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PROUDHON 37 veying as the three-arm protractor. The three- arm circular protractor is a modification of the station-pointer, differing from it in having its verniers movable and its arcs fixed, instead of the opposite. It consists of a graduated circular arc fixed to the middle one of three long flat arms which turn about its centre, from which diverge their straight fiducial edges. Fixed to each of the side arms is an index and vernier, by means of which those arms can be set so as to make any required angles with the middle arm. This instrument furnishes the readiest and most accurate graphic solution of the three-point problem on which hydrogra- phers so universally depend for determining positions of the sounding boat. The reflect- ing protractor, invented in January, 1874, by T. J. Lowry of the United States coast survey, enables one observer to measure at the same instant two adjacent angles, and plot them with the same instrument. It is obtained by placing between the fixed and each of the movable arms of the three-arm protractor an index arm ; and each of these is so connected with those by means of jointed parallelograms that it always bisects the angle contained by the fixed arm and its corresponding movable pro- tractor arm. Each of these index arms carries a mirror mounted perpendicular to its plane (and over its centre) of motion ; these mirrors may be mounted to move either in the same or in parallel planes. (See SEXTANT.) Slightly forward of these mirrors on the line of sight is fixed a horizon glass, half silvered to admit of direct and reflected vision. As the angular distance moved over by a mirror while mea- suring an angle is only half of the actual angle measured, and as each of these movable pro- tractor arms is driven along its arc simulta- neously with and twice as fast as its corre- sponding index arm, the angles contained by the fixed and movable protractor arms are the actual angles measured. When using the re- flecting protractor the observer brings its face into the plane passing through his eye and three objects, and then sets his index arm so that the reflected and direct images of the objects (say left-hand and middle) of one of the desired angles are not coincident, yet ap- proaching on account of the progress of the boat, and with the second index glass he makes the images of the right-hand and middle ob- jects coincident, and keeps them so with the tangent screw till the first two objects become coincident, then clamps, and the angles are measured and also ready set off on the instru- ment. He now places the instrument on the map and shifts it until the fiducial edges of its protractor arms traverse the three points ob- served on, and dots the centre of the position. PROIDHON, Jean Baptiste Victor, a French jurist, born at Chanans, Franche-Comt6, Feb. 1, 1758, died in Dijon, Nov. 20, 1838. During the revolution he was judge at Pontarlier and as- sistant deputy to the legislative assembly, and afterward a member of the civil tribunal at Besan?on. In 1802 he delivered free lectures on law ; in 1806 he was appointed professor of civil law in the school of Dijon, and in 1809 became dean of the faculty. His principal works are : Traite sur Vetat des personnel et sur le titre preliminaire du Code civil (1810) ; Traite des droits d'usufruit, &c. (9 vols., 1823-'6) ; and Traite du domaine public (5 vols., 1834-'5). PROtDHON, Pierre Joseph, a French political writer, born in Besancon, July 15, 1809, died at Passy, Paris, Jan. 19, 1865. He was edu- cated at the college of his native city, became apprentice to a printer, and in 1837 was taken into partnership by a printing firm at Besancon. He published an edition of the Bible with an- notations upon the principles of the Hebrew language, and reprinted Bergier's Elements primitifs des langues (1837), with an anony- mous Essai de grammaire generate, by himself, as an appendix. This essay received from the academy of Besancon a prize consisting of a triennial pension of 1,500 francs, which en- abled him to visit Paris. Here he became a contributor to Parent Desbarres's Encyclopedic catholique, and wrote for the Besangon acad- emy a prize essay, De la celebration du di- manche (1840), and a paper entitled Qtfest-ce que la propriete ? This pamphlet, which opened with the afterward celebrated dictum, La pro- priete c j est le vol, was censured by the academy, who at once cut short Proudhon's allowance ; but the economist Blanqui, who had been ap- pointed to examine it, declared that he found nothing objectionable in it. It was followed in 1841 by another pamphlet on the same question, and in 1842 by an Avertissement aux proprietaires, for which he was arraigned be- fore a jury at Besanc.on, but was acquitted. In the same year he went to Lyons, and from 1843 to 1847 was director of a company run- ning freight boats on the Sa6ne and Rh&ne. In the mean time he continued to propagate his opinions in De la creation de Vordre dans Vhumanite (1843), presenting the theory of a new political organization, and Systeme des contradictions economiques (2 vols. 8vo, 1846). On the breaking out of the revolution of Feb- ruary, 1848, he was in Paris engaged in the publication of his Solution du probleme social, a plan of social reform by means of a new organization of credit and monetary circula- tion. On April 1 he became the editor of Le representant du peuple, a daily journal of radi- cal opinions, suspended in August. On June 4 he was elected deputy to the constituent assembly, and on July 31 he came forward to urge a proposition which he had previously made for the establishment of a progressive income tax, the design of which was the abolition of interest on capital, and eventual- ly the consolidation of the republican govern- ment. This was almost unanimously voted down " as an odious attack upon the principles of public morality and an appeal to the worst passions." He closed his parliamentary career