EXP 
126 EXP 
But fy, my wand’ring mufe, how thou do'ft ftay l 
Expectance calls thee now another way. Milton, 
Something expedted : 
Tliere is expectance here from both the Tides, 
What further you will do. Shakefpeare. 
Hope ; that of which the expedition is accompanied with 
pleafure : 
Oh, what a noble mind is here o’erthrown ! 
The expectancy and rofe of the fair ftate. Shakefpeare. 
EXPECTANT, adj. [French.] Waiting in expedi¬ 
tion.—Her rnajedy has offered conceffions, in order to 
remove fcruples raifed in the mind of the expectant heir. 
Swift. 
EXPEC'TANT,/! One who waifs in expedition of 
any thing ; one held in dependence by his hopes : 
They, vain expectants of the bridal hour, 
My (lores in riotous expence devour. Pope. 
EXPECTATION, /. [ expcClatio , Lat.] The adt of 
expedting.—’Tis expectation makes a bleffing dear. Congreve. 
The trees 
Should have borne men, and expectation fainted, 
Longing for what it had not. Shakefpeare. 
The (late of expedting either witli hope or fear.—Live in 
a conbant and ferioirs expectation of that day, when we 
mud appear before the Judge of heaven and earth. Rogers. 
—Profpedt of any thing good to come.—My foul, wait 
thou only upon God, for my expectation is from him. 
Pj'al. lxii. -5.—The objedt of happy expedition ; the 
Mefiiah expedted : 
Now clear I underdand, 
What oft my deadied thoughts have fearch’d in vain, 
Why our great expectation fhould be call’d 
The feed of woman. Milton. 
A date in w'hich fomething excellent is expedted from us : 
You fird came home 
From travel with fuch hopes as made you look’d on, 
By all men’s eyes, a youth of expectation-. 
Pleas’d with your growing virtue I receiv’d you. Otway. 
EXPECTATION, f. in the dodtrine of chances, is 
applied to any contingent event, upon the happening of 
which fome benefit is expedted. This is capable of being 
reduced to the rules of computation : fora fum of money 
in expedition when a particular event happens, has a 
determinate value before that event can happen. Thus, 
if a perfon is to receive any fum, as 10I. when an event 
takes place which has an equal chance or probability of 
happening and failing, the value of the expectation is half 
that fum, or 5I. : but if there are three chances for failing, 
and only one for its happening, or one chance only in its 
favour out of all the four chances ; then the probability of 
its happening is only 1 out of 4, or i, and the value of 
the expedition is but a of 10I. which is only 2I. 10s. or 
half the former fum. And in all cafes, the value of the 
expedition of any fum is found by multiplying that fum by 
the fradtion exp'reding the probability of obtaining it. So 
the value of the expedition on iool. when tliere are three 
chances out of five for obtaining it, or when the probability 
of obtaining it is is of iool. w hich is 60I. And if s 
be any fum expedted on the happening of an event, h the 
chances for that event happening, and f the chances for 
its failing; then, there being h chances out of f + h for 
its happening, the probability will be 
h 
7 +A’ 
and the 
value of the expedition is -—- x -f. See the article 
J T 
Algfbra, vol.i. p.315. 
Expectation ok Life, in the doctrine of life annui¬ 
ties, is the (hare or number of years of life, which a per¬ 
fon of a given age may, upon an equality of chance, expedt 
to enjoy. By the expedition or lhare of life, fays Mr. 
Simpfon, in liis Seledt Exercifes, is not here to bp under- 
Hood that particular period which a perfon hath an equal 
chance of furviving ; this lad being a different, and more 
fimple confideratiou. The expedition of a life, to put 
it in the mod familiar point of view, may be taken as the 
number of years at which the purchafe of an annuity, 
granted upon it, without difeount of money, ought to be 
valued. Which number of years will differ more or lefs 
from the period above-mentioned, according to the difte- 
rent degrees of mortality to which the feveral dages of 
life are incident. Thus it is much mpre than an equal 
chance, according to the table of the probability of the 
duration of life, that an infant, jud come into the world, 
airives not to the age of ten years; yet the expedition or 
Oiare of life due to it, upon an average, is near twenty 
years. The reafon of which wide difference, is the great 
excefs of the probability of mortality in the fird tender 
years of life, above that refpedting the more mature and 
dronger ages. Indeed if the numbers that die at every 
age were to be the fame, the two quantities above fpeci- 
fied would alfo be equal; but when the laid numbers be¬ 
come continually lefs and lefs, the expedlation mud of 
confequence be the greater of the two. Mr. Simpfon lias 
given a table and rule for finding this expedlation. Thus, 
A Table of the Expectations of Life in London. 
Age. 
Expedlation. 
Age. 
Expedlation. 
age. 
Expedlation, 
I 
27*0 
28 
24-6 
55 
14-2 
2 
32-0 
29 
24-1 
5 6 
138 
3 
34 'o 
30 
23-6 
57 
1 3'4 
4 
35‘6 
31 
23-1 
58 
x 3 ” 1 
5 
36-0 
32 
22*7 
59 
I 2 ‘ 7 
6 
36-0 
33 
22’3 
60 
12*4 
7 
35-8 
34 
21*9 
61 
I 2*0 
8 
35 ’ 6 
35 
21-3 
62 
n*6 
9 
35 ' 2 
36 
21*1 
6 3 
1 r *2 
IO 
34'8 
37 
20*7 
64 
i0'8 
I I 
34’3 
38 
203 
6 5 
10-3 
I 2 
33‘7 
39 
19-9 
66 
10*1 
13 
33 ’i 
40 
i9’6 
6 7 
9-8 
14 
32-5 
4 i 
I9*2 
68 
9'4 
31-9 
42 
18'8 
69 
9 ' 1 
16 
3 1 '3 
43 
18-5 
70 
8-8 
17 
30-7 
44 
181 
7 i 
8-4 
18 
30-1 
45 
17-8 
72 
8-i 
*9 
2 9'5 
46 
17-4 
73 
7-8 
20 
28-9 
47 
17*0 
74 
7'5 
21 
28-3 
48 
i6* 7 
75 
7*2 
22 
27.7 
49 
16-3 
76 
6-8 
23 
27*2 
50 
i6’o 
77 
64 
24 
26 m 6 
5 i 
13-6 
78 
60 
25 
26-1 
52 
i 5‘2 
79 
5'5 
26 
23-6 
53 
I4‘9 
80 
5 '° 
27 
23-1 
54 
14-5 
For example, if it be requiied to find the expectation 
or fhare of life, due to a perfon of 30 years old. Oppo- 
fite the given age in the fird column of the table, bands 
23-6 in the fecond column for the years in the expedlation 
fought. See the article Algebra, vol.i. p.316. 
EXPECTER, f. One who has hopes of fomething._ 
Thefe are not great expeClers under your adminihration, 
according to the period of governors here. Swift. —One 
who waits for another: 
Signify this loving interview 
To the expeClers of our Trojan part. Shakefpeare. 
EXPECTORANTS,/. \_expeCloro, Lat. to difeharge 
from the bread. ] Medicines which promote a difeharge 
from the afpera arteria, or the lungs. 
Fd EXPECTORATE, u. a. [ex and peClus, Lat.] To 
ejedt from the bread.—Excrementitious humours are ex¬ 
pectorated by a cough after a cold or an adhma. Harvey— 
Morbific matter is either attenuated fo as to be returned 
into the channels, or expectorated by coughing. Arbuthrwt. 
EXPECTO- 
