ARC 
of Canterbury, to which appeals lie from 
ah the inferior courts within his province. 
ARCHETYPE, the first model of a 
work, which is copied after to make an- 
other like it. Among minters it is used for 
the standard weight by which the others 
are adjusted. The archetypal world, among 
Platonists, means the world as it existed 
in the idea of God, before the visible cre- 
ation. 
ARCHIL. See Lichen. 
ARCHIMEDES, in biography, one of 
fhe most celebrated mathematicians among 
t!ic ancients, who flourished about 250 
years before Christ, being about 50 years 
later than Euclid. He was horn at Syra- 
cuse in Sicily, and was related to Hiero, 
.who was then king of that city. The ma- 
thematical genius of Archimedes set him 
with such distinguished excellence in the 
view of the world, as rendered him both the 
honour of his own age, and the admiration 
of posterity. He was indeed the prince of 
the ancient mathematicians, being to them 
what Newton is to the moderns, to whom 
in his genius and character he bears a very 
near resemblance. He was frequently lost 
in a kind of reverie, so as to appeal' hardly 
sensible; he would study for days and 
nights together, neglecting his food; and 
Plutarch tells ns that he used to be carried 
to the baths by force. Many particulars of 
his life, and works, mathematical and me- 
chanical, are recorded by several of the an- 
cients, as Polybius, Livy, Plutarch, Pap- 
pus, &c. He was equally skilled in ail the 
sciences, astronomy, geometry, mechanics, 
hydrostatics, optics, &c. in all of which he 
excelled, and matte many and great inven- 
tions. 
Archimedes, it is said, made a sphere of 
glass, of a most surprising contrivance and 
workmanship, exhibiting the mol ions of the 
heavenly bodies in a very pleasing manner. 
Many wonderful stories are told of his dis- 
coveries, and of his very powerful and curi- 
ous machines, &c. Hiero once admiring 
them, Archimedes replied, these effects are 
nothing, “ but give me,” said he, “ some 
other place to fix a machine on, and I will 
move the earth.” He fell upon a curious 
device for discovering the deceit which 
had been practised by a workman, employ- 
ed by the said king Hiero to make a golden 
crown. Hiero, having a mind to make an 
offering to the gods of a golden crown, 
agreed for one of great value, and weighed 
out the gold to the artificer. After some 
time he brought the crown home of the full 
ARC 
weight; but it was afterwards discovered 
or suspected that a part of the gold had 
been stolen, and the like weight of silver 
substituted in its stead. Hiero, being angry 
at this imposition, desired Archimedes to 
take it into consideration, how such a fraud 
might be certainly discovered. While en- 
gaged in the solution of this difficulty, he 
happened to go into the bath ; where ob- 
serving that a quantity of water overflowed, 
equal to the bulk of his body, it presently 
occurred to him, that Hiero’s question 
might be answered by a like method ; upon 
which he leaped out, and ran homeward, 
crying out rjonxa ! eoook® ! I have found it 
out! I have found it out! He then made two 
masses, each of the same weight qs the crown, 
one of gold and the other of silver ; this be- 
ing done, he filled a vessel to the brim with 
water, and put the silver mass into it, upon 
which a quantity of water overflowed equal 
to the bulk of the mass ; then taking the 
mass of silver out he filled up the vessel 
again, measuring the water exactly, which 
he put in ; this shewed him what measure 
ot water answered to a certain quantity of 
silver. ThDi he tried the gold in like man- 
ner, and found that it caused a less quanti- 
ty of water to overflow, the gold being less 
in bulk than the silver, though of the same, 
weight. He then filled the vessel a third 
time, and putting in the crown itself, he 
found that it caused more water to overflow 
than the golden mass of the same weight, 
but less than the silver one ; so that, find- 
ing its hulk between the two masses of sold 
and silver, and that in certain known pro- 
portions, he was able to compute trie real 
quantities ot gold and silver in the crown, 
and so manifestly discovered the fraud. 
Archimedes also contrived many ma- 
chines for useful and beneficial purposes ; 
among these, engines for launching large 
ships; screw pumps, for exhausting flie 
water out of ships, marshes or overflowed 
lands, as Egypt, &c. which they would do 
from any depth. 
But he became most famous by his cu- 
rious contrivances, by which the city of Sy- 
racuse was so long defended, when be- 
sieged by the Roman consul Marcellus ; 
showering upon the enemy sometimes long 
darts and stones of vast weight and in 
great quantities; at other times lifting their 
ships up into the air, that had come near 
the wails, and dashing them to pieces by 
letting them fall down again; nor could 
they find their safety in removing out of the 
reach of his cranes and lev ers, for there he 
