BECIDIVISTS. 748 RECIPROCITY. countries are unsatisfactory because of varying laws and differing degr^s of success in enforcing them. The statistics serve roughly to show that recidivism is a serious aspect of crime and to throw light on the practical question of crime pre- vention. Driihms has figured from various sources the percentage of recidivists in the different countries as follows: Percentage England. Germany Holland. France .. Belgium. Norway.. Pruasia . It is clear that short sentences and fines do not protect society against instinctive and profes- sional criminals. Nothing short of jiermanent incarceration should be thought of in many in- stances. In others where the possibility of re- form may still be admitted the indeterminate sen- tence may wisely l)e employed. In England the Habitual" Offenders Act deprives the recidivist of the presumption of innocence until guilt is proved and keeps him under surveillance when not in jirison. A few timid experiments have been made here and there by American commonwealths in the direction of greater severity toward 'sec- ond offenders,' but in general American law on this subject is lax and unscientific. Sen- timentalism, indifference, and a prevailing belief (which has no basis in fact) that criminals in general are victims of circumstances and may usually be 'reformed' by humane treatment, have made the United States a veritable paradise of professional offenders. Consult: Yvernes, La recidive en Europe (Paris. 1874) ; Yines, Punish- ment and Reformation (Boston. 1895) : Driihms, The Criminal (Xew York, 1900). See Cbimixol- OGY; Penology. RECIFE, ra-se'fa. The capital of the State of Pernambuco, Brazil. See Pebxaiibuco. RECIPROCAL (from Lat. reciprocus, alter- nating. rcci|>rocal, probably from *recus, back- ward, from re-, back again, anew + procus. for- ward, from pro. liefore). One number is said to be the reciprocal of another if their product is unitv. E.g. a. - = 1, hence a and - are recipro- a a b cals. Also r • - =1, hence r and a ' are recip- rocals. The term is variously used in geome- try. See Pole and Polar; Duality. Reciprocal Equ.tioxs. An equation is said to be reciprocal when its roots admit of being arranged in pairs of the form r, . In the case of a reciprocal equation of even degree the co- efficients of the terms equidistant from the ex- tremes are equal and have the same sign. In the case of those of odd degree, the coefficients of the terms equidistant from the extremes have the same absolute value and have either the same or opposite signs. One root of a reciprocal equation of odd degree must therefore be + 1 or — 1. Di- viding by sc±l, such an equation reduces to one of even degree. RECIPROCITY ( from Lat. reciprocus, alter- nating, reciprocal). A tariff policy under which two or more sets of tariff's contemporaneously ex- ist ; a high schedule of duties for countries which have entered into no special agreement with the enacting country, and one or more lower schedules for such others as may be willing to offer corre- s[)ondingly reduced schedules in return. The reci- procity system sprang up as a means of relief from the old navigation laws, and was then grad- ually extended, not only to tariff duties, but to general matters of commercial privilege as well. The organization of the German Zollverein (q.v. ) gave a strong stimulus to the idea of mutual free- dom of exchange: and the movement thus begun gradually developed into a semi-free-trade era, which lasted until about 1870. Great Britain re- pealed the corn laws during the years succeeding 1840, and in 18G0 negotiated a treaty with Fiance containing liberal commercial concessions. Tliis was followed by some twenty-seven other re- ciprocal arrangements between the leading Euro- pean States, which resulted in gi-eat freedom of exchange, and largely stimulated trade. A simi- lar movement in the United States culminated in the liberal tariffs of 184G and 1857. Yery generous treaties of reciprocity were negotiated by the United States with the German Zollverein ami Mexico, respectively (1844 and 1859), but both failed of ratification. The first real experiment in reciprocity made by the United States is found in the Canadian treaty of 1854. Between the years 1846 and 1855, it was several times sought to secure the passage of 'concurrent legislation' by the two countries, making mutual tariff concessions. These efforts failed — partly for political reasons, but largely because of difficulties connected with the allied questions of fisheries and the navigation of the Saint Lawrence. Finally, the reciprocity treaty was negotiated, and passed by the Senate (receiving the President's signature August 5, 1854), owing largely to personal work in Wash- ington by Lord Elgin, then Governor-General of Canada. As ultimately adopted, the Canadian treaty covered the navigation of the Saint Law- rence, the fisherv question, and provided for mu- tual free trade between Canada and the United States in the products of the two countries. The immediate effect of the treaty was apparently to stimulate trade. Its popularit.v, however, received a severe blow In the crisis of 1857, which reduced both the imports and exports of the United States in the Canadian trade, but the volume of business almost immediatel.v revived. Yarious complaints, however, arose against continuing under the treat.v. a principal objection being that the Cana- dian.-: were not keeping good faith. Commission- ers of the United States examining into the advis- abilitv of the reciprocitv relations made diamet- rically opposite reports. Between 1800 and 1865, the question of abrogating the treaty was much discussed in Congress. The strained relations with England on account of the Alabama claims brought the question to the front and finally, in 1865. a Senate resolution terminating the agree- ment was concurred in by the House, being signed by the President .January 18. 1865. The relations of the United States with Canada under the treaty closed ilarch 17 of the same .vear. Since that time numerous efforts have been made to renew the reciprocity trade relations between the two
