0.5

1 cm

S H A . 257

of the pyramid in the line G F, till it cut the point I, which

point will limit the Shadow of the pyramid.

Laftly, draw a line from C to I, and another from E to I,

and the triangle C I E will be the Shadow of the pyramid.

To gain the Shadow of an inverted pyramid K, draw perpen-

dicular lines from the angular points of its bafe, and form the

fubjacent plane, by means thereof, after the manner directed for

the fun.

And, from all the angles of this plane, draw lines to the bafe

of the torch G ; then from H, the central point of the flame,

draw other lines touching all the angles of the bafe of the inverted

pyramid, and dividing thofe of the plane, whereby the Shadow

will be defined.

The different difpof.tions and heights c/* Shadows by torch-light.

Shadows from the fun are all caft the fame way, and have the

fame difpofition ; it being impoffible that the fun fhould occa-

fion one Shadow to tend towards the eaft and another towards

the weft at the fame time.

It is true, in different times of the day it makes this difference;

but never in one and the fame hour.

But the torch, candle, and lamp have always this effect; for,

in what place foever one of thefe luminaries be found, provided

there be a number of objects about them, the Shadows will be

caft various ways, fome to the eaft, fome to the weft, fome to

the north, and others to the fouth, according to the fituation of

the objects around the luminary, the foot of which, here repre-

fented by A, ferves as a common center, from which they all

proceed ; and the flame, here reprefented by B, fhews where they

are to terminate, though at different diftances; as the neareft

produce the fhorteft Shadows and the remoteft the longeft. See

plate XIX, fig. 1.

The Shadow doubled. When two luminaries fhine on the

fame object, two Shadows muft be produced, each of the lumi-

naries occafioning its refpec~tive Shadow, and that in proportion

to the circumftances of the luminary.

If fuch luminaries, when at equal diftances, be equal, the Sha-

dows themfelves muft be equal; but if there be any difproportion,

that is, if one of them be a little bigger than the other, or one

of them a little nearer the objecf than the other, the Shadows

will be unequal.

Thus, the obje£t O being illuminated by two candles, the one

near at hand in P, the other farther off in Q_, it is evident the

Shadow of the candle P will be deeper than that of the candle

Q, as is expreffed in the figure. See plate XIX, fig. 2.

The rules for fuch Shadows are the fame with thofe already

given, both for the fun and the torch.

Vol. II. S We

of the pyramid in the line G F, till it cut the point I, which

point will limit the Shadow of the pyramid.

Laftly, draw a line from C to I, and another from E to I,

and the triangle C I E will be the Shadow of the pyramid.

To gain the Shadow of an inverted pyramid K, draw perpen-

dicular lines from the angular points of its bafe, and form the

fubjacent plane, by means thereof, after the manner directed for

the fun.

And, from all the angles of this plane, draw lines to the bafe

of the torch G ; then from H, the central point of the flame,

draw other lines touching all the angles of the bafe of the inverted

pyramid, and dividing thofe of the plane, whereby the Shadow

will be defined.

The different difpof.tions and heights c/* Shadows by torch-light.

Shadows from the fun are all caft the fame way, and have the

fame difpofition ; it being impoffible that the fun fhould occa-

fion one Shadow to tend towards the eaft and another towards

the weft at the fame time.

It is true, in different times of the day it makes this difference;

but never in one and the fame hour.

But the torch, candle, and lamp have always this effect; for,

in what place foever one of thefe luminaries be found, provided

there be a number of objects about them, the Shadows will be

caft various ways, fome to the eaft, fome to the weft, fome to

the north, and others to the fouth, according to the fituation of

the objects around the luminary, the foot of which, here repre-

fented by A, ferves as a common center, from which they all

proceed ; and the flame, here reprefented by B, fhews where they

are to terminate, though at different diftances; as the neareft

produce the fhorteft Shadows and the remoteft the longeft. See

plate XIX, fig. 1.

The Shadow doubled. When two luminaries fhine on the

fame object, two Shadows muft be produced, each of the lumi-

naries occafioning its refpec~tive Shadow, and that in proportion

to the circumftances of the luminary.

If fuch luminaries, when at equal diftances, be equal, the Sha-

dows themfelves muft be equal; but if there be any difproportion,

that is, if one of them be a little bigger than the other, or one

of them a little nearer the objecf than the other, the Shadows

will be unequal.

Thus, the obje£t O being illuminated by two candles, the one

near at hand in P, the other farther off in Q_, it is evident the

Shadow of the candle P will be deeper than that of the candle

Q, as is expreffed in the figure. See plate XIX, fig. 2.

The rules for fuch Shadows are the fame with thofe already

given, both for the fun and the torch.

Vol. II. S We