300 HORO 
To know the hours by refle&ibn; adapt a fmall mir¬ 
ror, an inch or two in diameter, to the fummit of the 
ftyle, and let it be fixed in a pofition exaftiy horizontal 5 
the light reflected from it will indicate the hour. 
Inltead of a mirror, a fmall goblet, an inch or two in 
diameter, may be applied to the fummit of the ftyle, and 
be filled with water till its fufface be exadtly on a level 
with the extremity of the ftyle; the light reflected from 
it will indicate the hours in the fame manner, and will be 
more eafily obferved in cloudy weather, when the fun 
fcarcelv appears; becaufe the furface of the water will 
generally have a fmall movement, which, by making the 
light tremulous, will render it perceptible, notwithftand- 
ing its weaknels. 
Another Method. —Place, in any part of the bottom of a 
window, a fmall goblet, and fill it with water to a given 
height. Place alio, on the bottom of the window, a fun- 
dial ; and, when the lhadow of the ftyle falls on the hour 
of noon, mark on the ceiling or wall, which receives the 
reflected light of the fun, the central point of the image 
of that luminary; do the lame thing in regard to all the 
other hours, and mark thefe points with the hours to 
which they correfpond. Two or three months after, 
when the fun’s declination has confiderably changed, if 
the fame operation be performed, you will have two points 
of each hour-line ; and, if the furface, on which they are 
traced out, be a plane, to obtain the required hour-line, 
nothing will be neceflary but to join them by a ftraight 
line. But, if the furface, which receives the reflefted 
light, be curved or irregular, to obtain the hour-line a 
greater number of points will be neceflary. To trace it 
out exaftly, the operation of finding a point for each 
hour-line ought to be repeated for five or fix months, 
from the one l'olftice to the other. If thefe points be then 
joined by a curve, they will give the hour-lines required. 
How the Shadow of a Style, on a Sun-dial, might go back¬ 
wards without a miracle .—-This phenomenon, which on the 
firft view may appear phyfically impoflible, is however 
very natural, as we lhall here Ihow. It was firft remarked 
by Nonius or Nugnez, a Portuguefe mathematician, who 
lived about the end of the fixteenth century. It is found¬ 
ed on the following theorem : “ In all countries, the zenith 
of which is lituated between the equator and the tropic, 
as long as the fun pafles beyond the zenith, towards the 
apparent or elevated pole, he arrives twice before noon at 
the fame azimuth; and the fame thing takes place in the 
afternoon.” 
Let Z, (fig. 19,) be the zenith of any place fituated 
between E the equator, and T the point through which 
the fun pafles on the day of the fummer folftice ; let the 
circle H A Q B K H reprefent the horizon ; R E Q one half 
of the equator; T F the ealtern part of the tropic above 
the horizon, and G T the weftern part. It is here evident, 
that from the zenith Z there may be drawn an azimuth 
circle, fuch as Z I, which fliall touch the tropic in a point 
O, for example ; and which fliall fall on the horizon in a 
point I, fituated between the points Q and F, which are 
thole where the horizon is interfered by the equator and 
the tropic; and, for the fame reafon, there may be drawn 
another azimuth, as ZH, which fliall touch in 0 the other 
part of the tropic. 
Let us now fuppofe that the fun is in the tropic, and 
confequentiy rifing in the point F; and let a vertical ftyle, 
of an indefinite length, be erefted in C. Draw alfo the 
lines IC K, and F C N ; it is evident that at the moment 
of fun-rife the lhadow of the ftyle will be projefted in 
C N; and that, when the fun has arrived at the point of 
contact O, the lhadow will be projefted in CK. While 
the fun is pafling over F O, it will move from CNtoCK; 
but, when the lun has reached the meridian, the lhadow 
will be in the line CB; it will therefore have gone back 
from CK to CB: from fun-riling to noon then it will 
have gone from CN to CK, and from CK to CB; con¬ 
fequentiy it will have moved in a contrary or retrograde 
LOGY. 
direction; fince it firft .moved from the fouth towards the 
weft, and then from the weft towards the fouth. 
Let us next fuppofe that the fun riles between the 
points F and I. In this cafe the parallel he defcribes be¬ 
fore noon will evidently cut the azimuth ZI in two 
points; and therefore, in the courfe of a day, the lhadow 
will firft fall within the angle IC CL; it will then proceed 
towards C K, and even pals beyond it, .going out of the 
angle; but it will again enter it, and, advancing towards 
the meridian, w'ill proceed thence towards the ealt, even 
beyond the line C L, from which it will return to dilap- 
pear with the letting of the fun within the angle LCB. 
It is found by calculation, that in the latitude of iz 
degrees, when the fun is in the tropic on the fame fide, 
the tw'o lines C N and C K form an angle of 9 0 48'; to 
pafs over which the lhadow requires z hours 7 minutes. 
Hence we may conftruCt a dial, for any latitude, on 
which the lhadow lhall retrograde or move backwards.— 
For this purpofe incline a plane, turned directly fouth, in 
fuch a manner, that its zenith lhall fall between the tro¬ 
pic and the equator, and nearly about the middle of the 
diftance between thefe two circles: in the latitude of Lon¬ 
don, for example, w'hich is 51 0 31', the plane muft make 
an angle of about 38°. In the middle of the plane, fix 
an upright ftyle of fuch a length, that its lhadow' fliall go 
beyond the plane; and, if leveral angular lines be then 
drawn from the bottom of the ftyle towards the fouth, 
about the time of the folftice the lhadow will retrograde 
twuce in the courfe of the day, as above-mentioned. This 
is evident, fince the plane is parallel to the horizontal 
plane having its zenith under the fame meridian, at the 
diftance of 12 degrees from the equator towards the north : 
the lhadows of the tw'o ftyles muft confequentiy move in 
the fame manner in both. 
Some may here fay that this is a natural explanation of 
the miracle, which, as we are told in the facred Scriptures, 
was performed in favour of Hezekiah king of Jerufalem; 
but we entertain no idea of leflening the credibility of this 
miracle. Belides, it is very improbable, if the retrogra- 
dation which took place on the dial of that prince had 
been a natural effedt, that it fliould not have been ob¬ 
ferved till the prophet announced it to him as a figii of his 
cure; for in that cafe it muft have always occurred w'hen 
the fun was between the tropic and the zenith; whereas 
we are not informed that it ever occurred before that 
time or after it. 
To know the hours on a Sun-dial, by the Moon Jhining on it .— 
This problem will not appear difficult to thole who know 
that the moon’s paflage by the meridian is every day later 
by about 48 minutes; that, when new, Ihe pafles the me¬ 
ridian exaftly at the lame time as the fun ; and, when 
full, 12 hours after. 
Firft, find the moon’s age, which is given in every com¬ 
mon almanac, where the days and hours of the new and 
full moon are always marked. Let us fuppofe then, that 
at the time w'hen you wifti to know the hour, 6 days and 
a half have elapfed fince new moon. Multiply 48 minutes, 
or 4 of an hour, by and the produft will be f, or 5 
hours 12 minutes, which muft be added to the hour indi¬ 
cated by the dial. . If the dial therefore indicates 4 hours, 
the real time will be 9 hours 12 minutes. 
But the hour may be found much more exactly in the 
following manner. Firft find at what hour of the day the 
moon has pafled, or will pafs, the meridian ; which may 
be determined by the help of a common almanac, where 
the times of the moon’s rifing and letting are marked; for 
if the interval between the rifing and letting be halved, 
it will give the time of the moon’s pafling the meridian 
nearly. 
Let us fuppofe then, that the moon has palled the me¬ 
ridian at 3 h 3o m in the afternoon ; the difference of this 
paflage from that of the fun, were the moon fixed in the 
heavens, would be 3! hours later than the fun. Confe¬ 
quentiy, if the moon indicates, on a lun-dial, i\ in the 
evening,. 
