The New York herald., 1874-11-30

body Is not aware that this apparent decrease In
size takes place according 10 nxed law. 1--we
imagine o straight line TO be drawn from the eye
to the top OF the traIp and another straight line
from the eye to the bottom, Of Ihs tram, these
two lines will form at the eye an angle.
which enlarges ss the train approaches,
and diminishes as the train recedes.
Whatever size this angle possesses at one miles
distance rom the train or other object, 1t will
measure half that size two miles, distance, one
third OF that size at three miles distance, one.
fourth al tour miles' distance, and SO on indef-
niely. This law does not hold good for short dis.
tances; but is sufficiently true OF the distances
10 which the heavenly bodies are removed from
us. We have instruments for measuring said
angle-the visual angle as 1t is caed-to an extra
ordinary degree OF accuracy. Knowing this
angle and the size Of an object we can determine
tue distance; or. given this angie ana the
distance. we can calculate the size OF any
object. Military engineers when about TO
lombard citadel or shell position,
measure the visual angle presented BY steepe.
wall, spire or some sucn object. the height Of
which they already know. in order to estimate
their distance therelrom, and I'LL their cannon
with the quantities OF powder and iron requisite
TO carry sucn distance. SO also, In throwing
forward masses OF sharpshooters 70 resist the
onset OF curassiers the distance OF the cavaliers
is calculated by measuring tue visual angle pre-
sented by line drawn from the heads OF the
latter TO their horses leet tthe height OF cava-
ryman's head from the ground is generally about
eight feetl; ana the distance being determined
the resisting cour.ns elevate or depress their
rides accordingly. Skilful rinemen invariably,
though perhaps unconsclously. estimate distance
DY mentaliy comparing the apparent size uI the
OBJECT aimed at with us actual size. The height
OF balloon is likewise estimated in similar way
TO illustrate
SOME OF THE PRINCIPLES
which underle all such CALCULATIONS, let US sup
pose an observer standing on the sun, and looa-
Ing toward the earth. To MIN tAe eartn's dame
Ter wou.d appear TO be an extremely shor, line.
IL would be about The seventy. w o-tnousand tn
part oI CIRCLE that Is, u I2OOo earihs were
ranged in contact on level and at equal dis
| tances from the sun, IN the same manner as oo,s
some times fix number OF marbles, as TO form
CIRCLE they would make q complete ring OF
eartns round the sun. The circumference OF this
ring would consequently measure 900 times the
diameter OF the earth. TIE solar observer, tnere-
lore would only need to find out with an accurate
angle measurer. what fraction OF whole circle
form simple multiplication In order to de-
termine the length Of the circumierence OF the
would be tne path or oroit IN winch the earth
moves round Inc sun, supposing 1t moved in o
circle. " Is evident that tne radius Of tus circle
distance the observer cOuid determine NY dlvi-
ding the circumference Dy the number 6.2S32, be-
cause circumference OF any circle contains its
radius 62S32 times. Let rs perform these arlth-
metIcal operations in round numbers. The angle
wnlcn the eartn's diameter presents to the
OF circle. The diameter OF the earth Is
nearly 5000 miles; 5000 miles multiplied by 1000
gives 576,0000 900 OF miles, This divided by 6.2S32
gives about 92,000,00o miies-the SUMS dis
tance from the earth. But Is 1t not idle TO talk
angle measured by an astronomer standing on the
sum Surely, we can never hope to realize
ueapa nsy as are And s "snous
flying away from this earth OF ours, to calculate
the exact bulk OF that angle by very simple
metnou based on one Ol the most beautiful truths
OF geometry, which comes down TO US rom the
snadowy cycles Of q gray Antiquity, like SO many
other gorgeous monume nts OF the mathematical
genius which nourlshed in days gone by. About
5000 years ago, II was discovered tnat when the
three corners OF any triangle are added together,
their sum Is exactly equal to TWO rignL angles.
Hence IL we know TWO OF the corners OF triangle,
we can readily calculate the magnitude OF the
rom two rlgnt angles. In fg. 2 ior example, II
we measure the angles At 4 and 3. we can tnd
and the length OF the eartn's diameter (Which can
he easily computed), the SUMS distance can be de-
rived according to tne principles ALREADY ex-
planned. And now exclatms the reader, why can.
not these angles at A and Zig. y be measured
any day, when The sun is visible. and when there
are angle measurers OF marvellous accuracy Win
METHODS OF THE ANcIENTs.
Such attempts have been frequently made, but
win very uncertain results. the ancient astrono-
mers tried It, put. owing TO the !mperfection q
ne M s a0' so be q one mae
miles. Arlstarchus oi samos, VINO aoprlshed
about the year 27o g. I'm observed ise wed a1 tnas
anu earth are at the corners OF triangle, the COR
ner at the moon being right angie. He tnen
pie subtraction before named. deduced the mag
nituGe OF the corner or angle at the sun. Thence
es more anas r a the Nc
how did the old astronomers succeed in
calculating the remoteness Of the latter
spherey TO an observer stationed at the moon
the earth's diameter would seem lOur times as
large as the moons diameter seems to US. Arls-
tarcnus, Archimed edes and others were enabled to
determine this visual angle presented by the
earth's diameter 70 the moon In the manner pre-
vlousy described, which tney did, though not
forms US tnat previous 70 tner time, the sun was
supposed to be ten miles OF. drifting soutnward
agoras computed the distance to be $4,000 miles.
The TACT Is tnat IN attempting to solve the problem
is Very dlnicut to tell when the moon is precisely
han iu.l, and very small error IN guessing that
moment would create mistake oil millions OF
miles as TO the distance OF the sun. Wltn the I'M.
pements at their disposal tney could gauge an
angle only to about the lS-l,OJ0 part OF q
measurement OF the visual angie at the sun
would cause mistake OF 60,000U00 or $4,000 900
miles al the very .east. WITH the instruments
1871, 600. 900 part oi circle; yet. even with
such prodgies Of delicate machinery, it is ex.
tremely difficult TO obtain the desired angle.
owing to the bending or reraction OF the SUMS
Rays IN passing through the aerial regions OF mid
DAY, the great iuInlhary often seems to Oe Wnere
he Is not really; moreover his rim, even when
viewed through the Telescope, during the neces-
sary observations is seen to culver In the same
manner as terrestrial objects tremDle when
viewed across the heated and waving atmOs.
pnere near strong FIRE. These, aud numerous
other difficulties which 1t Is needless to enumer-
ate mere, constituted formidable barrier against
the repeated and ingenious Efforts OF previous
scientists TO arrive at q settlement OF the
question. Still, as the centuries moved on,
cloud alter cloud disappeared, anu IN the sixteenth
century the scar distance was 10 oe GER
Was adopted by Kepler one OF the Titans Of astr0-
nomlcal history who spent his declining years as
Astronomer Royal at Prague, and TO whom We are
indebted for the discovery OF the celebrated laws
OF planetary revolutions to which We Will have 70
make reference again. lie subsequently calcu-
lated, however that the solar distance was not less
than 26 000 900 miles. In the following century, DR..
HALEY measured the solar angle from two dlstan t
stations and found IT to be much smaller than had
been previously imagined, but he believed the
limit OF the SUMS distance to be 90 000 700 miles.
Even this estimate, as subsequent calculations
have proved, was too small. In lact 1t was as.