distances are shown in the table (F is the principal focus and C the centre of curvature of the mirror MA).
| Position of Object. | Position of Image. | Character of Image. |
| ∞ Between ∞ and C C Between C and F Between F and A A |
F Between F and C C Between C and ∞ Between A and −∞ A |
Real. Real, inverted, diminished Real, inverted, same size Real, inverted, magnified Virtual, erect, magnified Erect, same size |
| Convex Mirror | ||
| Position of Object. | Position of Image. | Character of Image. |
| ∞ Between ∞ and A A |
F Between F and A A |
Virtual. Virtual, erect, diminished Erect, same size |
The above discussion of spherical mirrors assumes that the mirror has such a small aperture that the reflected rays from any point unite in a point. This, however, no longer holds when the mirror has a wide aperture, and in general the reflected rays envelop a caustic (q.v., see also Aberration). The only mirror which can sharply reproduce an object-point as an image-point has for its section an ellipse, which is so placed that the object and image are at its foci. This follows from a property of the curve, viz. the sum of the focal distances is constant, and that the focal vectores are equally inclined to the normal at the point. More important than the elliptical mirror, however, is the parabolic, which has the property of converting rays parallel to the axis into a pencil through its focus; or, inversely, rays from a source placed at the focus are converted into a parallel beam; hence the use of this mirror in searchlights and similar devices.
REFORMATION, THE. The Reformation, as commonly understood, means the religious and political revolution of the 16th century, of which the immediate result was the partial disruption of the Western Catholic Church and the establishment of various national and territorial churches. These agreed in repudiating certain of the doctrines, rites and practices of the medieval Church, especially the sacrifice of the Mass and the headship of the bishop of Rome, and, whatever their official designations, came generally to be known as “Protestant.” In some cases they introduced new systems of ecclesiastical organization, and in all they sought to justify their innovations by an appeal from the Church’s tradition to the Scriptures. The conflicts between Catholics and Protestants speedily merged into the chronic political rivalries, domestic and foreign, which distracted the European states; and religious considerations played a Very important part in diplomacy and war for at least a century and a half, from the, diet of Augsburg in 1530 to the English revolution and the league of Augsburg, 1688–89. The terms “Reformation” and “Protestantism” are inherited by the modern historian; they are not of his devising, and come to him laden with reminiscences of all the exalted enthusiasms and bitter antipathies engendered by a period of fervid religious dissension. The unmeasured invective of Luther and Aleander has not ceased to re-echo, and the old issues are by no means dead.
The heat of controversy is, however, abating, and during the past thirty or forty years both Catholic and Protestant investigators have been vying with one another in adding to our knowledge and in rectifying old mistakes; while an ever-increasing number of writersThe Reformation not exclusively
a Religious Revolution. pledged to neither party are aiding in developing an idea of the scope and nature of the Reformation which differs radically from the traditional one.
We now appreciate too thoroughly the intricacy of the medieval Church;
its vast range of activity, secular as well as religious; the
inextricable interweaving of the civil and ecclesiastical governments;
the slow and painful process of their divorce as the old
ideas of the proper functions of the two institutions have changed
in both Protestant and Catholic lands: we perceive all too
clearly the limitations of the reformers, their distrust of reason
and criticism—in short, we know too much about medieval
institutions and the process of their disintegration longer to
see in the Reformation an abrupt break in the general history
of Europe. No one Will, of course, question the importance
of the schism which created the distinction between Protestants
and Catholics, but it must always be remembered that the
religious questions at issue comprised a relatively small part
of the whole compass of human aspirations and conduct, even
to those to whom religion was especially vital, while a large
majority of the leaders in literature, art, science and public
affairs went their way seemingly almost wholly unaffected by
theological problems.
That the religious elements in the Reformation have been greatly overestimated from a modern point of view can hardly be questioned, and one of the most distinguished students of Church history has ventured the assertion that “The motives, both remote and proximate, which led to the Lutheran revolt were largely secular rather than spiritual.” “We may,” continues Mr H. C. Lea, “dismiss the religious changes incident to the Reformation with the remark that they were not the object sought, but the means for attaining the object. The existing ecclesiastical system was the practical evolution of dogma, and the overthrow of dogma was the only way to obtain permanent relief from the intolerable abuses of that system” (Cambridge Modern History, i. 653). It would perhaps be nearer the truth to say that the secular and spiritual interests intermingled and so permeated one another that it is almost impossible to distinguish them clearly even in thought, while in practice they were so bewilderingly confused that they were never separated, and were constantly mistaken for one another.
The first step in clarifying the situation is to come to a full realization that the medieval Church was essentially an international state, and that the character of the Protestant secession from it was largely determined by this fact. As Maitland suggests: “We could frame noResemblance of the medieval Church to
the State. acceptable definition of a State which would not comprehend the Church. What has it not that a State should have? It has laws, law givers, law courts, lawyers. It uses physical force to compel men to obey the laws. It keeps prisons. In the 13th century, though with squeamish phrases, it pronounced sentence of death. It is no voluntary society; if people are not born into it they are baptized into it when they cannot help themselves. If they attempt to leave they are guilty of crimen laesae majestatis, and are likely to be burned. It is supported by involuntary contributions, by tithe and tax” (Canon Law in the Church of England, p. 100). The Church was not only organized like a modern bureaucracy, but performed many of the functions of a modern State. It dominated the intellectual and profoundly affected the social interests of western Europe.
Its economic influence was multiform and incalculable, owing
to its vast property, its system of taxation and its encouragement
of monasticism. When Luther made his first great
appeal to the German people in his Address to the German Nobility,
he scarcely adverts to religious matters at all. He
deals, on the contrary, almost exclusively with the social,
financial, educational, industrial and general moral problems
of the day. If Luther, who above all others had the religious
issue ever before him, attacks the Church as a source of worldly
disorder, it is not surprising that his contemporary Ulrich von
Hutten should take a purely secular view of the issues involved.
Moreover, in the fascinating collection of popular satires and
ephemeral pamphlets made by Schade, one is constantly impressed
with the absence of religious fervour, and the highly
secular nature of the matters discussed. The same may be said
of the various Gravamina, or lists of grievances against the
papacy drafted from time to time by German diets.
But not only is the character of the Reformation differently conceived from what it once was; our notions of the process of change are being greatly altered. Formerly, writers accounted for the Lutheran movement by so magnifying the horrors of the pre-existing regime Historic continuity
of the Reformation.that it appeared intolerable, and its abolition consequently inevitable. Protestant Writers once contented themselves with a brief caricature of the Church,
