ASTRONOMY. 
with tliofe of Maupertuis and his affociates in the north, 
and that of Bouguer at the equator, there will refult fix 
different values of the ratio of the two axes, the arithme¬ 
tical mean of all which is that of i to 0-9953467, which 
may be confidered as the ratio of the greater axis to the 
lefs; which is as 230 to 22S-92974, or 215 to 214, or very 
near the ratio as alligned by Newton. 
Now, the magnitude as well as the figure of the Earth, 
that is, the polar and equatorial diameters, may be deduced 
from the foregoing problem. For, as half the latus rec¬ 
tum of the greater axis Aa is the radius of curvature of 
A, it is given in magnitude from the degree meafured 
there, and thence the axes themfelves are given. Thus, 
the circular arc whole length is equal to the radius being 
57-29578 degrees, if this number be multiplied by 5675,0 ■ 
toifes, the meafure of a degree at the equator, as Bouguer 
has lfated it, the produCl will be the radius of curvature 
there, or half the latus reftum of the greater dxis; and 
this is to half the fmaller axis in the ratio of the lefs axis 
to the greater, that is, 330-9953467 to 1 ; whence the two 
axes are 6533820 and 6564366 toifes, or 7913 and 7950 
Englifh miles; and the difference between the two axes 
about thirty-feven miles. And very nearly the fame ratio 
is deduced from the lengths of pendulums vibrating in the 
fame time, in different latitudes; provided it be again al¬ 
lowed that the meridians are real ellipfes, or the Earth a 
true fpheroid, which however can only take place in the 
cafe of an uniform gravity in all parts of the Earth. 
Thus, in the new Peterfburgh Ads, for the years 1788 
and 17S9, are accounts and calculations of experiments 
relative to this l'ubjed, by M. Krafft. Thefe experi¬ 
ments were made at different times and in various parts of 
the Ruffian empire. This gentleman has collected and 
compared them, and drawn the proper conclufions from 
them : thus he infers that the length x of a pendulum that 
fwings feconds in any given latitude A, and in a temperature 
of ten degrees of Reaumur’s thermometer, may be deter¬ 
mined by. this equation : 
w=:439 , i78-4-2-32i fine "A, lines of a French foot, 
or a-— 39-0045-|-o'206 l' me % in Englifh inches, 
in the temperature of 53 of Fahrenheit’s thermometer. 
This expreffion nearly agrees, not only with all the ex¬ 
periments made on the pendulum in Ruffia, but alfo with 
thofe of Mr. Graham in England, and tliofe of Mr. Ly¬ 
ons in 79 0 50' north latitude, where he found its length to 
be 431 -3s lines. It alfo fhews the augmentation of gravity 
from the equator to the parallel of a given latitude A: for, 
putting g for the gravity under the equator, G for that 
under the pole, and y for that under the latitude A, M. 
Krafft findsj— (1-5-0-0052848 fine e A) g- and therefore G 
—1-0052848^. 
From this proportion of gravity under different latitudes, 
the fame author infers that, in cafe the Earth is a homo- 
genequs ellipfoid, its oblatenefs muff be inflead of 
which ought to be the refult of this hypothelis : but, 
on the fuppofition that the Earth is a heterogeneous ellip¬ 
foid, he finds its oblatenefs, as deduced from thefe expe¬ 
riments, to be ; which agrees w ith that refulting froni 
the meafurement of fome of the degrees of the meridian. 
This confirms an obfervation of M. de la Place, that, if 
the hypothefis of the Earth’s homogenity be given up, then 
theory, the meafurement of degrees of latitude, and expe¬ 
riments with the pendulum, all agree in their refult with 
refpeCt to the oblatenefs of the Earth. See Memoires de 
PAcad. 1783, p. 17. In the Philof. Tranf. for 1791, Mr. 
Dalby has given fome calculations on meafured degrees of 
the meridian, from whence he infers, that thofe degrees 
meafured in middle latitudes, will anfwer nearly to an el¬ 
lipfoid whofe axes are in the ratio alligned by Newton, viz. 
that of 230 to 229. And as to the deviations of fome of 
the others, viz. towards the poles and equator, he thinks 
they are caufed by the errors in the obferved celellial arcs. 
Tacquet draws fome ingenious inferences, in the form 
of paradoxes, from the round figure of the Earth; as, iff, 
That, if any part of the furface of the Earth were quite a, 
Vol. II. No. 76. 
3 6 ? 
plane, a man could no more walk upright upon it than on 
the fide of a mountain. 2d, That the traveller’s head goes 
a greater fpace than his feet; and a horfeman titan a foot¬ 
man ; as moving in a greater circle. 3d, That a veil'd, 
full of water, being railed perpendicularly, fome of the 
water will be continually flowing our, yet the vefiel ftill 
remain full; and, on the contrary, if a vefiel of water be 
let perpendicularly down, though nothing flow out, yet it 
will ceafe to be full: confequently there is more water 
contained in the fame veil’d at the foot of a mountain, than 
on tlie top ; becaufe the furface of the water is compreffed 
into a fegment of a fmaller fphere below than above. Tac. 
Aftron. lib. i. cap. 2. We may here obferve, with refpeCt 
to the round figure of the Earth, that the equatorial dia¬ 
meter being but little more than thirty-four miles longer 
than the diameter from pole to pole, it conllitutes .1 diffe¬ 
rence too fmall to be reprelented on globes. Hence the 
difference between the equatorial and polar dimenfioiis, 
when compared with the Earth’s femidiameter, is but an 
inconliderable quantity, amounting in the whole to an ele¬ 
vation of little more than i6| of 3970; that is, to lefs than 
a 240th part of. tlie diltance from the furface of the Earth 
to the centre. If a meridional feftion of Inch a fpheroid 
were laid down upon paper, the eye w-oitld not diftinguilh 
it from a perfect circle. 
Mr. Boyle fufpeCts that there are great, though flow, 
internal changes in the mafs of the Earth. He argues 
from the varieties obferved in the change of the magnetic 
needle, and from the obferved changes in the temperature 
of climates. But, as to the latter, there is reafon to doubt 
that he could not have diaries of the weather fufficient to 
direCt his judgment. The notion of the magnetifm of the 
Earth was Halted by Gilbert; and Boyle fuppofes magne¬ 
tic effluvia moving from one pole to the other. See his 
Works abr. vol.i. p.285, 290. 
Dr. Knight thinks that the Earth may be confidered as 
a great loadftone, whofe magnetical parts are difpofed in 
a very irregular manner; and that the fouth pole of the 
Earth is analogous to the north pole in magnets, that is, 
the pole by which the magnetical ftream enters. He ob- 
ferves, that all the phenomena attending the direction of 
the needle, in different parts of the Earth, in a great mea¬ 
fure correlpond with what happens to a needle when pla¬ 
ced upon a large terella; if we make allowances for the 
different difpolitions of the magnetical parts, with refpeCt 
to each other, and'eonfider the fouth pole of the Earth as 
a north pole with regard to magnetifm. The Earth might 
become magnetical by the iron ores it contains, for all iron 
ores are capable of magnetifm. It is true, the globe might 
notwithftanding have remained unmagnetical, unlefs fome 
caufe had exilted capable of making that repellent matter 
producing magnetifm move inn ftream through the Earth. 
Now the doCtor thinks that fuch a caufe does exift. For, 
if the Earth revolves round the Sun in an ellipfis, and the 
fouth pole of the Earth is directed towards the Sun, at 
the time of its defcent towards it, a ftream of repellent 
matter will thence be made to enter at the fouth pole, and 
iffue out at the north. And he fuggefts, that the Earth’s 
being in its perihelion in winter may be one reafon why 
magnetifm is ftronger in this feafon than in dimmer. This 
caufe here alligned for the Earth’s magnetifm mud con¬ 
tinue, and perhaps improve it, from year to year. Hence 
the doCtor thinks it probable, that the Earth’s magnetifm 
has been improving ever lince the creation, and that this 
may be one reafon why the ufe'of the compafs was not dif- 
covered fooner. See Dr. Knight’s Attempt to demonftrate, 
that all the phenomena in nature may be explained by At¬ 
traction and Repullion, prop. 87. 
With refpeCt to the magnitude of the Earth, this has 
been varioully determined by different authors, both an¬ 
cient and modern. The ufual way has been, to meafure 
the length of one degree of the meridian, and multiply it 
by 360, for the whole circumference. Diogenes Laertius 
informs us, that Anaximander, a fcholar of Thales, who 
lived about 550 years before the birth of Chrift, was the 
5 A- firft 
