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 United States, 1740 churches and 292,654 communicants, of whom 177,270 were in Pennsylvania, and about one-sixth (50,732) were in Ohio. Other states in which the Church had communicants were: Maryland (13,442), Wisconsin (8386), Indiana (8289), New York (5700), North Carolina (4718), Iowa (3692), Illinois (2652), Virginia (2288), Kentucky (2101), Michigan (1666), Nebraska (1616), and (less than 1500 in each of the following arranged in rank) S. Dakota, Missouri, New Jersey, Connecticut, Kansas, W. Virginia, N. Dakota, Minnesota, District of Columbia, Oregon, Massachusetts, Tennessee, California, Colorado, Arkansas and Oklahoma.

See James I. Good, History of the Reformed Church in the United States, 1725–1792 (Reading, Pa., 1899), and Historical Handbook (Philadelphia, 1902); and the sketch by Joseph Henry Dubbs in vol. viii. (New York, 1895) of the American Church History Series.

REFORMED EPISCOPAL CHURCH, a Protestant community in the United States of America, dating from December 1873. The influence of the Tractarian movement began to be felt at an early date in the Episcopal Church of the United States, and the ordination of Arthur Carey in New York, July 1843, a clergyman who denied that there was any difference in points of faith between the Anglican and the Roman Churches and considered the Reformation an unjustifiable act, brought into relief the antagonism between Low Church and High Church, a struggle which went on for a generation with increasing bitterness. The High Church party lost no opportunity of arraigning any Low Churchman who conducted services in non-episcopal churches, and as the Triennial Conference gave no heed to remonstrances on the part of these ecclesiastical offenders they came to the conclusion that they must either crush their consciences or seek relief in separation. The climax was reached when George D. Cummins (1822–1876), assistant bishop of Kentucky, was angrily attacked for officiating at the united communion service held at the meeting of the Sixth General Conference of the Evangelical Alliance in New York, October 1873. This prelate resigned his charge in the Episcopal Church on November 11th, and a month later, with seven other clergymen and a score of laymen, constituted the Reformed Episcopal Church. Cummins was chosen as presiding officer of the new body, and consecrated Charles E. Cheney (b. 1836), rector of Christ Church, Chicago, to be bishop. The following Declaration of Principles (here abridged) was promulgated:—

I. An expression of belief in the Bible as the Word of God, and the sole rule of faith and practice, in the Apostles' Creed, in the divine institution of the two sacraments and in the doctrines of grace substantially as set out in the 39 Articles.

II. The recognition of Episcopacy not as of divine right but as a very ancient and desirable form of church polity.

III. An acceptance of the Prayer Book as revised by the General Convention of the Protestant Episcopal Church in 1785, with liberty to revise it as may seem most conducive to the edification of the people.

IV. A condemnation of certain positions, viz.:—


 * (a) That the Church of God exists only in one form of ecclesiastical polity.


 * (b) That Christian ministers as distinct from all believers have any special priesthood.


 * (c) That the Lord’s Table is an altar on which the body and blood of Christ are offered anew to the Father.


 * (d) That the presence of Christ is a material one.


 * (e) That Regeneration is inseparably connected with Baptism.

The Church recognizes no orders of ministry, presbyters and deacons; the Episcopate is an office, not an order, the bishop being the chief presbyter, primus inter pares. There are some 7 bishops, 85 clergy and about 9500 communicants. £1600 annually is raised for foreign missionary work in India. The Church was introduced into England in 1877, and has in that country presiding bishop and about 20 organized congregations. The Church has a theological seminary in Philadelphia.

REFRACTION (Lat. refringere, to break open or apart), in physics, the change in the direction of a wave of light, heat or sound which occurs when such a wave passes from one medium into another of different density.

When a ray of light traversing a homogeneous medium falls on the bounding surface of another transparent homogeneous medium, it is found that the direction of the transmitted ray in the second medium is different from that of the incident ray; in other words, the ray is refracted or bent at the point of incidence. The laws governing refraction are: (1) the refracted and incident rays are coplanar with the normal to the refracting surface at the point of incidence, and (2) the ratio of the sines of the angles between the normal and the incident and refracted rays is constant for the two media, but depends on the nature of the light employed, i.e. on its wave length. This constant is called the relative refractive index of the second medium, and may be denoted by ab the suffix ab signifying that the light passes from medium a to medium b; similarly ba denotes the relative refractive index of a with regard to b. The absolute refractive index is the index when the first medium is a vacuum. Elementary phenomena in refraction, such as the apparent bending of a stick when partially immersed in water, were observed in very remote times, but the laws, as stated above, were first grasped in the 17th century by W. Snell and published by Descartes, the full importance of the dependence of the refractive index on the nature of the light employed being first thoroughly realized by Newton in his famous prismatic decomposition of white light into coloured spectrum. Newton gave a theoretical interpretation of these laws on the basis of his corpuscular theory, as did also Huygens on the wave theory (see, II. Theory of). In this article we only consider refractions at plane surfaces, refraction at spherical surfaces being treated under. The geometrical theory will be followed, the wave theory being treated in and.

EB1911 Refraction Fig. 1.png . 1.

Refraction at a Plane Surface.—Let LM (fig. 1) be the surface dividing two homogeneous media A and B; let IO be a ray in the first medium incident on LM at O, and let OR be the refracted ray. Draw the normal POQ. Then by Snell’s law we have invariably sin IOP/sin QOR＝ab. Hence if two of these quantities be given the third can be calculated. The commonest question is: Given the incident ray and the refractive index to construct the refracted ray. A simple construction is to take along the incident ray OI, unit distance OC, and a distance OD equal to the refractive index in the same units. Draw CE perpendicular to LM, and draw an arc with centre O and radius OD, cutting CE in E. Then EO produced downwards is the refracted ray. The proof is left to the reader.

In the figure the given incident ray is assumed to be passing from a less dense to a denser medium, and it is seen by the construction or by examining the formula sin ＝sin / that for all values of there is a corresponding value of. Consider the case when the light passes from a denser to a less dense medium. In the equation sin ＝sin /. We have in this case <1. Now if sin <, we have sin /<1, and hence is real. If sin ＝, then sin ＝1, i.e. ＝90°; in other words, the refracted ray in the second medium passes parallel to and grazes the bounding surface. The angle of incidence, which is given by sin ＝1/, is termed the critical angle. For greater values it is obvious that sin />1 and there is no refraction into the second medium, the rays being totally reflected back into the first medium; this is called total internal reflection.

Images produced by Refraction at Plane Surfaces.—If a luminous point be situated in a medium separated from one of less density by a plane surface, the ray normal to this surface will be unrefracted, whilst the others will undergo refraction according to their angles of emergence. If the rays in the less dense medium be produced into the denser medium, they envelop a caustic, but by restricting ourselves to a small area about the normal ray it is seen that they intersect this ray in a point which is the geometrical