sub stilet

See substyle. substitute (sub's ti-tut), v. t.; pret. and pp.sub stituted, ppr. substituting. [ It. sustituire = Sp. sustituir = Pg. substituir = F. substituer ), place under or next to, put instead of, substitute, For real wit he is obliged to substitute vivacity. Goldsmith, The Bee, No. 1. 21. To appoint; invest with delegated authority. But who is substituted 'gainst the French I have no certain notice. Shak., 2 Hen. IV., i. 8. 84. act of substituting, or putting (one person or thing) in the place of another; also, the state or fact of being substituted. We can perceive, from the records of the Hellenic and Latin city communities, that there, and probably over a great part of the world, the substitution of common territory for common race as the basis of national reunion was slow. Maine, Early Hist. of Institutions, p. 75. 2. The office of a substitute; delegated authority. [Rare.] He did believe He was indeed the duke; out o' the substitution , And executing the outward face of royalty, With all prerogative. Shak ., Tempest, i. 2. 103. 3. In gram., the use of one word for another; syllepsis.-4. In Rom. law, the effect of appointing a person to be heir, in case the heir first nominated would not or could not be heir. This was called vulgar substitution. Pupilary substitution existed where, after instituting his child as heir, the testator directed that, if after the child should have become heir it should die before attaining puberty, another be substituted in its place. This was originally allowed only for children under age in the power of the testator, but was afterward extended to children who for any reason could not make a valid will. 5. In French law, a disposition of property whereby the person receiving it, who is called the institute (le grévé), is charged either at his death or at some other time to deliver it over to another person called the substitute (l'appelé). -6. In chem., the replacing of one or more elements or radicals in a compound by other elements or radicals. Thus, by bringing water and pota ium together, pota ium (K) is substituted for a hydrogen atom in water (H2O), yielding KOH, or caustic potash. By further action the other hydrogen atom may be replaced, yielding pota ium oxid (K2O). Substitution is the principal method employed in examining the chemical structure of organic bodies. Also called metalepsy. No generalization has, perhaps, so extensively contributed to the progre made by organic chemistry during the last fifteen years as the doctrine of substitution. E. Frank land , Exper. in Chem., p. 210. 7. In alg .: (a) The act of replacing a quantity by another equal to it; also, in the language of some algebraists, the replacement of a set of variables by another set connected with the first by a system of equations equal in number to the number of variables in each set. See transformation (which is the better term). ( b ) The operation of changing the order of a finite number of objects, generally letters, that are in a row, the change following a rule according to which the object in each place is carried to some definite place in the row, this operation being regarded as itself a subject of algebraical operations. For example, supposing we were to start with the row a , b , c , d , e, a substitution might consist in carrying us to the row b , c , a, e, d. Denoting this substitution by S, the repetition of it, which would be denoted by 82, would carry us to e , a , b , d , e . If T denote the substitution of e, d, e, b, a for a , b , c, d , e, then TS would convert the last row into d, e, a, c, b, while ST would convert it into d, c, e, a, b. One way of denoting a substitution to which the terminology of the theory refers is to write a row upon which the substitution could operate, with the resulting row above it. These two rows are called the terms of the substitution , the upper one the numerator, the lower the denominator of the substitution. The objects constituting the rows are called the letters of understood that no two of these affect the positions of the same letters. - Circular substitution, a substitution whose succe ive powers carry the letters which it displaces round in one cycle. - Cremona substitution a substitution of a Cremona transformation, especially of a quadratic transformation. - Derivant substitution, a substitution whose inverse multiplied by another substitution, and then this product by the derivant substitution itself, makes a substitution the derivate of that other substitution. - Derivate of a substitution, the product of three substitutions, of which the middle one is the substitution spoken of, while the other two are inverse substitutions. - Determinant of a linear sub stitution. See determinant. Doctrine of substitution, in theol., the doctrine that Christ suffered vicariously, as a substitute for the sinner. - Elementary substitution, a substitution into which only the elements 0, +1,-1 enter. - Identical substitution, a substitution which leaves the order of all the letters unchanged. Imprimitive substitution, a substitution not primitive.-Index of a system of conjugate substitutions, the quotient of the number of permutations of the letters by the order of the system. Interchangeable substitutions, two substitutions which give the same product whichever order they are multiplied - that is, ever is taken first in forming the product. - Inverse substitutions, two substitutions whose product is an identical substitution. - Isomorphous substitution group, one of two groups of substitutions such that every substitution of the one corresponds to a single substitution of the other, and every product of two substitutions to a product of analogous substitutions. - Linear substitution. (a) A circular substitution between a variable, a linear function of it, and the succe ive iterations of that function. (b) A linear transformation.Order of a substitution, that power of a substitution which is an identical substitution. - Order of a system of conjugate substitutions, the number of substitutions belonging to the system. - Orthogonal substitution. See orthogonal. - Permutable substitutions, interchangeable substitutions. -- Power of a substitution, the operation which consists in the repetition of the substitution spoken of as many times as the exponent of the power indicates. - Primitive substitution, a substitution whose order is a prime number or a power of a prime number.-Product of two substitutions, the result of performing two substitutions succe ively upon one row. -Rational substitution, a circular substitution between succe ive iterations of a rational function, such as Xm +1 = ( axm + b )/( cxm + d). - Reduced substitution, a substitution represented by an integral algebraic function having 1 for the coefficient of the highest power of the variable, and 0 for the coefficient of the next highest power and for the absolute term. - Regular substitution, a substitution whose circular factors are all of the same order. - Service by substitution. See sub stituted service, under servicel. - Similar substitutions, two substitutions which have the same number of circular factors and the same number of letters in the cycles.Substitution product, a chemical compound prepared by substituting an element or radical for some member of a complex molecule without altering the rest of the molecule. - System of conjugate substitutions, a group of substitutions-that is to say, such a collection of substitutions that every product of substitutions belonging to it is itself a substitution of the same collection. -Term of a substitution, one of the two permutations whose relation constitutes the substitution.