L I P 
I- I P 
L I L 
70 
life), appears by Table I. to be 10.443. The 
value of 1/. payable at the end of 14 years 
(see Compound Interest), is .505068, and 
the probability that the life will exist so Iona;, 
(See Expectation of Life) is 
These three values multiplied into each other 
are equal to 3.861, which being subtracted 
from 12.502 (the present value of the given 
life by 'Fable I.), we have 8.641, and this re- 
mainder multiplied by 20, gives 162/. I6i'. 4J. 
for tire value required. 
In a similar manner the value of an an- 
nuity for any given term, upon two joint 
lives, may be determined. 
Prob. II. To find the value of an annuity 
certain for a given term after the extinction of 
any given life or lives. 
Solution. Subtract the value of the life or 
lives from the perpetuity, and reserve the re- 
mainder. Then say, as the perpetuity, is to 
the present value of the annuity certain, so is 
the said reserved remainder, to a fourth pro- 
portional, which will be the number of years 
purchase required. 
Example. A and his heirs are entitled to 
an annuity certain for 14 years, to commence 
at the death of B, aged 35. What is the 
present value of A*s interest in this annuity? 
By Table I. the value of the life of B is 
12.502, which subtracted from 20, the per- 
petuity, leaves 7.498 for the remainder to be 
reserved. Then, as 20, is to 9.898 (the value 
of an annuity certain for 14 years), so is 
7.498 (the reserved remainder), to 3.7 107, the 
number of vears purchase required. 
Prob. Ilf. To find the value of an annuity 
for a term certain, and also for what may hap- 
pen to remain of a given life of lives after 
the expiration of this term. 
Solution. Find the value of a life or lives 
as many years older than the given life or 
lives as' are equal to the term for which the 
annuity certain is proposed. Multiply this 
value by 1/. payable at the end of the given 
term, and also by the probability that the 
given life or lives will continue so long. Add 
the product to the value of the annuity cer- 
tain for the given term, and the sum wdl be 
the answer. 
Example. Let the value be required of an 
annuity certain for 14 years, and also for the 
remainder of a life now aged 35 after the ex- 
piration of this term. By 'Fable I. the value 
of a life aged 49 (or 14 years older than the 
given life) is 10.443. The value of 1/. pay- 
able at the end of 14 years, is .505068, and 
the probability that the life will exist so long 
is 2.1.11. These three numbers multiplied 
into each other, produce 3.861, which being 
added to 9.898, the value of an annuity cer- 
tain for 14 years (see Annuities), becomes 
equal to 13 759, the number of years pur- 
chase required. 
Prob. IV. To determine what annuity 
any given sum will purchase during the joint 
lives of two persons of given ages, and also 
during the life of the survivor, on condition 
that the annuity shall be reduced one-half at 
the extinction of the joint lives. 
Solution. Let twice the given sum be di- 
vided by the sum of the two single lives, and 
the quotient will give the annuity to be paid 
during the joint lives; one-half of which is 
therefore the annuity to be paid during the 
remainder of the surv iving life. 
Example , A aged 27, and B aged 35, 
gre desirous of sinking 1000/. in order to re- 
ceive an annuity during their joint lives, and 
also another annuity of half the value during 
the remainder of the surviving life. It is 
required to determine what annuities should 
be granted them under those circumstances. 
By Table I. the value of a life of 27 is 1 3.377, 
and the value of a life of 35 is 12.502. 
2000( (or twice the given sum) being divided 
by 25.879 (the sum of the values of the two 
lives), gives 77.282 /. for the annuity to be 
granted during the joint continuance of the 
lives ; and its half, or 38.641/. is the annuity 
to he paid during the life of the survivor. 
Prob. V. B, who is of a given age, will, 
if he lives till the decease of A, whose age is 
also given, become possessed of a perpetual 
annuity, or of an estate of a given yearly va- 
lue; to find the worth of his expectation in 
present money. 
Solution. Find the Value of an annuity on 
two equal joint lives wdiose common age is 
equal to the age of the oldest of the turn pro- 
posed lives, which value subtract from the 
perpetuity, and take half the remaiuder : 
then say, as the expectation of duration of 
the younger of the two lives, is to that of the 
older, so is the said half remainder, to a fourF*. 
proportional; which will be the number of 
years purchase required when the life of B in 
expectation is the older of the two: but if 13 
be the younger, then add the value so found 
to that of the joint lives A and B, and let the 
sum be subtracted from the perpetuity, and 
you will also have the answer in this case. 
Example. Suppose the age of B to be 30, 
and that of A 20 years, and the value of the 
estate 50/. per annum. Then the value of 
two equal joint lives, aged 30, is, by Table II. 
10.255, and the perpetuity being 20, the dif- 
ference will be 9.745, the half of which is 
4.872. Therefore as 33.43, the expectation 
of A, is to 28.27, the expectation of 13, so is 
4.872, to 4. 1 19, which being multiplied by 50, 
the given annuity, w r e have 205.95/. for the 
required value of BV expectation. 
If the age of B had been 20, and tiiat of A 
30 years, then to 4.1 19, the value just found, 
add the value of the joint lives, which, by 
Table II. is 10.707, and the sum is 14.826, 
which subtracted from 20, the perpetuity, 
and the remainder multiplied by 50, gives 
258.7/. for the require*] value in this case. 
LIFE ESTATES are of two kinds, such 
as are created by the act of the parties, or 
such as are created by the operation of the 
law, as estates by curtesy or dower. 2 Black. 
120. 
Estates for life, created by deed or grant, 
are, where a lease is made of lands or tene- 
ments to a man, to hold for the term of his 
own life, or for that of another person, or for 
more lives than one; in any of which cases, 
he is called tenant for life: only when he 
holds the estate by the life of another, he is 
usually termed tenant pur auter vie, tor 
another’s life. 
Estates for life mav be created not only 
by the express terms before-mentioned, but 
also by a general grant, without defining or 
limiting any specific estate. 2 Black. 121. 
If such persons, for whose life any estate 
shall be granted, shall absent themselves se- 
ven year-, and no proof made of the lives of 
such persons, in any action commenced for 
the recovery of such tenements by the les- 
sors or reversioners, the persons upon whose 
lives such estate depended, shall be account- 
ed as dead ; and the judges shall direct the 
jury to give their verdict as if the person ab- 
senting himself was dead. 19 Car. II. c. 6. 
LIGAMEN F. See Anatomy. 
LIGa' 1 URE. See Surgery. 
LIGHT: See Optics. 
LIGHTS : stopping lights of any house is 
a nuisance, for which an action will lie, if the 
house is an antient house, and the lights an- 
tient lights : but stopping a prospect is not, 
being only matter of delight, not of necessity ; 
and a person may have either an assize of 
nuisance against the persons erecting any 
such nuisance, or he may stand on his own 
ground and abate it. 2 Salk. 247. 
LIGHTFOOTIA, a genus of the class 
and order polvgainia dioecia. The cal. is 
four-leaved; cor. none; fern, and her. stig- 
ma sessile; berry umbilicated. There are 
three species, shrubs of the E. Indies. 
LIGHTNING. See Electricity. 
LIGUSTICUM, lovage ; a genus of the 
digynia order, in the pentandria class of 
plants; and in the natural method ranking 
under the 45th order, umbellate. '1 he fruit 
is oblong, and quinquesulcated on each side; 
the florets are equal; the petals involuted or 
rolled inwards, and entire. There are eight 
species, of which the most remarkable are, 
the levisticum, or common, and the Scoti- 
ciini, or Scots, lovage. The first is a native 
of the Appenine mountains in Italy. The 
second is a native of Scotland, and grows 
near the sea in various parts of the country. 
The root of the first species agrees nearly 
in quality with that of angelica : the princi- 
pal difference is, that the lovage-root has a 
stronger smell, and a somewhat less pungent 
taste, accompanied with a more durable 
sweetness, the seeds being rather warmer 
than the root; but although certainly capa- 
ble ot being applied to useful purposes, this 
root is not regarded in the present practice. 
'Fhe leaves of the second are sometimes eaten 
raw as a salad, or boiled as greens, by the in- 
habitants of the Hebrides. They give an in- 
fusion of the leaves in whey to calves, to 
purge them. 
Ll GUST RUM, privet, a genus of the 
monogynia order, in the diandria class of 
plants; and in the natural method ranking 
under the 44th order, sepiariax 'I'he corolla 
is quadrifkl ; the berry tetraspermous. Tluere 
are three species ; of the common there are 
two varieties, the deciduous and the ever- 
green. They are hardy plants, rising from 
ten to fifteen feet high. They are easily 
propag: ted by seed, layers, suckers, or cut- 
tings. They are used for making hedges. 
The purple colour upon cards is prepared 
from the berries. \\ itiithe addition of alum, 
these berries are said to dye wool and silk of 
a good and durable green; for which pur- 
pose they must be gathered as soon as (hey 
are ripe. The leaves are bitter and slightly 
astringent. Oxen, goats, and sheep, eat the 
plant; horses refuse it. 
LIKE, in geometry, &c. denotes the same 
with similar. See Similar. 
LILAC, in botany, a genus of trees, other- 
wise called syringa. Sec Syringa. 
LILALITE. This stone appears to have 
been first observed by the abbe Poda, and 
to have been then -described by De I3orn. 
Hitherto it has only been found in Moravia 
