Page:The New International Encyclopædia 1st ed. v. 06.djvu/206

* DETAINER. 168 DETERMINANTS. common law for a witl.hoiaing of t^e possession of nroportv. The gist of tl.e aet is not the man ner n'whilh the adverse possession ^vas aequ.red !!!ll,is may have been Unvful or u..laNvlul-hut the continued detention of the ProP"ty/rom one vvho chums the right to the possession thereof No question of title or ownership is "<^;<'--^'' ^ involved in the notion of a detainer, as onejxho s not the owner may nevertheless be en .tied to ihe possession of the property, and on the other hand the owner may be guilty of an un awful detainer of his own land or goods. A detainer is always an aet of force, and u.ay be lawful or un- lawful. The appropriate remedy where goods are unlawfully detained is detinue or re,,/<-r.,.. and if. after demand made, the holder refuses to rXrn them, he is deemed to have converted them o U own use, and becomes liable to an action in trover for damages. An unlawtul Jyta-'-r o lands gives rise to a right of entry, or, m modern practice, to an action of ejectment. Trespass is not available if the original entry was rightful, nor can any action be employed whose purpose is to try the" question of title, as that is not in- volved. When a detainer follows upon a wrong- ful entry, it mav. nevertheless, be valid, as when one, in violation of law, forcibly >^«overs posses- sion of his land from an intruder. Here the ille- gal entry is punishable, but the subsequent pos- session of the owner of the land will "^'^ be dis- turbed. See CoNVERSio.v; Detinue; Iobcible ESTRY. D':^TAMPES, dft'tuxp', Duciiesse. bee E.sTA.MPKs. Anne de 1'essileu, Duchesse d. DETECTIVE (from Lat. delectus, from de- tenerc. expose, from </f- neg. + tegere, to cover). One who engages in the work ot securing infor- mation about wrongdoers for the purpose of bav- in" it used against them in civil or criminal pro- ceedings. He mav be a public officer or a private employee. In many cities there are extensive de- tective bureaus, whose members are in no wav connected with the official police or constabulary establishments. Some States forbul persons to aet as detectives without a license from a eoiirt or other official source. A detective does not be- come an accomplice ot a criminal even ^v^•Pn j^'^ knowledge of the criminal's plans would haNC enabled him to prevent the commission of the crime. His act in entrapping a criminal, if lim- ited to mere entrapment, does not render him liable to punishment, nor does it in any way excu-c or .■xon.rate the criminal. DETERMINANTS (T.at. dctermimns, pres. part, of dctermi,u,rc. from de- + termimre, to bound, limit). Certain •l?^'"-'^^,.'""''""";; jr" markable for their brevity of notation and their wealth of significant properties. |'';^ ,,^|, S ± <.,b« or (",6i) are merely other notations forojf.— n.b,. The first form is comnionly used in ele- mentarv mathematics. Similarly I a, J>, fi n- b. Cj n, 61 c, represents a^hiC, -f a.b,c, + a,h,c, — "-fi^Tt a.b,c, — <i,b,r'.- Such functions are called deter- minants. an<i the quantities a„ b,, r,. «„ !»;. . • • are called elements. The first or square form o! notation is cnlled the array notation. If there are more columns than rows the form is called a timfri'T An array of two columns and two rows is called a aetermiiuu.t of the second order, one of three colunuis and three rows a determinant of the third order, and so on. In the eN|.anMon of a determinant of the second order there arc two terms, each containing the lellcrs ,1. 6, hut dilTering in the arrangement »/, •'"'.^"'^: scripts 1. 2. In the expansion of a determinant of the third order there are six terms, each con- taining the letters fl, b, e, but d.tfenng 111 he arrangement of the subscripts 1. i, J. 1 >»» there are two terms in the expansion of a deter- minant of the second order, and six m one of the third order, half of which are positive and b. f ne-nitive. The signs arc selected according to the armngenient of the subscripts. If there is an even number of inversions in the order of the subscripts of any term, its sign is considered plus: if an odd number, its sign is considered Linus: e.g. in the term «.J..e„ 3 standing before ■■> is an inversion, since the natural order is _ before 3: likewise, 3 before 1 and 2 before 1 are inversions; there being t!''-<^e ■"f';^'""',- „,,','; sion is minus. A determinant of the fourt Older contains 10 element^, and Us expansion contains 24 terms. In general, a determinant of the «th order contains <r elements, and its expan ^ionHdi — 1) (" — 2) .... 2 • 1. or n! term-. Some of the leading properties of determinant- arc- (1) If two adjacent columns or rows ot a determinant are interchanged, the sign oiilyof thr determinant is changed; if a column or row i~ transposed over an odd number of columns ... rows, the sign only of the fterminant 1^ changed; if a column or row is transposed over an even number of colunuis or row's, the determi- nant is unchanged. (2) If the columns be made rows, and conversely, the determinant is un- changed. (3) If the elements of a row or column be aTlded to the corresponding elements of an- other column or row, the value o the deternn- nant is unchanged. (4) Multiplying the ce- ments of any column or row by a number inulti- plies the determinant by that number, (o) f two columns or two rows are """f",' > "^ '^ '^ elements of any row or column are all zeros, the determinant vanishes. Su.h properties are of creat aid in evaluating determinants. ^ Various methods of expansion have been de. vised, bv which the terms, each containing one element -and only one. from each <"" ""'" ""^ each row. can readily «"<! />-^*™V^'r'"r 1 formed. While these methods can bes be ob- a™ed from a text-book on the subject, minor determinants will be explained here since they ur^iish a simple means for «P""J;"^, 'l f;';,', nants of degrees higher than the thud If the ",,umu and%ow to which any "^u'nt belong are -oppressed, the resulting de erminant 18 called a first minor of the given f^-t7""""t^^or ,he cofaclor of the given element. If *""["«» uul two columns be suppressed, the resulting determinant is called a second minor of the given determinant, and so on. Thus, in o, b, c, rfi Oj b, Cj <?: a, bi c, d, o, b, c, d, ib.r.d,) is a first minor of A the leading element n„ and (a,b,) is a ""iT tir/co.-factors of «,. b,. C. d, be denoted 1^ A, B,. C,. D„ then it can be .show-n that A - aX + '.3.+ e.C. + rf-D,. It ehould be A= and a co-factor of second