long to remedy. His remedy is, so to invest | insurance premium, than for bringing in $25 the self-insurance or 66 how much in deposit" of life premium, would doubtless have been part of the funds, that no policy holder's share a slower growth of this branch of the busiof it can be used by the company to pay ex- ness. But, if there had been less of it, and less penses or any death claim but his own. The overloading and over-assessment, it would not same is the object of American laws prescribing now be showing signs of wasting away. The a fixed standard of reserve and net valuation. force of these remarks cannot be fully appreBut it is in its bearing on short endowment in- ciated without recurring to the elementary surance, or that which never extends beyond principles, and perceiving how the commuted 75, that the distinction between insurance and premium operates from the start. After once self-insurance becomes vitally important; and finding it, no matter whether it be single, limthe present decay and unpopularity of that ited annual, or annual during the term, the branch of the business, which flourished so effect on the company's risk, and the reserve marvellously from 1858 to 1869, must be at- that must be on hand at the end of each suctributed to its being wholly ignored up to the ceeding year, can be very readily ascertained latter date. This great practical mistake seems by means of the tables already given. Take to have arisen from an unfortunate, though for example the net annual premium for 32, not incorrect, definition or analysis of the en- death or 40, to insure $1,000, which we find to dowment insurance policy, the effect of which be $108 69. The claim being payable at the is described as follows in the "Insurance end of the year, if only the natural premium is Times" for November, 1873: paid at 32 for $1,000, and a claim occurs on have to pay $991 25; if $108 69 is paid, they the policy the first year, the co-insurers will will have to pay only $886 96. Hence, in this "Endowment insurance is commonly defined as the union of insurance with endowment in the same policy. If the endowment is of the same amount as the insurance, as is almost invariably the fact, and for the same term, then the whole policy may be and commonly is regarded as the union of a simple term insurance with a pure endowment for the same term. If the life contingency, or risk of death, is considered as a positive quantity in the former, it is a negative quantity in the latter. This means that if the company loses by the death during the term in the former case, it gains by it in the latter. According to this commonly accepted definition, this very useful policy, which provides for one's dependents in case of his own death, and for his own old age in case of his survival, is analyzed into two, both of which are affected by the law of mortality in contrary senses. The more you analyze in this way, the more people not well versed in algebra are mystified; for no other language than algebra has power to deal satisfactorily with positive and negative quantities in the same calculation. By a different analysis the negative quantities will all disappear. If, instead of regarding the policy as composed of the insurance of a given invariable amount for a term of years, united with an endowment of the same amount at the end of the term in case of survival, we regard it as the insurance of a decreasing series of sums, united to an increas ing accumulation, the amount of which latter at any period of the term, added to the sum then insured, shall equal the face of the policy, we shall have precisely the same thing as before, with the contingency, so far as the company is concerned, all on one side. The endowment' in a technical sense is annihilated. We have in its stead a mere series of savings-bank deposits, subject to certain peculiar conditions, or, in other words, a series of self-insurances, supplementary to the series of yearly insurances done by the company. Without affecting the practical results at all, we have got a new point of view from which the whole matter is as plain as insurance for a single year." Had the companies regarded the increase of the net premiums of the endowment insurance policies over those of the ordinary life policies, not as insurance premium at all, but mere self-insurance or savings-bank deposit, they would have abstained from doing two or three very unfortunate things. They would not have added more margin to the net endowment premiums than to the smaller net life premiums, but rather less. They would not, whatever the premium might be, have paid more to procure a given amount of short-term endowment insurance than of long, but rather less. They would not have assessed more for expenses on a given amount of short endowment insurance than of long, if as much. The consequence of paying the agent no more, if not less, for bringing in $100 of endowment 886-96 991-25 886-96 991-25 of It will latter case the company insures only 777-54 991-08 X * The "margins" of these two policies (column A) are those usually applied, the first being 22 per cent. of the net premium, and the second 40 per cent. Expenses are usually assessed according to these margins, with what effect will appear presently. Let it be observed that the insurance done by the company (column C) is always the face of the policy less the "selfinsurance" of the year. Let us suppose that the holders of No. 1 and No. 2 have lived through eight years. The insurance which the company has done for each is the sum of the numbers in column C against the eight years. For No. 1 it is $3,751 14; for No. 2 it is $7,564 17, a little more than double. Supposing the death claims to have been according to the table, and that the expenses have consumed half the margins (not an unusual experience), the insurance enjoyed by No. 1 has cost him the sum of column B plus half that of A= $128 54, and that by No. 2, $98 82. That is, at No. 2's rate, No. 1's insurance ought to have cost him only $49. If No. 2 paid enough, No. 1 paid at least $79 54 too much. As the policy No. 2 that was to extend beyond the eight years had a much greater interest than the other in having the company enlarged, in proportion to the insurance it enjoyed during the eight years, it would seem it ought to have been assessed for the expenditures devoted to that object in a higher ratio.-This brings us to the question, What is the measure of a member's interest in the company, as an insurance company? Plainly it is not the face of the policy or the premium, one or both, alone. A person who has a series of larger risks to be carried through 40 years, sick or well, if he should live so long, must have a larger interest than one who has a series of smaller risks to be carried only eight years, though the premium of the latter should be larger and the face of the policy the same. He may have a greater interest in it as a savings bank, and this is measured by the deposits. It is difficult to discover any nearer measure of the interest of a member in the insurance, than the present value of all the insurance contracted to be done under the policy, and this is found by discounting both by interest and mortality all the normal costs in column B. This process, already explained, gives column D, in which is placed against each age, under the head of "Insurance Value," the present value of all the future normal costs, including that just due. The insurance values given in No. 2 include, of course, the discounted normal costs of the 59 years of possible insurance not included in the table.—Îf the self-insurance fund accumulated on a policy can never be used properly by the company for any purpose but to pay the claim arising on the policy itself, it becomes an important question how far the company can justly appropriate it as a penalty for the non-fulfilment of the contract. The loss which the company will sustain by the non-performance of the contract can have no appreciable relation to the self-insurance or accumulated de the policy year in which he dies; but when the claim is known to be valid, it is usually paid within from 60 to 90 days. A wholelife policy is an agreement on the part of the company to pay a certain sum to those representatives of the insured mentioned therein on his death. About three fourths of all the policies issued are of this kind. A term policy is an agreement to pay to the representatives of the insured a certain sum on his death, provided that event happens within a certain fixed term. A simple endowment policy is an agreement to pay a certain sum to the insured at the end of a fixed term if he be then alive. The insured himself takes the risk of living till the end of the term. Such policies are seldom taken out in this country. An endowment insurance policy is an agreement to pay a certain sum to the insured at the end of a fixed term, or to his representatives on his death should that happen before the end of the term. When "endowment policies" are spoken of, it is this kind which is usually meant. A joint-life pol posits, but only to the insurance that remains to be done, that is, to the present value of it. This grows less while the self-insurance grows greater. Manifestly, then, the penalty for breach of contract should not increase with the age of the policy. It cannot therefore be a fixed percentage of the self-insurance fund, but it may perhaps justly equal or exceed it at first. There is therefore nothing to which it can to any appreciable extent have any just relation but the "insurance value." This principle is just beginning to be recognized by some of the largest offices. The "insurance value" of the policy is also beginning to be recognized as the proper basis for determining the addition to be made to the net premiums for expenses and adverse contingencies. This will have the effect to reduce the premiums on the shorter endowments, if not to increase those on the longer ones. It is also beginning to be seen that the expenses, so far as they exceed those of ordinary trust institutions, should be assessed upon the members, not according to the premiums they pay, or their self-insurance, but ac-icy is an agreement to pay a certain sum on cording to the value of their interest in the the death of one of two or more persons named. company as an insurance company. Nothing | In this and the following kind of policy usually can be more certain than that, as the business only two persons are named, upon the death of has hitherto been managed, it is better to put either of whom the policy becomes payable; the difference between the premiums of an but three or more may be. A survivorship endowment insurance policy and a term policy policy is an agreement to pay a certain sum for the same term into an ordinary savings to the survivor of two persons named on the bank, and take only the term policy of the life death of the other. Various other kinds of insurance company. It can only be politic to policies are sometimes issued, especially by take the endowment insurance policy when English companies; but those mentioned are the company's expenses in excess of one half the only ones issued in this country to any of one per cent. on its investments are assessed considerable extent. (See ANNUITIES.)—Life on the policy holders according to the then insurance is governed by the same legal prinpresent insurance values of their policies, dis- ciples, so far as they are applicable, as other counted at an interest as low as 4 per cent. In kinds of insurance. (See INSURANCE.) Any that case, no one who needs insurance at all can fraud or deceit in obtaining a policy, or misrep afford to deposit in an ordinary savings bank, resentation of essential facts, even innocently but will find it profitable to employ the life in- made, will render it void. Any person can insurance office both for insurance and accumu- sure the life of another upon whom he or she lation. Nor, in that case, will the redundancy is dependent for support, or in the continuance of the premium be any objection, because it of whose life he has an adequate pecuniary will be sure to return annually with interest. interest; and a wife is always held to have an If three things, to wit--1, the normal or tabu- insurable interest in the life of her husband. lar cost of carrying the risk of each year; 2, At present the policies of companies make spethe addition to the net premium made to meet cific provision in regard to most points which the working expenses and to provide against would be likely to give rise to disputes. As the possible excess of death claims in any year these provisions vary somewhat in different over the amount expected by the table; and 3, companies, they should be carefully examined the self-insurance of each year with that part and strictly complied with.-Some idea of the of the net premium devoted to its increase magnitude of the business of life insurance may were all stated distinctly in the policy itself, be formed from the following statistics of the and also kept distinct in the books of the com- New York state companies for the year 1873: pany, it would probably dispel most of the mystery which has so much bewildered policy holders, and remove the necessity of any more elaborate governmental supervision than that which is exercised over other fiduciary institutions. The following are the kinds of policies usually issued by life insurance companies. It is to be understood that a claim said to be payable "on the death of the insured" is payable according to the calculation at the end of Number of companies. Gross liabilities except capital.. 27 385.761 $1,051,099,364 180,895,408 158.516,842 22,379,061 If to these amounts we add those of the compa- LIGHT, that force in nature which, acting on the retina, produces the sensation of vision. It also has an important influence upon chemical affinity, as may be instanced in the union of hydrogen and chlorine gases, which in diffused light takes place gradually, but in the direct rays of the sun instantly. The manifestation of vitality in plants is almost entirely dependent upon it, and most animals cannot maintain their health for any considerable time without its presence. The sources of light are self-luminous bodies, such as the sun, the fixed stars, certain meteors, those planets which have not cooled below the point of redness, and terrestrial bodies in a state of incandescence and phosphorescence. The ancient Greeks were aware that rays of light proceeded from illuminated objects in straight lines, which were reflected as well as refracted by surfaces according to certain definite laws. But all the ancient philosophers had very inconsistent notions in regard to its connection with vision, believing this vital function to be performed by something which proceeded from the eye to the object; and it is remarkable that this illogical idea was entertained until the early part of the 11th century, when it was refuted by the Arabian astronomer Alhazen, who seems to have been the first to perceive that vision is produced by rays of light proceeding from the object to the eye.-Two principal theories have been advocated to account for the phenomena of light, the emission or corpuscular theory, and the undulatory theory. The emission theory, which was the first to be connected with optics on mechanical principles, originated with Descartes, who was the founder of modern mechanical philosophy. He conceived light to consist of small particles emitted by luminous bodies, capable like elastic balls of bounding from or being reflected by surfaces; and he explains the production of colors by assuming that a rotary motion is given to these particles under certain circumstances. But Newton was the founder of the emission theory, because he developed nearly all the doctrines by which it was maintained for more than a century, and also discovered many of the laws of optics by its means. The principal distinguishing hypotheses of this theory will be noticed in the course of this article. The undulatory theory assumes that the space between the celestial bodies is occupied by a kind of imponderable matter, which is infinitely elastic and of extreme tenuity, so that it not only occupies the space between bodies, but also enters into them and performs its function of undulation within them and between their particles. This subtile matter is called the luminiferous or cosmic ether (see ETHER), and the luminousness of a body is assumed to be due to a rapid vibratory motion of its molecules which is propagated in the ether in the form of waves. These waves proceed in all directions from every luminous point, resembling in that respect the waves of sound; the luminous wwwww FIG. 1. point, like that of the origin of sound, being the centre of a sphere. The waves, however, are propagated in different ways in the two cases. The sphere of sound is formed by alternate expansions and condensations of the air, the waves consisting of concentric shells of alternate density and rarity, and the motion of the aerial particles being to and fro in the direction of the radii of the sphere. In the case of light the propagation is also in the direction of the radii, but the motion of the particles of ether is supposed to be in a transverse direction, as represented in section in fig. 1. The transverse oscillations in a line of ether particles proceeding in a right line from the source of light, as from e to a, is called a ray, and that length of a ray which at any instant includes all the phases of an oscillation is called a wave; while the form of that part of the wave which is presented toward the direction of propagation is called a wave front. In the figure the vibrations are represented as taking place in one plane. Some regard each ray as cylindrical in form, and made up of a number of transverse vibrations which cross each other like the diameters of a cylinder; but it is only necessary to suppose that each ray vibrates in one plane, and that there are innumerable parallel rays with planes at every inclination to each other, as well as rays crossing each other in all directions. The velocity of light is known to be about a million times as great as that of sound, so that upon the undulatory theory air, or any other ponderable form of matter with which we are acquainted, would not be a sufficiently subtile medium for its propagation. For the purpose of explanation it therefore becomes necessary to assume some other medium which possesses adequate mechanical properties. Such a medium had been imagined by the ancients, and Hooke in 1664 proposed a theory that "light is propagated by a quick, short, and vibratory motion, in a homogeneous medium, in such a way that every pulse or vibration of the luminous body will generate a sphere which will continually increase and grow bigger, as the waves or rings on the surface of water do swell into bigger and bigger circles about a point in it." His theory, however, contained many erroneous hypotheses, and was unsupported by experimental or mathematical proof; but in the hands of Huygens it soon assumed a form capable of explaining most of the phenomena of light in accordance with established mathematical principles, and of standing the test of experimental demonstration to the present time. No better idea of the inception of the undulatory theory can be given than by quoting a few words from Huygens's Traité de la lumière (1690; Tractatus de Lumine, 1728). It will also thus be seen that he had formed views in regard to molecular physics which have but recently been adopted, and that he had a pretty clear idea of the doctrine of dissociation almost a century and a half before the birth of Sainte-ClaireDeville, its commonly reputed author. "No one will question," says Huygens, "but that light consists of a motion of a certain matter as regards its effects. It appears that light, when gathered into a focus by a concave mirror, has the property of burning like fire, that is to say, it dissociates the particles of bodies (quod disjungat partes corporum); and this most certainly indicates motion, at least according to that philosophy wherein the causes of all natural effects are conceived by means of mechanical reasons. . . . If we consider with what great velocity the rays of light are propagated on all sides, and how, setting out from various and even opposite quarters, they intersect without interfering with one another, we will easily understand that lucid bodies are not seen by means of a certain luminous matter coming from them to us, as a ball or an arrow passes through the air. . . . It therefore moves in another way, and to understand this it will be well to know how sound passes through the air." He then gives the explanation of the propagation of sound in a manner scarcely equalled by any modern writer, and proceeds: "There is no doubt but that light reaches us from luminous bodies by means of motion given to the interposed matter. . . . Light and sound, though they possess successive motion in common, yet differ very widely in other respects, as the motion which is the cause of each is differently produced, and the matter is different in which the motion takes place, and the mode different whereby the motion is communicated. For sound has for its cause a sudden concussion of the whole body, or of a large part of it, which puts the contiguous air in motion; but light must arise from the separate parts of the luminous body, so that they are all plainly seen. . . . In luminous bodies the motion is produced by a violent concussion of the particles, whereby an impulse is given to the ethereal matter. If we now inquire what is that ethereal matter wherein that motion springs, it will be seen that it is not the same as that which serves for the propagation of sound; for this is no other than the air we breathe, which being removed, the other still remains, a fact proved by placing the sonorous body in a glass vessel and removing the air by Boyle's machine." It is sometimes said that Huygens entertained the idea that light was propagated in the luminiferous ether in the same manner that sound is in the air, that is, by to and fro vibrations in the line of propagation; but according to the above quotation, and for other reasons, this conclusion is scarcely well founded. He does indeed compare the ... action to that which accompanies the impact of elastic bodies, but does not suggest any definite method of production of the vibrations. He concerns himself more with the forms of the wave fronts which are produced by the vibrations, and in that way arrives at mathematical results which, by the most rigid experimental and theoretical tests, have been found true. The composition of light by the union of rays of different degrees of refrangibility was not then known, and the cause of this difference of refrangibility not till more than a century after; several other of the phenomena of light, as interference and diffraction, had not been well observed, and required some additional hypotheses for their explanation; but the fundamental principles which enter into the explanation of all the phenomena, then as well as recently observed, were laid down by him, and will never be affected by any changes of hypothesis in regard to the precise mode of motion of the individual particles of ether. The additional hypotheses by which the theory has been brought to more completeness, the most important of which is that of transverse vibrations and the deduced principle of interference, were proposed (1801– 3) by Dr. Thomas Young of England, and hence many of his countrymen regard him as really the founder of the undulatory theory. The principle of interference, however, was not perfectly established and generally applied until Fresnel brought to bear upon the subject the analytical powers of his great mathematical genius. Euler, Malus, Cauchy, Arago, Biot, Sir David Brewster, Sir William Hamilton, Sir G. B. Airy, and other investigators have also added many important contributions. The definite conception of transverse vibrations of different lengths by which the rays of different refrangibility were propagated must, however, be considered as an important part of the undulatory theory as it now stands, and the principal hypothesis upon which a great share of the physical explanations depends. It may seem remarkable that this theory, whose fundamental laws were so clearly stated nearly two centuries ago, should not have been sooner accepted, as it is thought the emission theory can be put to the test of direct experiment. Experiments made by Mr. Bennet are pointed to as being conclusive. He suspended a slender straw horizontally by means of a spider's web, and attached a piece of white paper to one end of the delicate balance. He then introduced it into the receiver of an air pump, exhausted the air, and brought the focus of a powerful lens to bear upon it, but without producing any motion in the ponderable matter of the balance. It is asserted that on the emission theory the immense velocity of the luminous particles, although they might be infinitesimally small, would possess sufficient momentum to impart a sensible degree of motion to light bodies; and the position cannot well be denied. If a single molecule of light |