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A N N 
ANN 
A N N 
Uirm, and in which they are suffered to <*ool 
gradually. This is found to prevent their 
breaking so easily as they otherwise would, 
and particularly on exposure to heat. There 
is also this difference between annealed and 
unannealed glass, that when the latter is bro- 
ken it often flies into small powder, as is re- 
markably exemplified in the little glass bub- 
bles sold in the streets, and called Prince Ru- 
pert’s drops, which are drops of common 
bottle glass which fall from the rods on which 
bottles are made, into water, which suddenly 
cools them. See Rupert’s Drops. Va- 
rious theories have been started to account 
for these phenomena, but none of them quite 
satisfactory, and all that can be said is, that 
by gradually cooling, the glass becomes per- 
fectly chrystallized. 
A similar process is'used for rendering cast- 
iron vessels less brittle, and the effect depends 
probably on the same principles. 
ANNEXATION, in law, a term used to 
imply the uniting of lands or rents to the 
crown. 
ANNONA, in Roman antiquity, denotes 
.provision for a year of all sorts, as of flesh, 
wine, & c. but especially of corn. 
Annona is likewise the allowance of oil, 
salt, bread, flesh, corn, wine, hay, and straw, 
which was annually provided by contractors 
for the maintenance of an army. 
Annona, or Custard Apple, a genus of 
the polyandria polygynia class and order. The 
characters are: the calyx is a tviphylous pe- 
rianthium : the corolla consists of six heart- 
shaped petals: the stamina have scarcely any 
filaments; the anthers are numerous, sitting 
on the receptaculum: the pistilhim has a 
roundish germen; nostyli: the stigmata ob- 
tuse and numerous: the pericarpium is a 
large roundish unilocular berry, covered with 
a scaly bark: the seeds are numerous. There 
are 10 species; the most remarkable are: 
1. The annona muricata, or sour-sop, which 
rarely rises above 20 feet high: tiie fruit or 
apple is large, of an oval shape, irregular, and 
pointed at the top, of a greenish yellow co- 
lour, and full of small knobs on the outside: 
the pulp is soft, white, and of a sour and 
sweet taste intermixed, having many oblong, 
dark coloured seeds. It much resembles the 
black currant, and is a native of the West In- 
dies. 2. The annona palustris, or water-apple, 
grows to the height of 30 or 40 feet ; the fruit 
is seldom eaten but by negroes, and the tree 
grows in, moist places in all the West India 
islands. 3. "The annona reticulata, or custard 
apple, is also a native of the West Indies, 
where it grows to the height of 25 feet; the 
fruit is of a conical form, as large as a tennis- 
ball, of an orange colour when ripe, hav- 
ing a soft, sweet, yellowish pulp, of the 
consistence of a custard, whence it has its 
name. 4. The annona triloba, or North Ame- 
rican annona, called by the inhabitants papaw, 
is a native of the Bahama islands, and like- 
wise of Virginia and Carolina. The trunks 
of the trees are seldom bigger than the small 
part of a man’s leg, and are about 10 or 13 
feet high. The fruit grows in clusters of 3 or 
4 together: when ripe, they are yellow, co- 
vered with a thin smooth skin, which contains 
a yellow pulp of a sweet luscious taste. All 
parts of the tree have a rank, if not a fetid, 
smell ; nor 5 is the fruit relished by many ex- 
cept negroes. This last sort will thrive in the 
open air in England, if it is placed in a warm 
and sheltered situation ; but the plants should 
be trained up in pots, and sheltered in winter 
for 2 or 3 years till they have acquired 
strength. The seeds frequently remain a 
whole year in the ground; and therefore the 
earth in the pots ought not to be disturbed, 
though the plants do not come up the first 
year. All the other sorts require to be kept 
in a warm stove. 
ANN ONrE prospectus, in antiquity, an 
extraordinary magistrate, whose business it 
was to prevent a scarcity of provision, and to 
regulate the weight and ‘fineness of bread. 
ANNOTATION, in matters of literature, 
a brief commentary or remark upon a book 
or writing, in order to clear up some passage, 
or draw some conclusion from it. 
ANNOTTO, in commerce, a kind of red 
dye, brought from the V est Indies. It is 
procured from the pulp of the seed-capsules 
of a tree called bixa in South America. See 
Bixa. 
The annotto is prepared only by the Spa- 
niards ; the mode is as follows : the contents 
of the fruit or capsule are thrown into a 
wooden bowl, where as much hot water is 
poured on them as is necessary to suspend the 
red matter or pulp. When the seeds are left 
quite naked, they are taken out, and the 
wash is left to settle. The water is then 
poured off, and the sediment dried by degrees 
in the shade, after which i.t is made into balls 
or cakes for exportation. 
ANNUAL, an appellation given to what- 
ever returns every year : thus we say, the 
annual motion of (he earth, annual plants, &c. 
Annual, or Annuel, in the Scotch law, 
any yearly revenue, or rent, payable at the 
two great terms, "Whitsuntide and Martinmas. 
Annual plants, called also simply annuals, 
are such as only live their year, i. e. come 
up in the spring, and die again in I the 
autumn. 
Annual leaves, are such as come in the 
spring, and perish in autumn. 
aNnuent ES musculi, in anatomy, 
the same with recti inter ni minor es. 
ANNUITIES, periodical payments of money, 
amounting to a fixed sum in each year, and con- 
tinuing for a certain period, as for 10, 50, or 
100 years, or for an uncertain period, to be de- 
termined by a particular event, as on the failure 
of a life, or for an indefinite term ; which latter 
are called perpetual annuities. The times of 
payment are either yearly, half-yearly, quar- 
terly, weekly, or at any other intervals that may 
be determined on previous to the commence- 
ment of the annuity, or regulated during its 
continuance. 
All calculations relating to annuities are made 
on the principle of improving money at Com- 
pound Interest, and are generally for an an- 
nuity of 1/., from which the value of any other 
annuity is easily derived. Let r represent the 
amount of 17. in one year ; that is, one pound 
increased by a year’s interest, then r n , or 
raised to the power whose exponent is any given 
number of years, will he the amount of 1/. in 
those years ; its increase in the same time is 
r n — 1 ; now the interest for a single year, or 
the annuity answering to the increase, is r — 1 ; 
therefore, as r — 1 is to r 11 — 1, so is u (any 
given annuity) to a its amount. Hence vve have 
« X r n — 1 
by which the amount of an annuity for any 
number of years at any given rate of interest 
is found. In the same manner the present value 
of annuities is obtain i;l ; for, as 1/. is the present- 
value of r n , its amount in n years, and as the 
present value of any other amount, and conse- 
quently of — must bear the same 
r — 1 
proportion to that amount, we have 
X 1 - 
— 1 
-> or 
From these theorems, the other cases relating 
to annuities may be easily deduced ; but as the 
involution of high powers is a tedious operation 
by common arithmetic, most questions relative 
to annuities may he more conveniently answered 
by the help of logarithms. It is, however, sel- 
dom necessary to have recourse to either of j 
these methods, as very accurate tables of the 1 
amount and present worth of annuities have 
been calculated by Mr. J. Smart and others, and 
are inserted in most books that treat of Com- 
pound Interest or Annuities. 
TABLE I. 
Shewing the Amount of an Annuity of £.1, in 
any Number of Years, not exceeding 100, 
when improved at 5 per Cent, per Annum, 
Compound Interest. 
Yrs. 
Amount. 
Yrs. 
Amount. 
Yrs. 
Amount. 
I 
1,0000 
35 
90,3203 
69 
559,5510 
2 
2,0500 
36 
95,8363 
70 
588,5285 
3 
3,1525 
37 
101,6281 
71 
618,9549 
4 
4,8101 
38 
107,7095 
72 
650,9027 
5 
5,5256 
39 
114,0950 
73 
684,4478 
6 
6,8019 
40 
120,7998 
74 
719,6702 
7 
8,1420 
41 
127,8398 
75 
756,6537 
8 
9,5491 
42 
135,2317 
76 
795,4864 
9 
11,0266 
43 
142,9933 
77 
836,2607 
10 
12,5779 
44 
151,1430 
78 
879,0738 
11 
14,2068 
45 
159,7002 
79 
924,0274 
12 
15,9171 
46 
168,6852 
80 
971,2288 
13 
17,7130 
47 
178,1194 
81 
1020,7903 
14 
19,5986 
48 
188,0254 
82 
1072,8298 
15 
21,5786 
49 
1 98,4267 
83 
1127,4713 
16 
23,6575 
50 
209,3480 
84 
1184,8448 
17 
25,8404 
51 
220,8154 
85 
1245,0871 
18 
28,1328 
52 
232,8562 
86 
1308,3414 
19 
30,5390 
53 
245,4990 
87 
1374,7585 
20 
33,0659 
54 
258,7739 
88 
1444,4964 
21 
35,7192 
55 
272,7126 
89 
1517,7212 
22 
38,5052 
56 
287,3482 
90 
1594,6073 
23 
41,4305 
57 
302,7157 
91 
1675,3377 
24 
44,5020 
58 
318,8514 
92 
1760,1045 
25 
47,7271 
59 
335,7940 
93 
1849,1098 
26 
51,1135 
60 
353,5837 
94 
1942,5653 
27 
54,6691 
61 
372,2629 
95 
2040,6935 
28 
58,4026 
62 
391,8760 
96 
2143,7282 , 
29 
62,3227 
63 
412,4698 
97 
2251,9146 
30 
66,4388 
64 
434,0933 
98 
2365,5103 
31 
70,7608 
65 
456,7980 
99 
2484,7859 
32 
75,2988 
66 
480,6379 
100 
2610,0252 
33 
80,0638 
67 
505,6698 
34 
85,0670 
68 
531,9533 
EXAMPLE. 
To what sum will an annuity of £.42 amount 
in 30 years, at 5 per cent, compound interest ? 
The amount in the Table against 30 years is 
66,4388, which multiplied by 42, gives the an- 
swer 2790/. 8s. Id. 
TABLE II. 
Shewing the present Value of an Annuity of 
£.1 for any Number of Years, not exceeding 
100, at 5 per Cent, per Annum, Compound 
Interest. By the help of these tables many 
practical problems, which are daily occuring, 
may be worked by any persons versed in com- 
mon arithmetic. 
