Two forms of the Referendum should be carefully distinguished: the facultative or optional (brought into play only on the demand of a fixed number of citizens), and the obligatory or compulsory (which obtains in all cases that lie within its sphere as defined in the constitution). The Initiative exists only in the facultative form, being exercised when a certain number of citizens demand it. Both came into common use during the Liberal reaction in Switzerland after the Paris revolution of July 1830. In 1831 St Gall first adopted the “facultative referendum” (then and for some time after called the “Veto”), and its example was followed by several cantons before 1848. The “obligatory referendum” appears first in 1852 and 1854 respectively in the Valais and the Grisons, when the older system was reformed, but in its modern form it was first adopted in 1863 by the canton of rural Basel. The Initiative was first adopted in 1845 by Vaud. Of course the cantons with Landsgemeinden, Uri, Unterwalden, Appenzell and Glarus (where the-citizens appear in person) possessed both from time immemorial. Excluding these there were at the end of 1907 912 cantons, which had the “obligatory referendum” (Aargau, rural Basel, Bern, the Grisons, Schafihausen, Schwyz, Soleure, Thurgau, the Valais and Zürich), while 712 cantons possess only the “facultative referendum” (Basel town, Geneva, Lucerne, Neuchâtel, St Gall, Ticino, Vaud and Zug). Fribourg alone had neither, save an obligatory referendum (like all the rest) as to the revision of the cantonal constitution. As regards the Initiative, all the cantons have it as to the revision of the cantonal constitution; while all but Fribourg have it also as to bills or legislative projects. In the case both of the facultative referendum and of the Initiative each canton fixes the number of citizens who have a right to exercise this power. The constitution of the Swiss confederation lags behind those of the cantons. It is true that both in 1848 (art. 113) and in 1874 (art. 120) it is provided that a vote on the question whether the constitution shall be revised must take place if either house of the federal legislature or 50,000 qualified voters demand it—of course a popular vote (obligatory referendum) must take place on the finally elaborated project of revision. But as regards bills the case is quite different. The “facultative referendum” was not introduced till 1874 (art. 89) and then only as regards all bills and resolutions not being of a pressing nature, 8 cantons or 30,000 qualified voters being entitled to ask for such a popular vote. But the Initiative did not appear in the federal constitution till it was inserted in 1891 (art. 121), and then merely in the case of a partial (not a total) revision of the constitution, if 50,000 qualified voters require it, whether as regards a subject in general or a draft bill,—of course the federal legislature had an Initiative in this matter in 1848 already. The results of the working of these two institutions in federal matters up to the end of 1908 are as follows. Excluding the votes by which the two federal constitutions of 1848 and 1874 were adopted, there have been 30 (10 of them between 1848 and 1874) votes (obligatory referendum) as to amendments of the federal constitution; in 15 cases only (of which only one was before 1874) did the people accept the amendment proposed. In the case of bills there have been 30 votes (very many bills have not been attacked at all), all of course since the facultative referendum was introduced in 1874; in 11 cases only have the people voted in the affirmative. Finally, with regard to the Initiative, there have been 7 votes, of which two only were in the affirmative. Thus, between 1874 and 1907, of 57 votes 27 only were in the affirmative, while if we include the 10 votes between 1848 and 1874 the figures are respectively 67 and 28, one only having been favourable during that period. The result is to show that the people, voting after mature reflection, are far less radically disposed than has sometimes been imagined.
The method of referendum by itself is also in use in some of the states of the American Union (see United States) and in Australia, and under the name of plebiscite has been employed in France; but it is best studied in the Swiss constitution.
Authorities. W. A. B. Coolidge, “The Early History of the Referendum" (article in the English Historical Review for October 1891); T. Curti, Die schweizerischen Volksrechte, 1848 bis 1900 (Bern, 1900) (Fr. trans. by J. Ronjat with additions by the author, Paris, 1905)—Curti's earlier work, Gesohichte d. Schweiz. Volksgesetzgebung (Bern, 1882), is not entirely superseded by his later one; S. Deploige, The Referendum in Switzerland, Engl. trans. with additional notes (London, 1898); N. Droz, “The Referendum in Switzerland” (article in the Contemporary Review, March 1895); J. M. Vincent, Government in Switzerland, chaps. v. and xiv. (New York and London, 1900). See also, for the United States and generally, the American works on the Referendum by E. P. Oberholtzer (1893 and 1900).
REFLECTION OF LIGHT. When a ray of light in a homogeneous medium falls upon the bounding surface of another medium, part of it is usually turned back or reflected and part is scattered, the remainder traversing or being absorbed by the second medium. The scattered rays (also termed the irregularly or diffusely reflected rays) play an important part in rendering objects visible—in fact, without diffuse reflection non-luminous objects would be invisible; they are occasioned by irregularities in the surface, but are governed by the same law as holds for regular reflection. This law is: the incident and reflected rays make equal angles with the normal to the reflecting surface at the point of incidence, and are coplanar with the normal. This is equivalent to saying that the path of the ray is a minimum.[1] In fig. 1, represents the section 
Fig. 1. of a plane mirror; is the incident ray, the reflected ray, and the normal at . Then the law states that the angle of incidence equals the angle of reflection , and that , and are in the same plane.
This natural law is capable of ready experimental proof (a simple one is to take the altitude of a star with a meridian circle, its depression in a horizontal reflecting surface of mercury and the direction of the nadir), and the most delicate instruments have failed to detect any divergence from it. Its explanation by the Newtonian corpuscular theory is very simple, for we have only to assume that at the point of impact the perpendicular velocity of a corpuscle is reversed, whilst the horizontal velocity is unchanged (the mirror being assumed horizontal). The wave-theory explanation is more complicated, and in the simple form given by Huygens incomplete. The theory as developed by Fresnel shows that regular reflection is due to a small zone in the neighbourhood of the point (above), there being destructive interference at all other points on the mirror; this theory also accounts for the polarization of the reflected light when incident at a certain angle (see Polarization of Light). The smoothness or polish of the surface largely controls the reflecting power, for, obviously, crests and furrows, if of sufficient magnitude, disturb the phase relations. The permissible deviation from smoothness depends on the wave-length of the light employed: it appears that surfaces smooth to within 18th of a wave-length reflect regularly; hence long waves may be regularly reflected by a surface which diffuses short waves. Also the obliquity of the incidence would diminish the effect of any irregularities; this is experimentally confirmed by observing the images produced by matt surfaces or by smoked glass at grazing incidence.
We now give some elementary constructions of reflected rays, or, what comes to the same thing, of images formed by mirrors.
1. If be a luminous point and a ray incident at R on the plane mirror (fig. 1) to determine the reflected ray and the image of . If be the reflected ray and perpendicular
- ↑ This principle of the minimum path, however, only holds for plane and convex surfaces; with concave surfaces it may be a maximum in certain cases.
