436 
P I L 
P I L 
fophers, when weary of living, lay down upon their 
funeral pile without any vifible concern. Collier on the. 
Value of Life. 
I’ll bear your logs the while; pray give me it, 
I’ll carry’t to the pile. Shakefpeare's Tempejl. 
An edifice; a building.—The pile o’erlook’d the town, 
and drew the fight. Dryden. 
Thus fancy brings the vanilh’d piles to view, 
And builds imaginary Rome anew. Pope's Mifcell. 
A hair; [ pilas , Lat.]—Yonder’s my lord, with a patch of 
velvet on’s face; his left cheek is a cheek of two pile and 
a half, but his right cheek is worn bare. Shakefpeare's 
All's Well. —Hairy furface ; nap.—Many other lorts of 
Hones are regularly figured; the amianthus of parallel 
threads, as in the pile of velvet. Grew .— \Pilum , Lat.] 
The head of an arrow.—The dart ran into his forehead, 
and there ftucke the fteele pile, making way quite through 
his Ikull. Chapman. 
The pile was of a horfefly’s tongue, 
Whofe Iharpnefs nought revers’d. Drayton's Nymph. 
[Pila , Ital. Serenius derives this meaning from pil, (Lat. 
pilum.) an arrow, or the head of an arrow ; the fide of the 
coin having fuch a figure upon it : Henault from pillars, 
as the ftamp upon it.] One fide of a coin ; the reverie of 
crofs ; [from the Lat. pileus, a cap or hat.]—Other men 
have been, and are of the fame opinion, a man may more 
juftifiably throw up crofs and pile for his opinions, than 
take them up fo. Locke. — [In the plural piles.] The hae¬ 
morrhoids. See vol. xix. p. 168.— Wherever there is any 
uneafinefs, folicit the humours towards that part, to pro¬ 
cure the piles, which feldom mifs to relieve the head. Ar~ 
buthnot. 
Pile, in artillery, denotes a collection or heap of (hot 
or (hells, which are ufually piled up by horizontal courfes 
into a pyramidal form, the bale being either an equilate¬ 
ral triangle, a fquare, or a rectangle. In the triangle and 
fquare, the pile terminates in a Angle ball; but in a rec¬ 
tangle, in a Angle row of balls. In the triangle and fquare 
piles, the number of horizontal rows, or the number 
counted on one of the angles from the bottom to the top, 
is always equal to the number counted on one fide in the 
bottom row. In triangular piles, each horizontal courfe 
is a triangular number, produced by taking the fucceflive 
fums of the numbers i and 2; 1,2, and 3 ; 1,2,3, and 4- > 
&c. and the number of (hot in a triangular pile is the futn 
of all the triangular numbers taken as far, or to as many 
terms, as the number in one fide ol the bottom courfe. 
In order to obtain the number in a triangular pile, 
count the number in the bottom row, and multiply that 
number more two by that number more one; and the 
produdt multiplied by one-fixth of the faid number will 
be the whole fum required. 
In fquare piles, each horizontal courfe is a fquare num¬ 
ber, produced by taking the fquare of the number in its 
fide ; and the number of (hot in a fquare pile is the futn 
of all the fquares, taken from one as far as the number in 
the fides of the bottom courfe. To find the number, 
count the number in one fide of the bottom courfe; to 
that number add one, and to its double add one; multi¬ 
ply the two fums together, then their produfl being mul¬ 
tiplied by one-fixth of the faid number, will give the re¬ 
quired number of (hot in the pile. 
From the exemplification of thefe rules, it would ap¬ 
pear, that, when room is wanted, it is molt convenient to 
flow the (hot in triangular piles; for on the equilateral 
triangle, which is lefs than half the area of a lquare of 
one of its fides, there can be piled a greater number than 
half of thofe that can be raifed on the fquare: and the 
height of afquare pile is foraewhat lefs than that of a tri¬ 
angular one; becaufe a (hot will fink lower in thefpace 
between four others than between three others, when 
they are of equal diameter. 
In rectangular piles, each horizontal courfe is a re&an¬ 
gle, the upper one being one row of balls; and every 
fuch oblong pile may be confidered as confiding of two 
parts, one a fquare pyramid, and the other a triangular 
prifm. To find the number of fiiot in a rectangular pile, 
take the difference between the number in length and 
breadth, in the bottom courfe ; multiply the number in 
breadth, more one, by half the breadth ; the product mul¬ 
tiplied by the faid difference will give the number in the 
prifmatic pile ; upon the fquare of the breadth, find the 
number in a pyramidal pile; and the fum of thefe two 
piles will give the number required. 
We (hail repeat, in a more compendious form, from 
James’s Military Dictionary, the Rules for finding the 
Number in any Pile. 
1. Triangular Pile. —Multiply the bale by the bafe-]-i, 
this product by the bafe +2, and divide by 6. 
2. Square Pile. —Multiply the bottom row by the bot¬ 
tom row +1, and this product by twice the bottom row 
+G and divide by 6. 
3. ReSlangular Pile .—Multiply the breadth of the bafe 
by it felt -f-1, and this product by three times the differ¬ 
ence between the length and the breadth of the bafe, ad¬ 
ded to twice the breadth -f-i, and divide by 6. 
4. Incomplete Piles. — Incomplete piles being only fruf- 
tums wanting a fimilar (mall pile on the top, compute 
firlt the w hole pile as if complete, and alfo the fmall pile 
wanting at top; and then fubtraCf the one number from 
the other. 
7 b PILE, v. a. To heap; to coacervate.—In all that 
heap of quotations which he has piled up, nothing is 
aimed at. Atterbury.— Heaps of comments are piled fo 
high upon authors, that it is difficult fometimes to clear 
the text from the rubbiffi. Felton. 
Againft beleaguer’d heaven the giants move ; 
Hills pil’d on hills, on mountains mountains lie 
To make their mad approaches to the (ky. Dryden. 
Men pil’d on men, with aCfive leaps arife, 
And build the breathing fabrick to the (kies. Addifon. 
To fill with fomething heaped.—Attabaliba had a great 
houfe piled upon the fides with great wedges of gold. Ab¬ 
bot’s Defc. of the World. 
PI'LE-ENGINE. See the article Mechanics, vol.xiv. 
p. 695. 
PI'LE- WORM, J. See Teredo navalis. 
PI'LE-WORT. ” See Ranunculus. 
PI'LEATED, adj. [pileus, Lat.] Having the form of a 
cover or hat—A pitealed echinus taken up with different 
(hells of feveral kinds. Woodward on Foffils. 
PI'LEMENT, f [from pile.] Accumulation: 
What! had he nought, whereby he might be known, 
But coifly pilements of fome curious (tone ? Bp. Hall. 
PILEN'ITUM, /. An eafy kind of chariot, ufed by 
the Roman ladies at games and religious proceffions. 
PI'LEIJ, f. He who accumulates. 
PILES (Roger de), principally known as a writer on 
painting, was born at Clameci, in 1635, of a noble family 
of Nivernois. He was apparently brought up for the 
church, and ftudied theology for three years at the 
Sorbonne; but his inclination led him to the arts of 
defign, which he had learnt under Frere Luke, a recollet. 
In 1662 he became domeftic preceptor to the fon of M. 
Amelot, mailer of requells, whom he accompanied on a 
tour to Italy. In that country he perfedled his tafte 
and knowledge of painting ; and, on his return to Paris, 
acquired a name among artills and connoifleurs by fome 
treatifes which he publiffied on that art. In 1682, his 
former pupil having been nominated to the embafiy ol 
Venice, De Piles accompanied him as fecretary. He 
attended M. Amelot in the fame capacity to Liffion and 
Swilferland. In 169211c was fent by the French miniftry 
into Holland to refide incognito as a kind ot fecret nego¬ 
tiator to bring about a peace. He appeared as an ama¬ 
teur of painting; but, his real errand being difcovered, 
