EXP 
EXP 
The greatest deviation from these numbers is 
towards the beginning of the scale, when, 
owing to the smallness of the expansion, it is 
difficult to measure it with precision. It 
leads us to this remarkable conclusion, that 
the squares of the natural numbers beginning 
at f> indicate the increase of bulk which 10000 
parts of water experience for every ten de- 
grees they are heated above 82°. 5, or cooled 
below 12°.5, This rule will give the reader 
a more precise idea of the rate at which wa- 
ter expands when heated or cooled, than a 
bare inspection of the table could do. 
A considerable number of liquids has been 
tried to ascertain whether any of them, like 
water, have a temperature in which their 
•density is a maximum, and which expand 
when cooled below that temperature. Sul- 
phuric acid has no such point, neither have 
the oily bodies ; but some solutions of salt in 
water begin to expand before they become 
solid. These solutions, however, when cool- 
ed down sufficiently, crystallize with such 
rapidity, that it is extremely difficult to be 
certain of the fact, that they really do begin 
-to expand before they crystallize. 
That class °f bodies which undergo an ex- 
pansion when they change from a liquid to a 
solid body by the diminution of temperature, 
is very numerous. Not only water when 
■converted into ice undergoes such an expan- 
sion, but all bodies which by cooling assume 
•the form of crystals. 
The prodigious force with which water ex- 
pands in the act of freezing has been long 
known to philosophers. Glass bottles filled 
with water are commonly broken in pieces 
when the water freezes. The Florentine 
academicians burst a brass globe whose ca- 
vity was an inch in diameter, by tilling it 
with water and freezing it. The force ne- 
cessary for this effect was .calculated by Mu- 
% schenbroeck at 27720 lbs. But the most 
complete set of experiments on the expansive 
•force of freezing water are those made by 
major Williams at Quebec, and published in 
the second volume of the Edinburgh Trans- 
actions. This expansion has been explain- 
ed, bv supposing it the consequence of a 
tendency which water, in consolidating, is 
observed to have to arrange its particles in 
one determinate manner, so as to form pris- 
matic crystals, crossing each other at angles 
"of 60° and 120°. The force with which they 
arrange themselves in this manner must be 
enormous, since it enables small quantities of 
water to overcome so great mechanical pres- 
sures. Various methods have been tried to 
ascertain the specific gravity of ice at 32° ; 
that which succeeded best was to dilute 
spirits of wine with water till a mass of solid 
ice put into it remained in any part of the 
liquid without either sinking or rising. Tie 
specific gravity of such a liquid is 0.92, 
which of course is the specific gravity of ice, 
supposing the specific gravity of water at 60° 
•to be 1. This is an expansion much greater 
than water experiences even when heated to 
212°. We see from this, that water, when 
•converted into ice, no longer observes that 
equable expansion measured by Mr. Dalton, 
but undergoes a very rapid and considerable 
augmentation of bulk. 
The very same expansion is observed dur- 
ing the crystallization of most of the salts; all 
-of them at least which shoot into prismatic 
forms. Hence the season that the glass \es- 
Ypl, I, 
EXP 
t;8l 
sels in which such liquids are left, usually 
break to pieces when the crystals are formed. 
This expansion of these bodies cannot be 
considered as an exception to the general 
fact, that bodies increase in bulk when heat 
is added to them ; for the expansion is the 
consequence, not of the diminution of heat, 
but of the change in their state from liquids 
to solids, and the new arrangement of their 
particles which accompanies or constitutes 
that change. 
It must he observed, however, that ail bo- 
dies do not expand when they become solid. 
There are a considerable number which di- 
minish in bulk ; and in these the rate of dimi- 
nution in most cases is rather increased by 
solidification. When liquid bodies are con- 
verted into solids; they either form prismatic 
crystals, or they form a mass in which no 
regularity of arrangement can be perceived. 
In the first case, expansion accompanies soli- 
dification ; in the second place, contraction 
accompanies it. Water and all the salts fur- 
nish instances of the first, and tallow and oils 
are examples of the second. In these last 
bodies the solidification does not take place 
instantaneously, as in water and salts, but 
slowly and gradually; they first become vis- 
cid, and at last quite solid. Most of the oils, 
when they solidify, form very regular spheres. 
The same thing happens to honey, and to 
some metals. It has been thought that all 
combustible liquids contract, when they be- 
come solid, while incombustible liquids ex- 
pand; but there are exceptions to this rule. 
Sulphuric acid does not by congelation alter 
its appearance; but cast iron, and perhaps 
sulphur also, expand in the act of congealing. 
EX PARTE, a term used in the court of 
chancery, when a commission is taken out 
and executed by one side or party only, upon 
the other parties neglecting or refusing to 
join therein. When both the parties proceed 
together, it is called a joint commission. 
Ex parte talis, a writ that lies for a bai- 
liff or receiver, that having auditors assigned 
to pass his accounts, cannot procure from 
them reasonable allowance, but is cast into 
prison ; in which case the practice is to sue 
this writ out of the chancery, directed to the 
sheriff to take the four mainpernors to bring 
his body before the barons of the exchequer, 
at a certain day, and to warn the lord to ap- 
pear at the same time. 
EXPECTANT, in law, signifies having 
relation to, or depending on ; thus, where 
land is given to a man and his wife, and to 
their heirs, they have a fee simple estate ; 
but if it be given to them and the heirs of 
their bodies begotten, they have an estate 
tail, and a fee expectant, which is opposed to 
fee simple. 
EXPECTATION, in the doctrine of 
chances, is applied to any contingent event, 
upon the happening of which some benefit, 
&c. is expected. This is capable of being 
reduced to the rules of computation; for a sum 
of money in expectation when a particular 
event happens,has a determinate value before 
that event happens. Thus, if a person is to 
receive any sum as 10/. when an event takes 
place which has an equal chance or probabi- 
lity of happening and failing, the value of the 
•expectation is half that sum, or 5/. ; 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 
4 R 
the probability of ils happening is only one 
out ot four, or J, and the value of the expec- 
tation is but 5 of 10/. which is only 21. IQs. or 
half the former sum. And in all cases, the 
value of the expectation of any sum is found 
by multiplying that sum' by the fraction ex- 
pressing the probability ot obtaining it. So 
the value of the expectation on 100/. when 
thq^e are three chances out of five for obtain- 
ing it, or when the probability of obtaining it 
is 3-lifths, is 3-iilihs of 100/. which is 60/. 
And if s be any sum expected on the happen- 
ing of an event, h the chances for that event 
happening, and f the chances for its foiling; 
then, there being h chances out of f -j- h for 
its happening, 
the probability will be— 
an ■ value of the expectation is— ■■ 
j -j- h 
See Chances. 
X s. 
Expectation of Life , the -share of life due to 
a person of a given age, according to a table of 
mortality. The most obvious sense of the term, 
is certainly, “ the particular number of years 
which a life of a given age has an equal chance 
of enjoying this is the time that a person may 
reasonably expect to live; for the chances 
against his living longer are greater than those 
for it ; and therefore, he cannot entertain an 
expectation of living longer, consistently with 
probability : but this period does not coincide 
with what tire writers on Life Annuities call the 
Expectation of Life, except on the supposition 
of an uniform decrease in the probabilities of 
life, as Mr. Simpson has observed in his Select 
Exercises ; and Dr. Price adds, that even on this 
supposition, it does not coincide with what , is 
called the expectation of life, in any case of 
joint lives ; he therefore defines it more accu- 
rately to be, “ The mean continuance of any 
given single, joint, or surviving lives, according 
to any given table of observations:” that is, the 
number of years which, taking them one with 
another, they actually enjoy, and may be con- 
sidered as sure of enjoying ; those who live or 
survive beyond that period, enjoying as much 
more time in proportion to their number, as 
those who fall short of it enjoy less. 
The particular proportion that becomes ex- 
tinct every year, out of the whole number con- 
stantly existing together of single or joint lives, 
must, wherever this number undergoes no vari- 
ation, be the same with the expectation of those 
lives, at the time when their existence com- 
menced. Thus, was it found in any town or 
district, where the number of births and buriak 
arc equal, that a 20th or a 30th part of the in- 
habitants die annually, it would appear, that 20 
or 30 was the expectation of a child just bom 
in that town or district ; and if a 13th part of 
all the inhabitants of the age of 60 years and 
upwards die annually, the expectation of a per- 
son of 60 years of age is 13 years. These ex- 
pectations, therefore, for all single lives, are 
easily found by a Table of Mortality, shewing 
the number that die annually at all ages, out of 
a given number alive at those ages ; and the ge- 
neral rule for this purpose is, “ to divide the 
sum of all the living in the Table, at the age 
whose expectation is required, and at all greater 
ages, by the sum of all that die annually at that 
age, and above it ; or, which is the same, by 
the number in the table of the living at that 
age: and half unity subtracted from the quoti- 
ent will be the required expectation.” Thus the 
sum of all the living at the age of 60 and up- 
wards, in Table I, J is 27933, which divided by 
2038, the number living at that age, and the 
quotient less half unity, gives 13,21, the expec- 
tation of 60, as in Table II. 
