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others, cases will frequently occur in the that are injurious to the human frame ; and adjustment of pecuniary concerns, in which temperate climates being less liable to such it is desirable to be able to form an estimate changes are found to be most favourable to of the duration of life, and as it is evidently the duration of life. There are however in a subject on which certainty cannot be at almost every country, particular districts in tained, we must be content with that species which the inhabitants are found to live of knowledge which rests on probability. longer than in other situations, which proThis degree of knowledge, which is the ceeds chiefly from a free circulation of air, limit of our acquaintance, with many other uncontaminated by the noxious vapours and important facts, is, in a comprehensive view exhalations which destroy its purity in other of this subject, infinitely more useful and pro- parts ; thus hilly districts are almost uni. per than more positive knowledge would be. versally found to furnish more instances of

At whatever period the world was first long life, than low and marshy situations. inhabited, there is undoubted evidence that The knowledge of the duration of human for at least 3000 years past the general dura. life in general, and of its probable contition of human life has been much the same nuance at all ages, has been ascertained as it now is ; nor has any great difference with sufficient correctness for all practical been observed between the inhabitants of purposes from the observations which have different climates, the negro of Africa (in been made on the bills of mortality of difsome instances at least) attaining to as great ferent places. Dr. Halley formed a table age as the European. The human frame of the probabilities of life from the registers appears to adapt itself with little difficulty of the births and burials of the inhabitants to the atmosphere and local peculiarities of of the city of Breslaw, the capital of the the country in which it is born, or even into duchy of Silesia in Germany, from the year which it is afterwards removed. Thus not 1687 to 1691. 'A similar table was formed only the children of persons who have re- by Mr. Thomas Simpson from the London moved from Great Britain to different parts bills of mortality, from 1728 to 1737; and of the continent of North America, but also other tables of the same kind have been the emigrants themselves, have been found since published by M. Dupré de St. Maur, to live as long as in the former country. M. Kerseboom, M. de Parcieux, Dr. Price, Men can live equally well under very dif- and others, from which the following are se. ferent circumstances, it is sudden changes lected. TABLE I. Shewing the Probabilities of the Duration of Human Life at all Ages, formed

from the Register of Mortality at Northampton, for 46 Years from 1735 to 1780.

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1 2 3

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8 9 10



11650 3000
8650 1367
7283 502

6416 197

184 6065 140 5925 110 5815 80 5735 60 5675 52 5623 50 5573 50 5523 50 5473 50 5428 50 5373 53 5320 58 5262) 63 5199 67 5132 72 5060 75 4985 75 4910 75 4835 75


4760 26 4685 27

4610 28 4535 29 4460 30

4385 31

4310 32 4235 33

4160 54 4085 35 4010

3935 S7 3860 38 3785 39 3710 40 3635 41 3559

3482 43 3104 44 3326 45 3248 46 3170 47 3092 48 3014

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87

49 2936

2857 51 2776 59 269. 53 2612 54 2530 55 2448 56 2366 57 2281 58 2202 59 2120 60 2038 61 1956 62 | 1874 63 1793 64 1712 65 1632 66 1552 67 1472 68 1392 69 1319 70 1232 71 1152 72 1072

75 75 75 75 75 75 75 75 75 75 75 75 75 75 76 77 78 78 78 78 78 78 78

12 13 14 15 16 17 18 19 20

82 82 82 82 82 82 82 82 82 82 81 81 80 80 80 80 80 80 80 80





૧૨ 23 24


The probability that a life of any pre- In order to find the expectation of life at sent age shall continue a certain number of any age, from a table, like the above, which years, or shall attain to any other given age, shows the number that die annually' at all is the fraction whose numerator is the num- ages, divide the sum of all the living in the ber of the living in the table opposite to the table, at the age whose expectation is re. given age, and the denominator the number quired and at all greater ages, by the sum opposite to the present age of the given of all that die annually at that age and life. Thus the probability that a life of 25 above it; or, which is the same, by the shall attain to the age of 45, or live 20 years, number of the living at that age ; and half

3248 is The difference between this frac- unity subtracted from the quotient will give

the expectation required. Thus, at the age tion and unity gives the probability that the of 65, the sum of all the living at that and event will not happen; the probability that all greater ages, is 18,580 ; the number a life of 25 will not live 20 years, is there living at that age is 1,652 ; and the former 1512

number divided by the latter, and half fore consequently the odds of living unity subtracted from the quotient, gives

4760' to dying in this period are more than 2 to 10.88 for the expectation of the age of 65. 1. The probability that a person of 32 In this manner the following table is years of age shall attain to 59 years, ap- formed.

2120 pears by the table to be

or nearly an

4235' even chance.



Shewing the Expectations of Human Life at every Age, deduced from the Northampton

Table of Observations.

Ages. Expect. ||Ages. Expect. Ages. Expect. | Ages. Expect. Ages. Expect. Ages Expect.

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These tables suggest an easy method of ferent places, the fact is fully ascertained finding the number of inhabitants of a place that the duration of human life is greater from the bills of mortality; for, supposing in all its stages in country parishes and mothe yearly births and deaths equal, it is derate sized towns, than in large and only necessary to find in the way above de crowded cities. According to Simpson's scribed, the expectation of an infant just correction of Smarts Table for London, born, and this multiplied by the number of only one in 44 of the inhabitants attain to yearly births will be the number of inba- the age of 80 years; Dr. Price gives the bitants.

proportion somewhat greater, or about 1 in From all the observations which have 40, but observes that of those who are na. been made on the bills of mortality of dif- tives of London, a much less proportion

1 in 211

arrive to that age. The proportion of the the respective values of an annuity certain inliabitants of other places that live to the of n years payable yearly, half-yearly, of age of 80, has been found as follows : quarterly. It is found as the result of many At Edinburgh........... 1 in 42

investigations, that the first of these addi. Vienna. 1 in 41 tional quantities is about

4th of one year's purchase.
1 in 41

The second itth.
Berlin ....

1 in 37

The third zith.
1 in 27

LIFE bout. See Boat.
Northampton...... 1 in 24
Pais de Vaud

LIFE estates, or estates for life, are of two

kinds ; either such as are created by the act Among any considerable number of lives of the parties, or such as are created by the selected from the common mass, such as the operation of law, as estates by the curtesy nominees to a tontine, or the members of an

or dower. Estates for lite, created by deed assurance or annuity society, the duration or grant, are, where a lease is made of lands of life will always be found greater than it or tenements to a man, to hold for the term is represented by tables formed from gene- of his own life, or for that of another perral bills of mortality. Thus, M. Kersse

son, or for more lives than one; in any of boom found that among the state annuitants which cases he is called tenant for life, only in Holland 1 in 14 lived to upwards of 80 when he holds the estate by the life of ano. years of age, and the nominees to the life ther, he is usually termed tenant pur auter annuities granted by the governments of vie, for another's life. Estates for life may France and Great Britain have been found be created not only by the express terms to live longer than the duration given by before mentioned, but also by a general any table formed from bills of mortality. grant, without defining or limiting any speIn some few country situations, where the cific estate. Where estates are granted for injurious habits and artificial mode of living the lives of others, and they absent themwhich prevail iu large cities have made little selves seven years, and no proof is made of progress, the duration of life bas been found their being in existence; in any action comunusually great; thus at Ackworth in York- menced for the recovery of such tenements shire 1 in 14 died turned of 80 years of by the lessors or reversioners, they shall be age ; and according to an account of the

accounted as dead, and the jury shall give parish of Kingham in New England, in the their verdict accordingly; (19 Charles II. first volume of “ Memoirs of the American

c. 6.) and, on application to the Chancellor, Academy,” the number of deaths in 5. the party holding such estates may be comyears had been 1113, of which 1 in 13 had pelled to produce the persons on whose survived 80 years.

lives such estates depend. LIFE annuities. See ANNUITIES. Life

LIGAMENT, in anatomy, a strong comannuities secured by land, differ from those pact substance, serving to join two bones already described only in this, that the an- together. nuity is to be paid up to the very day of the A ligament is more flexible than a cardeath of the age in question, or of the per- tilage, not easily ruptured or torn, and son upon whose life the annuity is granted. does not yield, or at least very little, when To obtain the more exact value therefore of pulled. such an anvuity, a small sum must be added

LIGHT, is that principle or thing by to the same as computed by the rules in the which objects are made perceptible to our article ANNUITIES, which will be different

sense of seeing; or the sensation occasionaccording as the payments are yearly, half. ed in the mind by the view of luminous ob. yearly, or quarterly. Dr. Price has enterjects

. The nature of light has been a subed at large on the subject, and according ject of speculation from the first dawnings to him the addition is,

of philosophy. Some of the earliest philoY_ for annual payments.

sophers doubted whether objects became

visible by means of any thing proceeding h for half yearly payments.

from them, or from the eye of the specta

tor, but this opinion was qualified by Em9 for quarterly payments.

i pedocles and Plato, who maintained, that

vision was occasioned by particles contihere n is the complement of the given age,' nually flying off from the surfaces of bodies, or what it wants of 86 years; and y, h, 9, are which met with others proceeding from the VOL. IV.



4 n


eye; while the effect was ascribed by Py. The velocity of the rays of light is truly thagorus solely to the particles proceeding astonishing, amounting to nearly two hunfrom the external objects, and entering the dred thousand miles in a second of time, which pupil of the eye.

But Aristotle defines is about a million times greater than the ve. light to be the act of a transparent body, locity of a cannon ball. And this amazing considered as such ; and he observes, that motion of light has been manifested in valight is not fire, nor yet any matter radiat- rious ways, and first from the eclipses of Juing from the luminous body, and transmit piter's satellites. It was first observed by ted through the transparent one.

Roemer, that the eclipses of those satellites The Cartesians have refined considerably happen sometimes sooner, and sometimes on this notion ; and hold that light, as it ex later, than the times given by the tables of ists in the luminous body, is only a power them; and that the observation was before or faculty of exciting in us a very clear and or after the computed time, according as vivid sensation ; or that it is an invisible the earth was nearer to, or further from Jufluid present at all times and in all places, piter, than the mean distance. Hence Roebut requiring to be set in motion by a body mer and Cassini both concluded, that this cir. ignited or otherwise properly qualified to cumstance depended on the distance of Jumake objects visible to us.

piter from the earth; and that, to account Father Malbranche explains the nature for it, they must suppose that the light was of light from a supposed analogy between about fourteen minutes in crossing the it and sound. Thus be supposes all the earth's orbit. This conclusion, bowever, parts of a luminous body are in a rapid mo- was afterwards abandoned, and attacked tion, which, by very quick pulses, is con

by Cassini liimself: but Roemer's opinion stantly coinpressing the subtle matter be found an able advocate in Dr. Halley, who tween the luminous body and the eye, and removed Cassini's difficulty, and left Roe. excites vibrations of pression : as these vi.

mer's conclusion in its full force. brations are greater, the body appears It has since been found, by repeated exmore luminous ; and as they are quicker or periments, that when the earth is exactly slower, the body is of this or that colour. between Jupiter and the sun, his satellites The Newtonians maintain, that light is not are seen eclipsed eight minutes and a quara Huid, but consists of a great number of ter sooner than they could be according to very small particles, thrown off from the la- the tables ; but when the earth is nearly in minous body by a repulsive power, with an the opposite point of its orbit, these eclipses immense velocity, and in all directions. happen about eight minutes and a quarter And these particles, it is also held, are emit later than the tables predict them. Hence, ted in right lines : which rectilinear motion then, it is certain that the motion of light is they preserve till they are turned out of not instantaneous, but that it takes up their path by some of the following causes, about sixteen minutes and a half of time to viz. by the attraction of some other body pass over a space eqnal to the diameter of near which they pass, which is called inflec- the earth's orbit, which is at least one huntion, or by passing obliquely through a me- dred and ninety millions of miles in length, dium of different density, which is called or at the rate of near two hundred thousand refraction; or by being turned aside by the miles per second, as above-mentioned. opposition of some intervening body, which Hence, therefore, light takes up about is called reflection; or lastly, by being to. eight minutes and a quarter in passing from tally stopped by some substance into which the sun to the earth ; so that, if he should they penetrate, and which is called their be annihilated, we should see him for eight extinction. A succession of these particles minutes and a quarter after that event following one another, in an exact straighit should happen; and if he were again created, line, is called a ray of light; and this ray, we should not see him till eight minutes in whatever manner its direction may be and a quarter afterwards. Hence also it is changed, whether by refraction, reflection, easy to know the time in which light tra. or intiection, always preserves a rectilinear vels to the earth, from the moon, or any of course, ull it be again changed; neither is the other planets, or even from the fixed it possible to make it move in the arch of a stars, when their distances shall be known; circle, ellipsis, or other curve. For the these distances are, however, so immensely above properties of the rays of light, see great, that from the nearest of them, sup. the several words REFRACTION, REFAC posed to be Sirius, the dog-star, light takes nox, &c.

wp many years to travel to the earth : and

it is even suspected, that there are many which a constant emission of particles must stars whose light has not yet arrived at us occasion in the luminous body, and theresince their creation. And this, by-the-bye, by, since the creation, must have greatly dimay perhaps sometimes account for the ap- minished the matter in the sun and stars, as pearance of new stars in the heavens. Our well as increased the bulk of the earth and excellent astronomer, Dr. Bradley, after-' planets, by the vast quantity of particles of wards found nearly the same velocity of light absorbed by them in so long a period light as Roemer, from his accurate observa- of time. But it has been replied, that if tions, and most ingenious theory, to ac- light were not a body, but consisted in count for some apparent motions in the fix- mere pression or pulsion, it could never be ed stars; for an account of which see ABER- propagated in riglit lines, but would be RATION of light. By a long series of these continually inflected ad umbram. Thus, Sir observations, he found the difference be- Isaac Newton: “A pressure on a fluid me. tween the true and apparent place of seve. dium, i. e, a motion propagated by such a ral fixed stars, for different times of the medium, beyond any obstacle, which imyear; which difference could no otherwise pedes any part of its motion, cannot be probe accounted for, than for the progressive pagated in right lines, but will be always rays of light. From the mean quantity of inflecting and diffusing itself every way, to this difference be ingeniously found, that the quiescent medium beyond that obstathe ratio of the velocity of light to the velo- cle. city of the earth in its orbit, was as 10,313 The power of gravity tends downwards ; to 1, or that light moves 10,313 times faster but the pressure of water arising from it than the earth moves in its orbit about the tends every way with an equable force, and sun; and as this latter motion is at the rate is propagated with equal ease and equal of 1811 miles per second nearly, it fol- strength, in curves as in straight lines. lows that the former, or the velocity of Waves, on the surface of the water, gliding light, is at the rate of about 195,000 miles by the extremes of any very large obstacle, in a second; a motion according to which inflate and dilate themselves, still diffusing it will require jnst 8' 7" to move from the gradually into the quiescent water beyond sun to the earth, or about 95,000,000 of that obstacle. The waves, pulses, or vibramiles.

tions of the air, wherein sound consists, are It was also inferred, from the foregoing manifestly inflected, though not so consiprinciples, that light proceeds with the same derably as the waves of water; and sounds velocity from all the stars. And hence it are propagated with equal ease through follows, if we suppose that all the stars are

crooked tubes and through straight lines; not equally distant from us, as many argu

but light was never known to move in any ments prove, that the motion of light, all the curve, nor to inflect itself ad umbram.way it passes through the immense space It must be acknowledged, however, that above our atmosphere, is equable or uni- many philosophers, both English and foform. And since the different methods of reigners, have recurred to the opinion, that determining the velocity of light, thus agree light consists of vibrati propagated from in the result, it is reasonable to conclude, the luminous body, through a subtle ethethat in the same medium, light is propa- real medium. gated with the same velocity after it has Dr. Franklin, in a letter dated April 23, been reflected as before. For an account 1752, expresses his dissati faction with the of Mr. Melville's hypothesis of the different doctrine, that light consists of particles of velocities of differently coloured rays, see matter continually driven off from the sun's Colour.

surface, with so enormous a swiftness. To the doctrine concerning the mate- “ Must not,” says he, “ the smallest portion riality of light, and its amazing velocity, se- conceivable have, with such a motion, a veral objections have been made, of which force exceeding that of a twenty-four the most considerable is; that as rays of pounder discharged from a cannon ? Must light are continually passing in different di- not the sun diminishi exceedingly by such a rections from every visible point, they must waste of matter; and the planets, instead necessarily interfere with each other in such of drawing nearer to him, as some have a manner as entirely to confound all dis- feared, recede to greater distances, through tinct perception of objects, if not quite to the lessened attraction ? yet these particles, destroy the whole sense of seeing; not to with this amazing motion, will not drive bemention the continual waste of substance, fore them, or remove, the least and slight

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