Page:Collier's New Encyclopedia v. 07.djvu/522

HATHENOW 436 BATIO built, legs short and strong, with long curved fossorial claws, tail short, ear- conches rudimentary. General colora- tion iron-gray on the upper, and black on the lower surface, reversing the gen- eral plan of coloration, which is gener- ally lighter on the under surface. A marked white stripe divides the gray of the upper parts from the black in the Cape ratel, which is «aid to live princi- pally on honey. Jerdon says that M. mdica, which he calls the Indian badger, is found throughout India, living usually in pairs and eating rats, birds, frogs, white ants, and various insects; and in the N. of India, where it is accused of digging out dead bodies, it is popularly known as the grave-digger. It doubt- less also, like its Cape congener, occa- sionally partakes of honey and is often very destructive to poultry. In confine- ment it is quiet, and will eat fruits, rice, etc. RATHENOW, a town of Prussia, on the right bank of the Havel (here crossed by a stone bridge), 43 miles W. by N. of Berlin. Optical instruments, ^ wooden wares, machinery, bricks and tiles, are made. Pop. about 25,000. RATHLIN, a crescent-shaped island off the coast of Antrim, 6% miles N. of Ballycastle. ' Area, 3,398 acres. St. Colomba established a church here in the 6th century; and Bruce in 1306 took refuge in a castle, now a ruin. EATIBOR, a town of Prussian Silesia ; on the left bank of the Oder, 44 miles S. S. E. of Oppeln It is the chief town of the principality of Ratibor, which, a sovereign duchy from 1288 to 1532, has since 1742 been subject to Prussia. The town manufactures tobacco, shoes, paper, glass, sugar, furniture, etc., and has large ironworks. Pop. about 40,000. RATIFICATION, in law, the con- firmation, sanction or approval given by a person who has arrived at his majority to acts done by him during his minority. It has the effect of giving validity to such acts as would be otherwise voidable. Ratification by a wife, in Scotch law, a declaration on oath made by a wife be- fore a justice of the peace (her husband being absent) that the deed she has exe- cuted has been made freely. RATIO, in law, an account; a cause, or the giving judgment therein. In mathematics: (1) The measure of the relation which one quantity bears to an- other of the same kind; that is, it is the number of times that one quantity con- tains ^ another regarded as a standard. This is found by dividing the one by the other. The quotient or ratio thus ob- tained is the proper measure of the rela- tion of the two quantities. Some writers define the ratio of one quantity to an- other as the quotient of the first quantity divided by the second, while others define it as the quotient of the second divided by the first. Thus, the ratio of 2 to 4, or of a to 6, may be taken either as 2-^4 or 4-f-2, and a^h or h-r-a. In every ratio there are two quantities compared, one of which is supposed known, and is assumed as a standard; the other is to be determined in terms of this standard. These quantities are called terms of the ratio; the first one, or that which is antecedently known, is called the ante- cedent, and that whose value is to be measured by the antecedent, is called the consequent. Ratios are compared by comparing the fractions; thus, the ratio of 8:5 is compared v/ith the ratio of 9:6, by comparing the frac- tions % and %; these fractions are re- spectively equal to •^^o and 4%o aiid since ^%o is greater than 4%o, the ratio of 8:5 is greater than that of 9:6. Ratios are compounded together by multiplying their antecedents together for a new an- tecedent, and their consequents together for a new consequent; thus the ratio of a:h, compounded with that of c.d, is ac: hd. Proportion is the relation of equal- ity subsisting between two ratios. See Proportion. (2) A name sometimes given to the rule of three in arithmetic. Compound ratio: (a) The ratio of the product of the antecedents of two or more ratios to the product of the conse- quents: thus if 3 : 6 : : 4 : 12. then 12:72 is the compound ratio. (6) When one quantity is connected with two others in such a manner that if the first is in- creased or diminished, the product of the other two is increased or diminished in the same proportion, then the first quantity is said to be in the compound ratio of the other two. Direct ratio, two quantities are said to be in direct ratio when they both in- crease or decrease together, and in such a manner that their ratio is constant. Duplicate ratio, when three quantities are in continued proportion, the first is said to have to the third the duplicate ratio of that which it has to the second, or the first is to the third as the square of the first to the square of the second. Inverse ratio, two quantities or mag- nitudes are said to be in inyerse ratio, when if the one increases the other neces- sarily decreases, and, vice versa, when the one decreases the other increases. Mixed ratio or proportion: a ratio or proportion in which the sum of the ante- cedent and consequent is compared with the difference of the antecedent and con- sequent. Thus, if ah'.'.c:d, then a + ft: