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Application of the foregoing Tables.
Table I. To find the value of an annuity for a person of any
given age. RULE.“ Multiply the number in the table against the given age, by the sum, and the product is the answer.”
Ex. What should a person, aged 45, give to purchase an annuity of 60l. per annum during life, interest being reckoned 5 per cent. ? : The value in the table against 45 years is 11.105, and this multiplied by 60 gives the answer,
Table II. To find the value of an anpuity on the longest of
two single lives. Rule. " From the sum of the values of the single lives subtract the value of their joint continuance, and the remainder will give the value of the longest of the lives.”
Ex. What is the value of the longest of two lives aged 10 and 15? Table I. $ The value of a life at
10 = 15.139 15 14.588
29.727 Table II. The value of the joint continu
ance of two lives of 10 & 15 = 12.302
17.425 "Therefore an annuity of 100l. a year upon longest of two lives, oné 10 and the other 15,
would be worth nearly 17 years and a half pur. chase, or more accurately, 17421. 10s.
Upon similar principles the value of the longest of three lives, &c. is found : and all other questions, relating to annuities, are likewise solved. See Re
Light, in physics, that substance, of the presence of which we are informed by the sensibility of the visual organs; from which bodies receive their colours ; and wbich is, in some way, connected with heat.
Light is an object of research, both in opties and in chemistry; the first inquires into its form and laws; the second, its essence.
I. “Of light, in optics.” Light, according to the Newtonian doctrine, which no subsequent discovery or theory seems to have discredited, is com. posed of inconceivably small particles of matter, of different magnitudes; which are emitted or reflected from every point in the surface of a luminous body, in right lines, and in all directions, with an unparalleled velocity; and whose power or intensity decreases as the squares of the distance in
That light is a material substance, appears from its being propagated in time, and from its acting upon and producing great alterations in other bodies; but that its particles are inconceivably small appears from this, that the greatest quantity of flame is fowd to have scarce any sensible gravity or weight: also because these particles pervade the pores of all transparent bodies, however hard or heavy: yet, sınali as they are, the rays of light consist of different sorts of these particles; and that this difference arises from their different magnitudes, seems evident from the different directions in which the several sorts of rays move, after they have passed through a budy of glass, water, &c. of some special figure, especially that of a prism.
Since the weight of bodies is proportional to the quantity of matter, it follows, that, where the latter is diminished indefinitely, the former will be so too; therefore the weight of light must be imperceptible. Boerhaave caused a globe of iron, twelve inches in diameter, to be heated red-hot, and suspended at the end of a very exact balance, and nicely counterpoised by weights at the other end, and thus let it bang till all the particles of heat or light were escaped, when he found the equilibre of the balance in no wise altered.
That the particles of light have not only magnitude, but, also, in different degrees, is another, and perhaps the most subtil, discovery of the Newtonian philosophy. This is absolutely proved by the different refrangibility they are found to display in passing through a prisiatic figure of glass or water;
for the power of the prism detains the issu ing particle, and draws it a little towards the surface; and, since this power is the same, it would have the same effect on all the particles of light, if they were all of an equal magnitude, because they have all an equal velocity. But since this effect is different among the particles, some being detained and drawn aside to a greater distance than others, it follows, they must be less in magnitude, to become more subject to the influence of the attracting surface; in like manner as the electric effluvia will act upon and agitate very small and light bodies
and more easily, than they can move those which are larger.
According to some very elaborate experiments of Dr. Bradley, light moves at the rate of one hun. dred and ninety-five thousand two hundred and eighteen miles in a second. Another account states the number of miles at one hundred and seventy thousand. The velocity of light exceeds that of a cannon-ball by one million five hundred and fifty thousand times. It is calculated to travel from the sun to the earth in eight minutes and thirteen seconds.
II. “ Of light, in chemistry.” Light is considered, by modern chemists, and apparently with reason, as a simple elementary body; but they have not yet been able to form a theory on this subject, in which considerable difficulties are not involved.
Light manifests itself to the mind through the mediums of two senses. To the organs of vision it presents forms and colours; and to those of touch, the phenonienon of heat. It is observable, that experience so uniformly teaches us to unite the ideas of light and heat, that none but the philosopher, and he scarcely with intelligibility, would talk of fire that is not luminous, or light that is not warm : the first step, therefore, toward an analytical examination of this matter, is to separate in our minds, the warmth and the light of our hearths. To assist this attempt, we must remember that fire certainly can exist, without the company of light, since both coals and iron may frequently be met with in a state of perfect blackness, combined with violent heat.
To instance the existence of light without warmth, as in the temperature and brightness of a frosty day, is equally easy; yet, after all, light and heat still recur to the mind as inseparable things; and even of those habituated to abstract considera. tions, numbers are disposed to affirm that they are one and the same.
That they are not one and the same, has certainly never been proved; but this, of the two, appears the more probable conclusion. Heat, as is shown in the article Fire, is one of the attributes of caloric; but caloric is not conceived to possess the attribute of light, also ; and though heat and light are usually found together, this connection has been attributed rather to mutual antipathy than to homo.. genuousness.
The question is, Why do combustible bodies, in the act of consuming, give out ligbt? It is answer. ed, Because there is a repulsion between light and caloric.
Taking for granted the previous proposition, that all combustible bodies, in greater and less degrees, . .contain both caloric and light, it is agreed that, supposing the reality of the repulsion, these two substances cannot be accumulated in the same body beyond a certain degree. Arrived at that, if the. caloric predominate, it will tend to drive off the. light; if the light, on the contrary, happen to prevail, it will displace the caloric. It is on this prin-!" ciple that light flies off, in the form of fame, during combustion
The present state of this inquiry will not allow another conclusion than an abrupt one, to this article. The properties of light, and the extent of