INCLINED PLANE, THE, is reckoned one of the mechanical powers (q.v.), becanse. by rolling it up a plane, a man may raise a weight which rigy.cbitid not lift.
principle is extensively made use of, chiefly in the raising of weights and in road making. It is here unnecessary to go into a mathematical investigation of the theory of the inclined plane, as it may be seen in the common books on mechanics, but the result is as follows: '[he force required to lift a body (viz., its weight) hears to the force required to keep it from rolling down an inclined plane; the same proportion that the length of the inclined plane hears to its height; • also the weight of the body bears to the weight which tends to bend or break the inclined plane, the same proportion that the length of the plane bears to its base. Let us suppose a plane, whose length is 18 ft.; base, 12 ft. ; and height, 5 ft.; and let the weight be 780 lbs. Then the force which can sustain 780 lbs. on the inclined plane is Ave-thirteenths of 780, or 300 lbs. (i.e., a force which could just lift 300 lbs.); also the force which presses perpendicularly on the plane is twelve-thirteenths of 780, or 720 lbs. When the weight has not only to be sustained on the plane but drawn up it, the resistance of friction (q.v.) has to be added to the power necessary to sustain the weight. In common roads, engineers are agreed that the height of an incline should not exceed one-twentieth of the length, or, as they phrase it,the gradient should not be greater than one in twenty. It may here be mentioned that knives, chisels, axes, wedges, and screws are merely modifications of the inclined plane, but the last two being generally classed as distinct mechanical powers, will be treated each under its own head.
IN CtENA DOMINI, a celebrated papal bull, so called from the ancient day of its annual publication, Holy Thursday. It is not, as other bulls, the work of a single pope, but with additions and modifications at various times, dates back from the middle ages; some writers tracing it to Martin V., others to Clement V., and some to Boniface VIII. Its present form, however, it received from the popes Julius II., Paul III., and finally Urban VIII., in 1627, from which year it continued for a century and a half to be pub lished annually on Holy Thursday. The contents of this bull have been a fertile subject of controversy. It may be briefly described as a summary of ecclesiastical censures, especially of those with which grievous violation of the faith of the church, or of the. rights of the church or of the Roman see, are visited; excommunication being denounced against heresy, schism, sacrilege, usurpation of the rights of the church or of the pope, forcible and unlawful seizure of church property, personal violence against ecclesiastics, unlawful interruption of the free intercourse of the faithful with Rome, etc. The bull, however, although mainly dealing with offenses against the church, also denounces under similar censures other crimes, as piracy, plunder of shipwrecked goods, forgery, etc. This bull, being regarded by most of the crowned heads of Europe as an infringement of their rights, encountered in the 17th c. the determined oppOsition of nearly all the courts, even the most Catholic; and at length, in 1770, Clement XIV. discontinued its publica tion, which has never since been renewed.