RELATIVITY interference fringes when the apparatus is ro- Fitzgerald and Lorentz independently sug- (1) becomes h and after rotation through 90 degrees the retardation has the same value. Hence the null effect in the Michelson-Morley experiment is explained. For If we accept this explanation the difficulty is only moved one step farther. While we could compare lengths of objects moving with known velocities it would be impossible to determine the absolute distance of points in space. the only way we can measure distances is by means of material scales. If such scales are subject to the Fitzgerald contraction, scales moving with different velocities give different values for the distance between the same points of space. Since no means has been found for determining which scales are moving and which are not, there appears to be no way of determining, and so defining the distance between two points. Similar difficulties are encountered when we try to determine simultaneous instants of time at different points. The ordinary way of transferring time from a point A to a point B is by moving a clock from the one point to the other. If the clock is subject to the Fitzgerald contraction, however, its parts will change length when in motion. This may change the period of vibration, and so the time determined at B will depend on the speed which the clock is moved and the path along which it is moved from A to B. Any other mechanism (velocity of chemical action, for example), may be similarly affected. time by means of light or electromagnetic If we attempt to transfer signals, since the absolute distance between points is unknown, we cannot determine the interval required for the signal to pass from A to B and, even if the distance were known, the time of passage would seem to depend on the absolute velocities of A and B. Einstein's Relativity of Time and Space. -In 1905 A. Einstein took up the question as to what might properly be understood by time and space. He assumed a system of points at rest with respect to each other and with respect to a system of co-ordinate axes. This means merely that an observer attached to the system and measuring distances with a scale finds no evidence of motion. He further assumes a system of clocks attached to the points on which time can be measured. It is necessary first to synchronize the clocks, i.e., determine simultaneous instants of time at the different points. To do this a ray of light starts from a point A, goes to a point B, and is there reflected back to A. Let ta, ta' be the times on the A-clock when it starts and when it returns, and to the time on the B-clock when it is reflected. If ous. = to la ta' · tb, the clocks at A and B are said to be synchron(2) This definition merely expresses that the time required for light to go from A to B equals the time required to return. This is a case of the principle of relativity. For if a means of measuring time existed such that the absolute motion of the system made these intervals different, it could be used to detect absolute motion. In referring to the time of an event it is always understood that the time is measured on the clock at the point where the event occurs. Let S' be a second set of points at rest with respect to each other but appearing to the inhabitants of S to move with velocity V. The same events may be observed by the inhabitants of S and S', each measuring time with his own clocks and distance with his own meter stick. Einstein's first fundamental problem was to determine the relation between the distances and times thus obtained. To do this he made two assumptions which are generally called the first and second postulates of relativity. I. The Principle of Relativity. The laws of physical phenomena are the same whether stated in terms of one system of co-ordinates or another moving with constant velocity with respect to it. II. The Principle of Constant Light-Velocity. -The velocity of light is a constant independent of its source and of the system with respect to which it is measured. The principle of relativity as here stated is equivalent to the impossibility of defining absolute motion. For, if there were any law that differed at different velocities of the reference system, that law could be used to distinguish such differences of absolute velocity, and, conversely, such differences could only be detected by observing some phenomenon which changed with the velocity. That the velocity of light is independent of the observer is a special case of the principle of relativity. That it is independent of the source is a physical assumption for which there is considerable independent evidence. For example, if the velocity of light changed with the velocity of the source, the total change in the time of passage of light from some of the fixed stars would be so great that the star would be seen in two different points of its orbit at the same time. Let OX, OY, OZ be a system of rectangular axes in S, the X-axis pointing in the direction of motion. Let O'X', O'Y', O'Z' be a similar set of axes in S', the two origins coinciding when t=t'=0 Let t be the time and x, y, z, the co-ordinates of a point when the inhabitants of S see an event occur. Let t' be the time and x', y', z' the co-ordinates of the point where the inhabitants of S' locate the same event. We shall now determine the equations connecting x, y, z, t and r', y', z', t'. particle appears to both observers to move in These equations must be linear. For a free a straight line with constant velocity. Hence a first degree equation should transform into a first degree equation. Since each particle of RELATIVITY S' moves parallel to OX with velocity V, the equations have the form = xa (x-vt) + a2y + a2z, y' b1 (x-vt) + b1y + b2, c1 (x — vt) + c2y + c2, t' = d1 x + day + daz + dat. The first three equations show that the points y=0 lie in a fixed plane of S'. Similarly, the points = 0 lie in a fixed plane of S'. These may be taken as the planes y'=0 and z'=0, respectively. By symmetry these planes in S' will be perpendicular, for there is no reason why one of the angles they determine should be greater than the other. In the same way the points x-vt=k, when k is constant, lie in a fixed plane of S' perpendicular to O'X'. Hence the equations reduce to the form 339 (4) By Einstein's second postulate, the same particle moves with velocity c with respect to S'. Hence (4) must have as consequence (6) t = 3 (1 + x). = dx dt 1 v dx' c2 dt 1. dz' di = If then the velocity of a particle has components ux, uy, uz with respect to S and u1, uy1, uz1 with respect to S1, These formulas give the result of subtracting a velocity with components v, o, o from one with components ux, uy, uz. The result is not obtained as in ordinary mechanics by merely subtracting corresponding components. In relativity mechanics the mass of a particle is not constant but depends on its velocity. The mass is determined by assuming that the mutual actions of a system of particles do not change the total momentum with respect to a given system. Suppose mo is the mass of a ball at rest and m its mass when moving with velocity v. Take two identical balls, one attached to a system S, considered at rest, the Using the above value of m, this reduces to Fds = c2dm. The result is the increase in the kinetic energy of the particle. Hence the increase in kinetic energy is equal to the increase in its mass multiplied by the square of the velocity of light. If now the body comes to rest, this increase in mass will be transmitted to other bodies as energy. It is then reasonable to assume that mass and energy are merely different aspects of the same entity. In ergs of energy, one gram of mass is equivalent to c2 (3 X 1010)29 X 1020, Four-Dimensional Geometry of Minkowski. An event occurs at a point x, y, z and at a time t. Minkowski considered the four variables as the co-ordinates of a point in a space of four dimensions. The motion of a particle is represented by a line in that space. In his first paper Minkowski used as co-ordinate along the time axis ct-1. In a later paper of Minkowski and in most of the papers of more recent writers the co-ordinate along that axis is ct. The four co-ordinates are then X1X, X2y, x3=2, x1 = ct. The Lorentz transformations appear as the changes of variable from one set of co-ordinate axes in the four-dimensional space to another. The values of x, y, z, ct obtained by observers moving with different velocities are merely the co-ordinates of the same point in four dimensions referred to different axes. The principle of relativity requires that when stated in this four-dimensional form, physical laws must be independent of the axes used. That is, the laws of physics must be expressible by equations invariant in the space of Minkowski. Take two points x1, y1, 21, ct1, and 2, y2 22, ct2 in the four-dimensional space. The quantity 8=√ c2 (t2 — 11)2 — ( X2 — X1 ) 2 — (Y2 — Y1 ) 2 ——— (22 — 81)2 may be considered as a sort of distance between the points. By applying the Lorentz transformations it is easily shown to be independent of the reference system. In particular, if the two points represent consecutive positions of a moving particle where u is the vector representing ordinary velocity and k. is a unit vector along the time axis. Since mu is the momentum of the particle and m its energy or mass, the laws of conservation of momentum and of mass or energy of an isolated system are all expressed by the one equation Emow const. = In all the interactions of a system of particles, the total extended momentum is thus constant, To give any adequate conception of the form in which Minkowski represented the equations of electromagnetic theory, it would be necessary to use a considerable amount of four-dimensional vector-analysis. It is sufficient to say that there exists a four-dimensional two-vector (analogous to a directed section of a plane) M resolvable into a sum of two parts M=H+E, where H lies in the three-dimensional space and E passes through the time axis. The magnetic perpendicular to H and the electric intensity intensity is a vector in the observor's space a vector along the line in which E intersects that space. The various values of magnetic and electric intensity as seen by observers moving with different velocities are obtained by referring this same two-vector M to different sets of four-dimensional co-ordinate axes. To an observer moving with a given velocity, 1 RELAY RELIEF a spatial forms can be represented in three dimensions. To an observer moving with a slightly different velocity, there appears slightly different space. Since the practicable range of velocity is so small, we can to a high degree of approximation consider these spaces the same. If we could experience all velocities up to that of light, the ensemble of all such spaces would be the four-dimensional space of Minkowski. If the principle of relativity is correct, this four-dimensional universe has as great reality as the three-dimensional one consciousness presents to us, but as yet our experiences have been limited to only a thin sec÷ tion of it. H. B. PHILLIPS, Professor of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass. RELAY. See ELECTRICAL TERMS. RELEASE, in law, is the name given to a common-law conveyance, in which the word "release" is the operative verb. A release operates in five modes: (1) By passing an estate, as when a joint-tenant or coparcener conveys his estate to his cojoint-tenant or coparcener; (2) by transferring a right, as when a disseizee (a person who has been unlawfully dispossessed) discharges his right to the disseizor; (3) by extinguishment, as the lord releasing his seignorial rights to his tenant; (4) by enlarging a particular estate into an estate commensurate with that of the person releasing; (5) by entry and feoffment, as a disseizee releasing to one of two disseizors, which is equivalent to entry on the property and enfeoffment after putting an end to the disseizin. Blackstone says (Commentaries, book II and chap. 20): "Releases are a discharge or conveyance of a man's right in lands or tenements to another that hath some former estate in possession." In simple language a release is the discharge of a right, by an instrument in writing, by which estates, rights, titles, entries, actions and other things are extinguished and discharged; and, in general, the term signifies a person's surrender of the right or action he has, or claims to have, against another or his lands. RELIANCE. An American yacht. See YACHTS AND YACHTING. RELICS, the mortal remains of departed saints; also, objects associated in memory with them, such as articles they used in life-clothes, vestments, the pectoral cross or the pastoral staff of a holy bishop, or the like: similar reminders of the life and death of Jesus Christ are also relics; and the religious veneration of all such relics when they are duly authenticated is expressly approved by the Catholic Church. The Council of Trent in Sec. xxv of its Acts and Decrees regarding invocation of saints condemns those who hold that "veneration and honor is not due to relics of saints"; but all the Protestant churches teach that veneration of relics, or relic worship, is a sin of the nature of idolatry. In favor of the Catholic doctrine is cited the teaching of the early Fathers, who find both in the Hebrew Scriptures and in the New Testament the highest sanction for the veneration of relics, for example, the incident of the coming to life again of a corpse on contact with the bones of the prophet Eliseus (Elisha: 2 Kings xiii, 21); 341 and that recounted in Acts xix, 12 (compare y, 15), of sick persons being healed with "handkerchiefs or aprons" that had touched the living body of Saint Paul: "there is a power," says Saint Cyril of Jerusalem (Catecheses xviii) "latent even in the bodies of the just." And the practice of the faithful in the first ages of the Church is fully consonant with this belief in the physical and spiritual efficacy of relics. The early Christians were careful to save the remains of martyrs from desecration. In the year 107 the bones of Saint Ignatius, bishop of Antioch, were gathered and wrapped in fine linen, to be guarded thereafter "as a priceless treasure left to the Holy Church." In the year 167 the faithful of Smyrna exhumed the remains of their bishop, Saint Polycarp, who had been burned alive 10 years before under Marcus Aurelius and treasured them as "more precious than costly stones and more valuable than gold." When Saint Cyprian, bishop of Carthage, was about to be decapitated (258 A.D.), the Christians cast towels and napkins before him that they might be soaked in his blood. After the persecutions were over, the practice of veneration of sacred relics persisted in the Church, as is testified by the writings of Saint Ambrose, Saint Augustine, Saint Jerome and indeed by all the Fathers of the 4th and 5th centuries. In all ages there have been abuses connected with the practice. A canon of the Fourth Council of Lateran in the year 1215 forbade relics to be sold or to be exposed outside of their cases or shrines and prohibited the veneration of new relics till their authenticity had been approved by the Pope and these laws are confirmed in decrees of the Council of Trent. The veneration of relics has attained its maximum in the Roman Church and there, according to Addis and Arnold (Catholic Dictionary'), these articles comprise the "bodies, or fragments of the bodies of departed Saints: articles, or portions of articles, which they have used; the holy nails, lance, spear, or fragments of the True Cross; and the girdle, veil, etc., of the Blessed Virgin." In the Roman Breviary there are special offices for the Most Holy Relics (to be said on the fourth or last Sunday in October), for the Crown of Thorns, the Lance and Nails, etc. RELIEF, in old English law, a fine or composition paid by the heir of a tenant, holding by knight's service or other tenure, to the lord on the death of the ancestor for the privilege of succeeding to the estate, which by strict feudal law had lapsed or fallen to the lord on the death of the tenant. In physical geography, the undulations or surface elevations of a country. In painting, the appearance of projection and solidity in represented objects, so as to cause them to appear precisely as they are found in nature. In sculpture and architecture, the prominence of a figure from the plane surface to which it is attached; according to the degree of prominence, it is known as alto-relievo or high relief, mezzo- or demi-relief and bas- or low-relief. In ordinary language, release from a post or duty by a substitute, who may act either permanently or temporarily; specifically, the release of a sentry from his post, which is taken by another soldier, also the person who thus relieves or takes the place of another. RELIEF SCULPTURE. See SCULPTURE. RELIGIO MEDICI was the first of Sir Thomas Browne's books and has always been the one most generally read. It was first printed in an unauthorized edition in 1642, followed in the next year by an edition under Browne's own supervision. The book was the fruit of much reading and much quiet observation and reflection, but is not Browne's most characteristic work. Enthusiasts are more likely to turn to his 'Pseudodoxia Epidemica or Enquiries into very many received Tenets and commonly presumed Truths' (1646) or to his 'Hydriotaphia, Urneburiall (1658) as giving with fullest body the peculiar flavor of Browne's somewhat whimsical personality and as exemplifying that sombre magnificence of style in rhythm and phrasing, not unworthy to be compared with Milton's at their best, which is the special virtue of Browne's most admirable prose. The preference of the general reader for 'Religio Medici' is largely due to its theme and to Browne's highly characteristic attitude toward this theme. The religion of a physician, to translate Browne's title literally, is an arresting topic. It is always interesting when a man who has been deeply concerned with the facts of the natural world abandons himself to speculation on the supernatural possibilities of human existence. Browne's interest in this subject is almost purely speculative. He lived in an age of controversy and at a time when dogmatic opinion flourished, but he acknowledged himself unsuited to follow the controversial method and unable to condemn categorically opinions which he could not share. If one sought for it, so he thought, one would find some good in everything. His habit of mind was to steer a middle course between credulity and scepticism, with a strong leaning toward the latter. But nobody so charitable toward strange views as the sceptic turned loose in the field of speculation, and in reading Browne, one is continually being caught up by his defense of such opinions as the belief in witchcraft, by his apparent desire to put faith in the existence of "changelings" (though he will not go so far as to say that a man can be "despeciated" into a horse), or by his occasional defense of ecclesiastical practices which in his day the normal Protestant (and Browne asserted that the only thing he disliked about Protestantism was the name) would never have thought of defending. In short, Browne loved to sport in paradox and intellectual hyperbole, habits of mind often annoying to the literalminded reader. Beneath these eccentricities, however, there lay a solid foundation of character and belief, an open-mindedness and readiness to see the best in everything, which make of him a better proponent of his views than an orthodox dogmatist, or a bitter iconoclast could have been. GEORGE PHILIP KRAPP. RELIGION has been variously defined according to a multitude of epistemological and ethical systems. The pantheist Hegel takes it to be "the knowledge acquired by the finite spirit of its essence as Absolute Spirit." Kant makes duty to follow his categoric imperative of the practical reason; and religion to be "the recognition of all our duties as divine commands." Huxley defines religion as "rev erence and love for the ethical ideal, and the desire to realise that ideal in life." According to Max Müller, religion is "the perception of the infinite." Schleiermacher says, it is "a determination of man's feeling of absolute dependence." Matthew Arnold, the apostle of sweetness and light, finds that religion is "morality touched by emotion." The latest definition is that of Reinach, 'Orpheus' (1909): "Religion is a collection of scruples that are a stumbling-block to the free exercise of our faculties." Waiving these definitions, based upon false philosophical systems, one may begin by conceiving a man's religion as his Godwardness. Cicero, De Natura Deorum,' II, xxviii, derives religio from re-legere, to re-collect, to recall to mind, to reflect. Lactantius, 'Institutiones Divinæ, IV, xxviii, throws over this derivation, and traces religio back to re-ligare, to bind again. This etymology is commonly accepted. Man is bound to God as creature to Creator; by religion he renews this bond, whensoever in word or deed he acknowledges a dependence upon God. Religion, then, in its essence, is generically a practical acknowledgment of man's dependence upon a Supreme Power that is beyond control. This article will treat: first, revealed religion as it is accepted by those who believe in the supernatural revelation of God to man; second, natural religion, as it is found among those who admit not that supernatural revelation. I. Revealed Religion. They who believe in God's revelation of Himself to the human race as the basis of religion do not deny that_man's acknowledgment of dependence upon God is postulated by the very nature of the universe; to this form of natural religion they superadd the obligation of worship consequent upon revelation. "What is known of God is clear" even to the heathen. For, "ever since the creation of the world, the unseen truths about God, His everlasting power and divinity, are to be reasoned out and seen by His works" (Romans i, 19-20). And yet "God, who of old, at many times and in many places, spoke to our ancestors by the prophets, hath in these latter days spoken to us by a Son" (Hebrews i:1-2). This communication of truth by God to the human race through the prophets and the Son is the basic fact of revealed religion. 1. Possibility of Revelation.- Subjective idealists and Kantians deny the possibility of knowledge has no objective validity, and there revelation; for, in their systems of philosophy, can be no certainty that God speaks to man. The adherents to revealed religion believe in a Personal Deity, Creator of man. Since this Creator has bestowed upon man the faculty of communicating his ideas with fellow-men, He undoubtedly may in like manner communicate with us. The deist errs in assigning to God such transcendence as to preclude the possibility of revelation. For the infinity of God includes omnipresence; and His omnipotence demands that He may communicate with His creature wherever He is. Such communication is not opposed to the divine wisdom. For the authority of God revealing gives to man greater certainty of religious and moral truth than does the authority of reason unaided by revelation. Moreover, fallen human nature, tainted by original sin, has tendencies to evil |
