PRACTICE, a rule of arithmetic, appropriately so termed because it hardly contains any new principle, but depends for its application upon the memory and dexterity which the operator acquires from practice. Thus, in the following simple question, "How much do 40 yards cost at 18d. a yard," some arithmeticians (unpractised) might find it neces sary to multiply 40 by ]8 and divide the result by 12, for the number of shillings in the answer; but a practised arithmetician would imme diately see that 18d. is a shilling and a half, so that 40s. must be allowed for the shilling, and 20s. for the half shilling, making altogether 60s. More complicated examples may require greater subdivision, but the method of proceeding has been completely described in the pre ceding. Suppose, for instance, it is required to find the price of 2531 yards at 2/. 13s. 7fd. a yard. The application of the rule of practice is as follows :— The process hardly needs more description than is given on the left; the only difficulty is the division of the price into portions each of which is a simple aliquot part of one of the preceding, and this diffi culty is to be overcome by practice. It is also to be noticed that easy verification's often occur : thus, iu the last process but one, it can easily be verified that 253/ farthings is 5s. 31d. 1.
When both the factors which are to be multiplied contain complicated fractions, this rule can be easily applied by turning the money factor into pounds and decimals of a pound, as in lemma. Thus, suppose it is required to find the price of 22 tons 17 cwt. 1 qr. 10 lbs., at 13/. 16s. 4d. a ton, or Wo have then So that the proper answer is less than a farthing above 316/. The preceding process is much shorter than the application of the rule of three, and also than a kind of double rule of practice once in use,whieh is not given in modern works, and is not worth revival.
This method of practice is also a convenient way of reducing fractions of weights or measures to decimals. Thus, if 17 cwt. 1 qr. 191b. is to be reduced to a decimal fraction of a ton, we have PRzEFECTUS URBI (prefect or warden of the city), the title of a Roman magistrate, said to have been instituted by Romulus (Tacit., Annal.; vi. 11) to supply the place of the kings in their absence from the city, within the walls of which he was for a time invested with kingly power, where he had the imperium in urbe. (Livy, i. 59.) He was appointed from among the senators. (Dionys., ii. 12.) During the time of the republic the prwfectus urbi was appointed by the consuls, or by the senate (Dionys., viii. G4) when the consuls were obliged to be absent from the city. During the time of his office he
exercised in the city the power of the consuls : he had the right to convoke the senate (Varro., 'Ap. Gall.,' xiv. 7, comp. with xv. 8) and to hold the comitia (Liv., i. 60). But in the course of time the prefect of the city was superseded by the praetor urbanus, on which the former magistrate became merely a shadow of what he had been, and was appointed while the consuls were absent from Rome for the purpose of celebrating the Feria' Latina". This office, being of no importance, was often filled by young men, and Julius Caesar even appointed several youths under age as prefects of the city. (Tacit, I. c., iv. 36 ; Dion Cass., xlix., p. 476.) This shadow of a magistrate seems to have con tinued to be appointed during the Ferim Latium, even after Augustus had made a permanent priefeetus urbi. (Suet., ' Nero,' 7.) Augustus invested this new prefect with considerable power, gave him the super intendence of public works, roads, aqueducts, the navigation of the river, and the corn to be distributed among the people. (Suct.,' Octay.; 37 ; Tacit., 1 c. ; Dion Caas., p. 547.) He was also invested with jurisdiction over slaves and turbulent citizens. lie was thus some thing like a chief officer of the police; but his powers became gradually more and more extensive, so that almost all the powers formerly belonging to the office of proctor urbanus in the end were transferred to the prcfectus urbi (` Dig.; L, t. 12 ; De Off. Prof. Urbi; comp. with Tacit., Annal.; xiv. 41) ; and from the beginning of the 3rd century he not only exercised the inferior but also the criminal juris diction, and that not only in the city, but at the distance of one hundred miles from it. During the early period of the empire the prefect of the city seems always to have held his office for a number of years ; but from the time of Valerian we find a new prefect almost every year. Respecting the titles by which he was addressed, see Brinson, De Form.; p. 296. At the time when Constantinople was raised to the rank of second capital, it received a prefect of the city, who, like the prefect in the west, was the direct representative of the emperor, and next to him the first person in the city. The whole administration of the city, all its corporations and institutions, were under his superintendence ; every month he made a report to the emperor of the transactions of the senate and people (Symmach., Epist.; x. 44); in the assemblies of the senate he gave his vote before the consubus Varian,' vi. 4), and was the medium through which the emperors communicated with the city.