Year: 1869




T0i the Editor of the Commercial


in your issue of to-day find the follow
ing;


:. In yourrepOrt of the eclipse, yOT stat
ed it came on at t:29, was at its height at
$40, and of OF G:23. VIII you or some of
your readers inform us how il came to pass
off in six minutes less time than it requir-
ed to go on, and greatly oblige


STUDENT.''


A clear and logical answer to this ques-
ton would require more space in your pa
per than would be proper to appropriate
to such a discussion. | will, however,
without taking too much of your space.
endeavor to give Il brief and somewhat
mechanical Illustration of the causes
which produces such an unexpected phe-
nOmcnon.


In order to simplify the case, we will
suppose the central line of the eclipse ira
verses the earth's equator from beginning
to end.


Now let Student draw a circle near
the lower end of sheet of paper, which
circle is designed to represent the earth.
Across this circle draw two diameters-
one virtical or parallel with the length of
the sheet, and the other horizontal. Mark
the right hand end of the horizontal one
W for west, and the left-hand end T. for
east, and the upper end of the virtual line
Il for zenith.


Near the upper end of the same sheet





and mark it :. This circle may be much
smaller than the first one, Because the
sun being so much further away from
than the earth is, seems to be much small
er.


The progressive motion of an eclipse is
due to the difference i'll the motion of the
sun and moon in their apparent orbits
around the earth. The sun appears to
move ffrom west to cast entirely around
the earth once in year, while the moon
appears to revOlve around it, in the same
direction, nearly thirteen times during the
same period.


TO simplify still further this very intri-
cate problem, we may suppose the motion
of the sun is reduced to nothing, while
that of the moon is reduced by the same
! amount or to the difference of velocity
! between the two motions. This last sup
! position will produce no sensible error in
! the duration of the eclipse. but will ena-
| BILE us to show how the rotation of the
earth on its eXis should lengthen the du-
ration of an eclipse to observers situated
on its surface. And il will also enable us
| to show how one-half of an eclipse may
be heightened out more than the other
| half to those who are peculiarly situated
on the surface of this rotating sphere.
! Now, let Student cut out circular
disc of cardboard. smaller than S. say half
the diameter, and call it the moon. If 5
| be a shining body, and the moon be placed
half way between 5 and w, then S would
be totally obscured at u single point at w.
But, if the moon were brought a little
4 nearer to W.. then small round shadow
would be found at w, constituting cir
| Gle of total observation. Now, let the
moon be moved from right to left with
uniform velocity, so that its shadow would
move from west to east, along the line w
| +. at Il Uniform rate, if permitted to fall
| there But. as the earth is a solid. Opaque
| spherical body, the shadow would touch
/ at w. pass over the curved surface through
| 4. and off at L. If it were possible for an
observer to pass from w through Il to r.,
| during the same interval of time that the
shadow did, then he would experience n
! total eclipse of the sun during the whole
| four hours-more or lesS-required for the
moons shadow to sweep across the whole
diameter of the earth. If the earth's ro-
tation on its axis were sufficiently raplu
| to carry him through that space IN that
| time. then the duration of the total eclipse
would be prolonged from three or four
minutes to three or four hours, simply oy
i the earth's rotation on its axis.
! But the earth does not rotate so rapid
| ly; still it rotates, and this rotation real
/ ly does prolong the duration of an eclipse;
but in some positions more than in others
and this is the particular point to be illus
| trated.


! Let an observer arrive at w by the
earth's rotation, at the same instant that
the eastern limb of the moon reaches the
4 straight line joining tne western iiiho VI
the sun and w. To him this would be the
beginning of the eclipse, and it would oc-
cur exactly at the moment of sunrise
At this moment he would be moving in
the direction of the sun, or at right angles
to the line w E, consequently this motion
would not tend to Jprolong the duration OF
the eclipse: but immediately afterward
he would be carried along the curve to-
ward Z, thus inclining his course little
in the direction of E, or in that direction
in which the black shadow is following
him, and finally, when he shall nave ave ar ar
rived at point about one,sixth OF the als, aho
tance from W toward Il, the center oi '"o