place computed the ellipticity of the earth to be shy, 
t later experiments and computations of other men of 
ence concur in making it nearly 535. 
"In the Philosophical Transactions of the Royal Society 
for 1818, Capt. Kater has stated the results of his pendu- 
Jum experiments in London, and determined the length 
of the pendulum vibrating seconds, or completing one 
vibration in .gigo part of a mean solar day, when 
easured in a vacuum at the mean level of the sea and 
a temperature of 62° Fahr. to be 39°13842 inches of 
Standard yard, which was legalised in 1824 as the 
arliamentary Standard of length. The latitude of his 
lace of observation in London was 51° 31'4” N. He 
subsequently made a slight correction in this determina- 
‘on, making the length of the seconds pendulum to be 
13929 inches, as shown in Phil. Trans. 1819, and this 
ih, or rather 39°1393 inches, was declared to be the 
e length in the Standards Act of 1824. 
It was, however, discovered by Bessel that the correc- 
tion which had ordinarily been applied, and was applied 
Kater, for reducing the vibrations of a pendulum, as 
obs: rved in ord nary air, to vibrations in a vacuum, ought 
“to be greatly increased. The experiments were conse- 
"quently repeated by Capt. (now Sur Edward) Sabine, with 
oe reference to the form of pendulum usually em- 
ployed in England. In Phil. Trans. 1821, Sir Edward 
"Sabine has shown as the results of his experiments on 
the acceleration of the pendulum in different latitudes, 
that the mean diminution of the force of gravity from the 
pole to the equator was 0°0955138, in other words, that a 
weight of 100 Ibs. at the equator would be less by 0°55 1381b. 
at the pole; whilst the resulting mean ellipticity of 
the earth deduced from his pendulum observations, was 
a6 Sir Edward Sabine has also shown as the result 
of his experiments on the length of the seconds pendulum 
in Greenwich Observatory, that its length vibrating 86,400 
seconds in the 24 hours, at the temperature of 62° F., and 
jn a vacuum, was found to be 39°13734 inches. 
In his paper on the Yard, the Pendulum, and the 
Metre, Sir J. Herschel has observed that the true measure 
of the earth’s attraction (independent of centrifugal force 
arising from its rotation), is best to be derived trom an 
~ ideal seconds-pendulum supposed to vibrate at the extre- 
mity of the earth’s polar axis ; and that the mean length 
of the polar or of the equatorial pendulum must be de- 
rived from the general result of observations of the lines 
of oscillation of one and the same invariable pendulum 
* at a multitude of geographical stations in all accessible 
latitudes in both hemispheres ; but that no two combi- 
nations agree in giving the same precise length, in conse- 
quence of the local deviations of the intensity of gravity, 
due to the nature of the soil or crust of the earth, and the 
configuration of the ground immediately beneath and 
i around the places of observation. And further, that since 
the pendulum cannot be observed at sea, the whole sea- 
~ covered surface of the globe is of necessity excluded from 
furnishing its quota of observations to the final or mean 
conclusion. Water being on the average not more than 
one-third the weight of an equal bulk of land, such as 
the earth surface consists of, and only 74 of the mean 
density of the globe, the force of gravity at the surface 
of the sea is less than at the sea-level on land by the 
attractive force of as much material taken at twice the 
specific gravity of water (or at 7; that of the globe), 
as would be required to raise the bottom to the surface. 
With regard to the determination of the earth’s ellip- 
ticity, as shown by actual measurements of the dimen- 
sions of our globe, and the relauve length of the equatorial 
diameter and the polar axis of the earth, the most recent 
determination is that by Major Clarke, as stated in his 
“ Comparison of Standards of Length,” published in 1866, 
This memoir has been declared by Sir J. F. M. Herschel, 
to be the most complete and comprehensive discussion yet 
~ 
269 
received on the subject of the earth’s figure, and to be 
held as the ultimatum of what scientific calculation is as 
ue enabled to exhibit as to its true dimensions and 
orm. 
Major Clarke’s results were computed, not from 
pendulum experiments, but from the combination of all 
the separate measurements of arcs of meridians in Peru, 
France, Prussia, Russia, Cape of Good Hope, India, and 
in the United Kingdom. They are as follows :— 
Metres ac- 
cording to 
Feet. Inches. Metres. Capt. Kater’s 
equivalent. 
Length of Polar axis.) 41,706,858 | 500,482,296 | 12,712,136 | 12,712,020 - 
Longer equatorial axisi : 
(long. 15° 347 E.)...0+f 41,853,700 | 502,244,400 | 12,756,588 | 12,756,470 
Shorter equatorial axis 
(long. Tos? ge ck 41,839,958 | 502,079,496 | 12,752,701 | 12,752.588 
Length of meridian} 
Aaanvarit of Dene 32,813,524 | 393,762,292 | 10,001,472 | 10,001,38r 
Length of minimum 
Prk we (long x5 32,808,772 gee 10,000,024 | 9,999,953 
34 E.).ccossee . 
In computing these equivalents, Major Clarke takes 
the metre at the temperature of 32° F. from his own 
measurements to be equal to 1°09362311 yard at 62°, that 
is to say to 3°28086933 ft., or to 3937043196 in., instead 
of the more generally received determination by Capt. 
Kater of 39°37079 in. The metric length according to 
both these equivalents is here given. 
From the determination of the earth’s dimensions, it 
may be easily computed, that the earth’s ellipticity in 
the longitude of Paris, is z4,, whilst its mean ellipticity 
in all longitudes is s}5. 
Hence also the mean length of a degree of latitude in 
the longitude of Paris is 32,813.524'38 _ 364,591 ft., or 
69'05 miles. The mean diameter of the earth is 41,800,173 
ft., or 72162 miles, and its mean circumference 23,871 
metres, 
Thus not only each longitudinal meridian, but also the 
equator is slightly elliptical. 
Sir H. James has shown in his preface to Major 
Clarke’s paper that the longest meridian in 15° 34’ east 
longitude, nearly corresponds to the meridian in the 
eastern hemisphere which passes over fhe greatest 
quantity of land ; and in the western hemisphere to that 
which passes over the greatest quantity of water, as it 
passes through the centre of the Pacific Ocean. The 
shortest meridian in 105° 34’ east longitude nearly 
corresponds to that which passes over the greatest 
quantity of land in Asia; and in the western hemisphere, 
and that which passes over the greatest quantity of land 
of North and South America. 
The connection here shown to exist between the de- 
finition of weight and the measurement of the dimensions 
of our globe, leads naturally to the definition of the 
second principal head of the subject, viz. of measure. 
Measure is generally understood to mean the determi- 
nations of a body with relation toa fixed standard unit, or 
the measure of extension; and it is in this sense that it 
will now be taken in discussing the “ science of measuring.” 
The measure of extension comprehends 
The measure of length, or linear extension ; 
The measure of suriec2, or square measure ; 
The measure of volume, or solid or cubic measure ; 
The measure of capacity, or the cubical quantity con- 
tained in any vessel for measuring dry goods, 
liquids, or aériform fluids. 
All these measures of extension are based upon one 
fixed standard unit of length; and as all measures of 
length vary according to their temperature from expan- © 
sion or contraction, the length of the standard must be 
fixed at a normal temperature, 
