet.
t 11,.
I t rnigt~t,I,(! o f intercnt to record here that MakGln which rims from
rrlnirl sIlr,w.y rrLngo at. R tlistancn of 12 m i l n ~tjo t,he e t ~ of
~ t M0~1ll)
11
Everest liiw also h e l l ru-observed for height. Prolri tlio Llarjeoling hills,
this peak dominates the landscape rather than Mount Everest bocause it
is about 12 miles nearer.
I t is supposed to be the fifth highest in the world and has boen very
lnuch in the news lately, as an American Expedition made a bid to
conquer it in 1954 for the first time but had to turn back due to bed
weather and difficult terrain.
MakBlu was observed in 1849-50 from six low lying stations in the
plains, a t distances of about 110 miles from it. Like Mount Everest, its
height was also computed with a faulty value of the coefficient of
refraction and without proper considerations of datum and deflection of
the plumb-line and the value adopted was 27,790 feet. I n 1952-53,
observations were taken to this peak from five stations a t distances
varying from 35 to 80 miles. The value resulting from these observations
after taking due count of the geoid under MakLlu is 27,8 24 feet. This
is the value which will be adopted for the future.
I t might be noted that although the present observations enable
the height of Mount Everest to be determined with a high degree of
precision, they do not contribute to the question of the uplift of the
Himslayas. The question of the amount of erosion a t the top of such
high hills and the secondary rise to achieve isostasy must still remain a
matter of speculation. Although the rock summit is subject to violent
seasonal winds, it is never bare of snow and the erosion is not Likely
to be considerable.
Analysis of the older values of 29,002 feet and 29,141 feet for
Mount Everest.-The above two figures are so well known that to avoid
Suture misunderstandings regarding them, it is worthwhile putting down
their exact significance. 29,002 feet is a vague height determinod from
oarlier computations of 1850 or so which can be reckoned to be either as
being above the geoid or above the Everest spheroid so oriented as to be
t.angentia1 to the geoid in the plains south of NepL1. The datum surface
was ignored during its derivation and the coefficient of refraction
used was faulty. The reasons why it agrees so closely with the new
value is due to a lucky cancellation of errors as the following will show.
9.
Error in the assumecl heights of the observing stations raked the
height by 8 feet ; the neglect of plumb-line deflections made the height
lower by about 30 feet. Neglect of geoidal rise between the plains of
BihLr and Mount Everest raised the height by 115 feet or so and taking
311 excessively largo coofficient of refraction made the height lower by
about 120 feet. If the last two sources of error had conspired in the
same direction, the derived height would have beell hi error by over
200 feet. I t will bc scen that two sources of error mitcle the heights
lower ancl two higher, resulting in a, lucky cancellation of errors.
Of much greater interest is thc reason why Burrard, who was ecluippecl
wit,h much better information, went astray by a niuch greater aliloulit
ill his conclusions. He was one of the niost ~ ~ L I I ~ O Igeoclcsisbs
IS
of liis
time and did a lot of work on the determinetion of 11eight.sof lofty pciblis.
In his Himslayan Geogmphy*, lie gives nn nccoullt of how in 1!)05
he derived the value 29,141 feet for tho height of Rloulit Everest by
utilizing the later observations of 1880 as well. He was ttble to efioct one
* " A sketoh of the Gleogl*aphyand Goology of tho HimAIaya Alountnills a~btlTibot " by
Burrard, Hayden L Heron ( 1933), pp. 66-57.
important ilnprovelnent in that he could make use of the latest knowledge
on refraction. He was convinced, and i t has often been stated in several
publications, that his figure of 29,141 feet was much more accurate than
29,002 feet. On page 57, Burrard comments that although this figure is
by no means final, "The height 29,141 feet is still probably too small,
as it has yet to be corrected for the effects of deviations of gravity".
He discusses this question again in detail* in a later paper, and points out
the difficulty of finding a base for height measurement of the Himllayan snow peaks. Burrard makes a fundamental and a persistent
error of principle in his arguments regarding choice of datum. He
visualized the possibility of abnormal deformation of sea-level by as much
as 300 feet under Tibet, but conteilded that this had no bearing on the
question of the heights of peaks and that the spheroidal heights were all
that would be of interest to the geographers. I n view of the remarks in
para 7, it would be apparent that this is not correct. The estimation
of geoidal rise between the stations of observation and Blount Everest
involves an extra step but it has to be done.
Actually, Burrard's figure of 29,141 feet is ever1 more vague than the
earlier determination. Although, refraction has been treated more
rationally, his values derived from stations in the plains are on an Everest
spheroid, while these derived from hill stations are above different
Everest spheroids tangential to the geoid a t those stations.
He visualized correctly that the application of deflections would
increase his figure of 29,141 feet, ancl recent observations show that this
incraase would be only 30 feet. Tlle consideration of the geoidal rise,
howover, which he ignored necessitate3 a diminution of over a 100 feet,
so that on the whole the above figure would be decreased.
Summary.-The newly determined height of Mount Evcrest is
It is but timely that the challenge of its height determinolion sllould have been met shortly after its actual conquest. This is
the first time that the height of an imporlant illaccessible peak has been
cleterlnined by a rigorous tecllniyue involving a relatively conlplicatccl
nexus of facts and idens. Geodetic observations had to be carried close
to the peak to get quantitative figures for the distortion of the inean
sea-level and thc tilt of t,he vertical producerl by the colossus.
10.
29,028 feet.
The new determination stiulcls in a class by itself and its close agreement with the older valuc cloes not signify that the latter was well cletermined. I t is really due to the fiict that like iu not being coliiparecl with
like. Judged hernodern standards, the eerlicr deduction of tho height of
Mount ~vercut/v?i;uc in sevcl-:rl respects, and was burdened with larw
?
error8 on account of neglect or incomplete consicleration of cert~tin
physical factors. It so happened that by chance, the various individual
crrors, although largc, havc tcndetl to cancel cacli other.
Thcre arc several outvtancLi11g peaks in the HiinSluyan range
KLnchenjung~, Nanga Piwhat, DheulQiri, etc.-which
also
rlccd trcatment similar to that in this paper. Doubt still rerllains
kvhcther Ka or Klnchenjungz shoul(1 occupy the next placc. Their
;~cceptedheights are 28,260 feet. and 28,146 foot respectively and thc
cliffcronce is well within the errore of older determination. Some recent
obscrvatione have been taken to Kiinclienjunga and preliminary computatioru show that its adopted height needs increasing by 60 feet or so.
-K2,
--
-
-
-
-
--
--
-
--.--
---
-
-
-- -
"The Placo of Mou~itEvcrcst in History " by Col. Sir S. G. U~rrrard. Empire Srirrey
I(ovic w, fjcpternbcr 1034, p. 450.
TABLE1.-Height
Height of
observing
station
in feet
Observing
station
I
I
Distance of
ohserving
station
from the
peak in
miles
I
I
/
of Mount Everest from observations from the plains
Date of
observation
I
KO. of
observa tions
Observer
Observed
angle of
elevation
Height in
feet
aboveMean
sea -level
I
Coefficient
of
refraction
i
I
1
Direction
of the
peak from
t h e observing
station
Xstronomical time of
observation
I
'
1
Jirol
T.S.
231
118.661
MirzZpi~r
T.S.
254
108.876
Dec. 5 & 6,
1949
Jan jipati
T.S.
263
108. 362
Dec. 8 & 9,
1819
Nv.
1
I
Mr. J. 0.
Nicholson
+
This
T.S.
242
108.861
Harpur
T.S.
226
111.523 !Dec.l7&18,
18.19
3Iinai
T.S.
235
113.561
Jan. 17,
1850
24-Inch
.Theodolite
I
Dec. 12,
1849
i
SE.
J
I
hm h m
3 40
TABLE?.-Height of Mount Everest from observations from Darjeeling Hills
I
I Distance of
Height of
obser~ing I
ubeerrlng
station
Date of
station
I from the i observation
in feet
I peak in
I
'
miles
i
Ul~ber\1n2
stat1011
h.>.
1
1
Tigcr Hill
has. I
$607
Suberkum
87.636
I1
107.952
Sandak~hu
Mag 30,
Phalut
I
b.s.'
h.s.
I
11816
1
h.s.
8399
I
1
'
'
T. & S.
12.No. 11
1 1
I 26, 1883
I
Senchal
6
I
,
1
85.553
I
108.703
I
1902/1
T. & S.
12-
1
Lt. Cowie
I
1
1
refraction
,
I
9stronomionl time of
ob~eruation
XW.
1 35 1 1
Early in the
morning
.
,
29140
29141
Not mentioned
1
I
29137
I
.0463
1
"
1
-
6
I
113750.2
I
19142
29140
39151
1
"
.0457
,,
,,
4450
,,
1)
-0511
,,
B1
I
12023.4
1
I
I
i
1
Direction
of the
peak from
the observing
etation
e
Mean
6
1'
1
I -- I
1 21 44
2
I
I
1
i
Meail
March 16,
Feh. 23,
1902J
I
Height in
feet
aboro Yean
sea-level
1 35 13
h.s.
I
I,
Oct.
I
,
Observed
angle of
elevation
1
--
I
I
j
hatru-
No. of
observa-
I
I
0
/
11641
Obser~er
I
i
1
duberhom
!
1
I
I
I
,
29134
Mean
29143
GeneralMcan
29141
--
1
I
i
I
I
-.
TABLE3.-Deflections
Serial, Sheet
NO.
No.
i1
Stat~on
I
I
I
-
-
- --
I
Height
in
feet
2
I
I
1
I
,,
' Sondahi
;
I Jar01
12 J
MirzBpur
..
T.S.
..
I
201
193
I
..
T.S.
219
Ladnia
..
Th.
6 '
,,
,
Herpur
..
T.S.
7
,,
Sarunga
11.u.
..
1289
8
,,
K. 109
..
..
568
(Top)
2615
9
,,
10
,,
11
,,
Chautare
I
h.d.
..
..
K. 108
..
..
3714
Dungre
h.3.
..
6953
13
*
72 I
,,
Meenashi
KhHmtel
L.8.
11.9.
..
..
..
6318
. . I
4373
G 26
A 26
G 26
A
G 26
A
G 16
A27
G 27
A 27
G 27
46
51
52
G
1
G
I
A
G
/
I
12
,
40
40
37
37
30
30
30
31
25
25
22
22
40
40
A
199
1
I
-
--
0
G
A
1
Longitude
p
p
%
26
26
26
26
86
26
26
26
26
26
26
26
26
A
G
A
G
A
I G
A
208
Deflections* on
International spheroid
A
k4
..
58
04
03
08
09
.
0
1
1
!
I
l
9;
I
i
I
P.V.
Meridional
7
5
I
1
- 0.4
-
7.1
1
-
1.4
-- 9 . 1
-
7.7
-
8.6
-
0.6
-
6.8
-
6.2,
-
8-5
+
1.3
-
7.2
1
- 24-7
I
-
- 15.9
29.8
1 - 40.3
-
7.1
14.4
14.3
1
I
-41.3
I
- 37.7
1
1
1-31.4
I
1
I
I
- 15-6
- lSm6
-
6.0
-38.4
kO
+
..
..
..
..
-19.2
-
..
1
..
8.0
-
6.4
11.7
-
8.0
- 15.0
- 15.5
- 16.2
I
I1 - 1 ' 7 . 1
1
1
I
+
I
-
)
P.V.
I-lc
b5
) - 4.1
i
Maridional
7-7c
-
I
'
Hayford . k n o m r h
Depth of compensation
-113.7 kms.
0.3
.
51.69
A 8 5 26 20.43
55.73
G 86 26 31-01
39-35
A 86 35 34-90
43.27
G 85 36 51-86
50.10
-4 85 55 12.77
55.00 1 Q 85 55 32.11
51.00
A 86 16 19.06
02.15
G 86 16 38.09
40.13
A 86 36 56.06
50.32 I G 86 37 15.04
17-74
A 86 46 14-42
25.23
G 86 46 31.92
22.05
-4 86 34 15-84
50.21
G 86 34 41-69
A
08.99
G 86 34 11-55
15-04 1 A 86 34 59.43
00.93
G 86 35 25.17
A
46-79
G 86
02-77
A
44.96
G 86 % 68.22
44-60
A 8 6 39 17.19
19.66
G 96 39 33-65
19.86
A 86 43 03-44
01.95 1 G 86 43 34.77
'l'ha rnerld~onalcornpone~~to
ot deflect on I~avebeen corrected for
curvature of the vertical.
In bold type ~ n d ~ c athat
t e aeitroliomical observations were not taken a t these stations.
Nok :-Veloee
'
I
-.-
1
,,
5
T.S.
1
228
I
1
--
..
Bnlikipur T.S.
,
3
4
72 F
I
Latitude
I
1
and Hayford Anontaliec
- 13.2
- 9-4
- 8.9
-
8.2
- 7.7
-
8-2
( cmltd. )
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TABLE3.-Deflections and Havford Anomalies-( conclcl. )
I
Serial' Sheet I
No.! No. I
1
Station
I
I
Height
1
Deflections* on
International spheroid
Longitude
Latitude
P.V.
Meridional
27
28
30
/
/
1
31
-- .--
.--- -
-- -
--
-
-
-- -- . -- --
72 I
~ u s r i k h a r k aresected station
,.
Aimehe B a r k resected atation
,,
Mt. Everest
..
Liori Danda h.s.
721
Maplm h.s.
---
.
I
8806
12713
..
..
..
11877
. . I
..
! A 2 i 09
23-59
5016
33
1
1
,,
Poynagi h.e.
..
..
8112
/
,,
Oarhi h.s.
!
,
i Agejung h.s.
I
:
78 A
1
I
Akkaae h.s.
Phalut h.8.
..
I Tonglu
I
h.8.
.
I
..
..
..
,,
7303
1
j
38
30
G
A
G
A
7063
.
37
I
..
. .
..
..
11798
:
11915
A27
25
27
27
27
27
A 27
G 2i
A 2i
G 27
-457
G 37
21
22
18
1S
15
16
14
G 37 09 49.89
A 27 12 07.12
G 2i 12 41.82
05 25-20
G 2 i 06 11-61
A 25 01 10.75
G 27 01 63.54
.
I-lc
I
-63.4
-16.8
-
7.6
1i
- 42.5
- 13.0
-
-
3-6
;
-46.1
-
8.9
-
12.9
- 35.1
- 29.9
- 31.3
+ 7.8
- 19.4
-
9.4
A 86 12 44-79
; B 86 43 13.6 1
A 86 42 56.33
6 86 43 12.0
A
i G
I
A
G
A
G
A
G
A
G
I
-4 27
I
t
,
!
;
..
,,
G 27 jg"15.86
40 41:03
1 1 38.3
48 00.12
43 16.5
A068
Cbainpor h.8.
:
I
27
27
27
27
15
12
12
13
13
..
36
A
G
A
G
10918
/I
35
I
1
/
I
..
O
;
Hayford Anomalies
Depth of compensation
-113.7 kma.
Meridional
P.V.
~
O
30.56
19.49
01-98
41-3s
58-20
31.83
51.87
26-93
10.33
49.18
41-40
23.32
32
31
I
I
-
I
1
3
n
_
I
!
I
86
86
86
87
87
85
85
87
85
87
87
87
87
A
G
A
G
A87
G 87
A 98
G88
A 87
GSS
A, 85
C: 8S
65 '39-51 1
55 00.46
56 20.44 1
00 51-3L !
00 62.53 1
16 18.89
16 50.85 1
24 54-84 1
25 27.83 /
39 42.92 ,
39 66.55 1
49 46.41
50 15.81
1
50
51
00
01
59
00
05
01
* The meridiorlal colrlpone~~ts
of tleflcction h a r e beer1 correoted for normal clil.i-;ct~~re
of thc vertical.
Note.-Ve1ue.a in bold type indicate thet astronomical observations \\-crc. n o t t ; l k t , ~ la t theso statione.
5.2
+ 1.0
0
-
.
1.3
+ 2.2
+ 3.0
- 13.6
+
1.0
..
..
- 20.2
..
..
- 35.2
-
-38.2
-16.6
..
..
..
..
- 4.7
..
..
..
..
..
+
..
..
33.99
-20.6
09.86
39-59 ,
31-1
00.83 ,
35-98 :
42.6
02.10:
03.96
- 39.2
02-90
-
3.2
-22.2
- 9-0
11.2
..
I
(
TABLE4.-Vertical
22
1
angles to- Mount Everest
!
Station
--
Date
-
-
Time
Deflection
correction
on Intarnational
spheroid
Obscrved
vertical
a n
~Press~~re
I
I
I
I
I
I
I !
( Season : 1952-53 )
I
iI
Ma.yim
Liori D a ~ l d a h.s. 1 26-3-1.963
B9
..,, 11
SD
,,
9,
27-3-1953
28-3-1963
129-3-1963
Aisytlukhnrkn h.s.1
PI
9
12
12
12
12
12
12
12
12
15
12
3-2-1963
,, ) 9-2-1953
/
1
01 to
33
OR
08 to
26
07to
17
29to
11
27 to
i
v
.
PI
Pike Sub.
..
9s
,. !
20-21963
1
2612-1962
/1
,, 1
28-12-1962
3
.,
30-12-1962
h.8.
1
16
11
13
12
15
13
65.2
5
4 05 69.38
+46.17
19.29
19.40
60.3
65.6
1 4 06 00.65
4 4 06 03-96
$46.17
+46.17
19-30
66.3
6 / 4 0 5 5 8 - 6 4 +46.17
22.11
45.0
i26i45617..il
+63.22
22.07
61.0
I'
22
4 66 13.72
+63.22
22.11
1523
23
4 b6 16-01 + 6 3 2 2
20.76
67.9
10
20.73
68.1
464446698
150-74
20.87
54.1
29
4 44 67-57
+60.74
379
60
4 09 30.8
+49.69
47 1 4 0 9 4 6 . 9
+49.69
4 Og 48.6
+49-69
6 02 4 4 - 3
+64.81
28 I 5 02 37.9
+Ma81
,
*
01 ,
60 to
24
02 to
30
01 to 1
'1
/
19.49
1990
/
i
1
i 4 44 63.60
Sollung
19.68
9~
1 15 07
.,
,*
6-1-1953
1
h w e r Raujo
h.s.
UpparRaujs
h.s.26-2-1953
,,
vv
,.
..
10-1-1963
27-2-1951
128-2-1953
( Seusov~: 1955-54 )
Chhlllyirnu
Piko S i ~ b .
2-12-1953
11.0.
h.8.
12
14
12
i 14
1 1
116
i 10
16
11
1 12
!
UpperRelljo
18.31
6 23 35.4
+68.90
11.58
50501.45
+64.83
68 to
17.46
01 1
3 1 t o / 17.63
35 i
5 06 01-20
4-64-01
46.6
1
41.6
06 02.88
+am83
21 14
46 01.0
+hU.74
1970
09 42.4
+49.69
20.13
02 41.4
f64.81
~
I
1
1
5-12-1953
9 53 to
10 13
11
16
h . ~ . 11-12-1953
12
I 15
I
h.a. i 16-12-1963
14
!
14
i
'
I
+Ma81
04
19-74
1
6 02 37-0
I
l
hllung
36t0
13 I
08 to
01 1
41to
40.9
+ma74
1
1
66 to 1
20
26 to
32
24to
31
17.88
30.1
/
3 (60603.47
-t-64.83
(
23
)
TABLE5.-Height of Mount Everest
Station
Distunre
Season
I
Height
of
st:~tion
1
1 6Nrise=between
Oenidnl 1
Spheroitlnl
height
(lifirenrc
Qcohlal
height of
the station tin(l
Mount
Mount
I Everert
1
Everest
= (:Jr(7)
(7)
Sum
1
(6)
I
I
I
feet
feet
29038 - 7
May iim
/
/
61
32.6
62
31.0
Pike Snh.
..
..
1952-53
41
12060.3
17011.8
29071.1
47
Sollung
. . 1952-53
36
11657.9
17411.4
29060.3
Lower Rnuje
..
..
30
13357.4
15700.8
1 20058~21
40
Chhulyirnu
Upper Rauje
1952-53
1952-53
1992-53
I
Sollung
.. '
1953-54
Pike Sub.
..
1953-54
Upper Rauje
Chhulyiimll
..
..
1
1953-64
1953-54
I
1
1
41
29
36
41
29
41
10160.4
I8920 1
29080.5
50
30.5
24.1
14762.1
'
::::::1
14762.1
10160.4
1
I
14293.1
29055.2 1
17409.9
29067.8
17015.3
14290.7
18917.8
I
I
29.3
32
26.2
30
25.2
40
29074.6
I
I
1
27.8
27.6
1 29052.8 1
30
22.8
290782
60
29028.2
1
1