RAT 



portion; but the expression 3 is to 4 in 

 the same proportion as 6 to 8, denotes 

 that the ratios of 3 to 4 and 6 to 8 are 

 equal; 3 bearing the sanae proportion 

 to 4, as 6 to 8, that is, being three-fourths. 

 Ratios, however, may be unequal. Thus 

 it is said that the ratio of 9 to 4 is greater 

 than that of 7 to 6, because ^ is greater 

 than J ; it being thus that ratios are 

 measured. 



2. Ratio, direct. When two quantities, 

 or magnitudes, have a certain ratio to 

 each other, and are, at the same time, 

 subject to increase or diminution; if, 

 while one increases, the other increases 

 in the same ratio, or if, while the one 

 diminishes, the other diminishes in the 

 same ratio, the proportions, or compari- 

 sons of ratios, remain unaltered, and 

 those quantities, or magnitudes, are said 

 to be in a direct ratio or proportion to 

 each other. Thus if a yard of cloth be 

 ■worth a pound, ten or any number of 

 yards will be worth so many pounds, and 

 the proportion of value continues un- 

 altered. 



3. Ratio, inverse. But, if the quan- 

 tities, or magnitudes, are such, that, 

 when one increases, the other necessarily 

 diminishes ; and vice versd, when the 

 one diminishes, the other increases, the 

 ratio, or proportion, is said to be inverse. 

 Thus, there is, at any moment, a certain 

 ratio of the length of the day to that of 

 the night; but this is an inverse ratio, 

 for in proportion as the length of either 

 increases, that of the other must dimi- 

 nish. 



4. Ratio, compound. A compound 

 ratio is made up of the product of two, 

 or more, simple ratios ; that is, of the 

 product of their first terms, which are 

 called antecedents, compared with the 

 product of their second terms, called 

 consequents. Thus 24 I 3 is a compound 

 ratio of 4 : 1 and 6:3; this, being 

 made up of two simple ratios, is called a 

 duplicate ratio. When three simple 

 ratios are compounded, they form a tri- 

 plicate ratio ; when four, a quadruplicate 

 ratio ; and so of other compounds. 



5. Ratio, Extreme and Mean, A line 

 is said to be so divided, when the rect- 

 angle under the whole line and the lesser 

 segment is equal to the square of the 

 greater segment ; and, hence, the whole 

 line is to the greater segment, as that 

 greater segment is to the lesser. The 

 segments of such a division, being in- 

 commensurable with the whole line, 

 cannot be exactly given in numbers, but 



RE A 



the geometrical construction is easy. 

 See Euclid's Elements, book ii. prop. 11. 



RATIONAL QUANTITY. A quan- 

 tity, algebraic or arithmetical, which can 

 be expressed without the use of the signs 

 of evolution, such as those of the square 

 root, the cube root, &c. See Irrational 

 Number. 



RAY {radius, a beam or rod). A single 

 radiation, or the smallest form in which 

 light or caloric is emitted from bodies. 

 Calorific rays are those rays which excite 

 heat ; luminous rays, those which impart 

 light ; chemical rays, those which, with- 

 out producing heat or light, produce 

 chemical change, as that of darkening 

 the white chloride of silver. The last 

 are also called deoxidizing or hydro- 

 genating rajs, from their characteristic 

 effect in withdrawing oxygen from water 

 and other oxides. 



REA'CTION. The resistance made 

 by all bodies to the action or impulse of 

 others, which endeavour to change their 

 state, either of motion or of rest. Action 

 and reaction are always equal to each 

 other ; that is, the effect which any force 

 exerts— or, what is the same, its mo- 

 mentum — is equal to the resistance 

 which the body it sets in motion offers 

 to it. The intensity of the moving power 

 is therefore estimated by the mass and 

 velocity of the body set in motion. 



REA'GENT or TEST. In Chemistry, 

 a substance which indicates the presence 

 of any body existing in a minute propor- 

 tion in a solution, by rendering it turbid, 

 by imparting a particular colour to it, or 

 by depositing a precipitate. Thus, a 

 solution of nitrate of silver is a most 

 powerful reagent in detecting chloride of 

 sodium. 



REAL DEFINITION. A definition 

 which explains the nature of the thing 

 defined ; viz. either the whole nature of 

 it, as in Mathematics, or else something 

 beyond what is necessarily understood 

 by the term (see Nominal Definition). 

 In the strict sciences, the nominal and 

 the real definition exactly coincide ; the 

 meaning of the word, and the nature of 

 the thing, being exactly the same. This 

 holds good also with respect to logical 

 terms, most legal, and many ethical 

 terms. 



REA'LGAR. The protosulphuret of 

 arsenic. It is either native, and dug out 

 of the earth in China; or factitious, pro- 

 cured by boiling orpiment, or the sesqui- 

 sulphuret, in subliming vessels. 



RE'ALISM. The opinion of a class of 



