tn 



srnTANOBNT. 



INIC GROUP. 



-re 



mlly, if for .r wo write a + p, and U p be erroneous by a quantity of 

 the onto r* , we (ball have, by one more substitution, 



lie i-rrur of *(a+i>) will be of the order <", and that of 

 f (a-f />) uf the order r' + '. There is then a oontiuu.il approximation 

 V> the raluc of jc. 



Beginning with jc-a + t^t, in which the errur a of the order *, wo 

 hare 



a = a + ef (a + fo), 



in which the arror U of the thhrd order. Rejecting termi of the third 

 order, we have 



Substitute thin again, and we bare 

 *- a -r f { 



In which the error U of the fourth order. Rejecting term* uf the 

 fourth order, 



*- + * + <ff a + 1 1 



and so on : the development being made by TAYLOR'S THKORKM. Thin 

 would lead in effect to the celebrated theorem of L&grange ; but the 

 actual method of substitution is sometimes preferable. 



8UBTANGENT, SUBNORMAL. [TAXOEJIT.} 



St'HTKXSK. means any line, angle, Ac., opposite to or nAtmiling a 

 line or angle spoken of. Thus the chord of a circle is the subtense of 

 the arc and of the angle at the centre. The terra is now not MII.II 



SUBTRACTION, SUBTRAHEND, MINUEND. The process of 

 subtraction is the removal of a part equal to the less from the greater. 

 The quantity to be diminished (minuendum) was called the minuend ; 

 the quantity to be withdrawn (nAtrahendum), the luhlrahnul ; and the 

 remaining part, the remainder. The terms subtrahend and minuend 

 are almost out of use, though often very convenient 



The operation of subtraction is often described in a way which 

 might be practised, but is not; and the explanation of the possible 

 mode applied to the actual mode makes confusion. It is obvious 

 enough that if parts of A be subtracted severally from greater parts of 

 B, the remainders put together moke up the whole remainder. Thus, 

 J4 can easily be taken from 76, for 7 tens exceeds 2 tens by 5 tens, 

 and 6 exceeds 4 by 2, so that 52 is the remainder required. But when 

 we come to take 48 from 98, the preceding mode of partition is use- 

 less. To remedy this, it is proposed in the explanation to borrow 1 of 

 the 9 tens in 94, and to put it on to the 4 : then 8 from 13 leaves 5. 

 Now take the 4 tens of 48, and subtract from the remaining 8 tens of 

 93, and 4 tens ore left : the answer then is 45. The process would be 

 as follows : 



8 from 8, impossible ; borrow a ten from 90 ; 8 from 13 leaves 

 5. Take 4 tens from the remaining 8 tens, one of the 9 

 tens having been borrowed, and 4 tens remain. 



n 

 u 



u 



This process is actually used on the Continent ; but with us, as all 

 the world knows, there is a different process, as follows : 



8 from 3 impossible : take 8 from 13, and 5 remains. Com/* 

 one to 4, giving 5, and subtract 5 tens from 9 tens, giving 4 



t. n-. 



3 

 48 



48 



There is quite a different principle in this process, which is as 

 follow* : If two numbers be equally increased or equally diminished, 

 the difference remains the same. Having arbitrarily increased the 8 

 in the upper line by 10, the lower line must be somewhere or other 

 increased by 10, in order to keep the difference (which is all that is 

 wanted) unaltered. 



The object in view is attained by increasing the upper line by ten 

 (Hub, and the lower line by one lea. 



For further detail, see COMPUTATION. 



JU( ' KSSIUN. This is a legal term derived from the Roman 

 ' Buccesrio," which signifies a coming into the place of another, and 

 Successor is he who comes into such place. . 



The Roman term signifies a coming into the place of another so as 

 to have the same rights and obligations with respect to property which 

 that other had. There might be successio either by coming into the 

 place of a person living, or by becoming the successor of one who was 

 ded. Gaius (iii. 77, Ac.) gives instances of successio in the case of 

 persons living, one instance of which is the Bonorum Cessio according 

 tB the Lex Julia. .Succession was again either Universal or Singular. 

 The instances of universal succession (per universiUtem) which Uaiua 

 (tt.97) enumerates, are the being made a person's heres, getting thu 

 P 1 """ 11 " t the bona of another, buying all a man's property, adoptin<; 

 a person by adrogatio, and admitting a woman into the manus as a 

 wife ; in all of which cases all the projwrty of the several persons 

 enumerated passed at once to the person who was made heres, or got 



Tta student nujr well uik frmn !,, > The term "ctrry" Is not tlic 



H , ... 



the bonorum possesmo, or bought the whole property, or adopted 

 another by adrogation, or married the woman. An instance of singular 

 succession is the taking of a legacy under a man's will. 



The term Succession U used in wir language. We speak of :l,.- 

 succession to the crown or the regal dignity, and the term implies that 

 the successor in all things represents the predecessor. In.l..-.|, Un- 

 king, as a political person, never dies, and upon the natural death of a 

 king the heir immediately succeeds. The English lu-ii tit-law takes 

 the descendible lands of his ancestor as universal successor ; ami th.- 

 executor takes [the chattels real and other personal property of hi- 

 testator as universal successor. The general assignee or assignees of a 

 bankrupt or insolvent take by universal succession. 

 Blackstone says that " corporations aggregate consist of many persons 

 united together into one society, and are kept up by a perpetual 

 succession of members, so as to continue for ever." It is true that 

 when members of a corporate body die, others are appointed to fill up 

 their places, but they do not succeed to the others in the Human sense 

 of succession they simply become members of the corporation. But 

 it has been established in some cases that the use of the word " suc- 

 cessors " impliei that the legislature meant to establish a oorpoi 

 and yet it is certain that a feoffraent of land to a corporation aggregate 

 without the word " successors " is a valid grant In a feoffinent to a 

 corporation sole the word "successors" is necessary. The succession 

 in the case of a corporation sole follows tho nature of tin i 

 succession. In the case of a corporation aggregate there is n 

 cession, and the rule that a corporation may be established by the use 

 of the word "successors" in a statute is founded on an ermnrons 

 understanding of the term " successors." 



SUCCESSION DUTIES. For many years persons succeeding to 

 personal property (including leaseholds) whether they took by will as 

 executors or legatees, or merely as administrators or next of kin, w.-ru 

 charged with Legacy Duties, which were payable over and abo\ 

 stamp duty, then and still levied in the first instance, on the gi 

 probate or letters of administration, according to the estimated sworn 

 value of the person.il property of the deceased. The legacy duty was 

 chargeable after the estate of the deceased had been realised and 

 administered, on the property distributed among the legatees or next 

 of kin, as the case might be ; and varied in amount, according to tho 

 consanguinity of the next of kin, or the absence of any relationship 

 between the legatee and the testator. The exemption of real estate 

 from this species of taxation long complained of as creating an undue 

 preference in favour of the holders of landed property, has at last been 

 removed. By the Succession Duties Act, 1853, duties are imposed on 

 every succession to property, whether real or personal, according to 

 the value and the relationship of the parties to the predecessor. 

 Where the successor is the lineal issue or lineal ancestor of the 

 predecessor, II. per cent. ; where a brother or sister, or a descendant of 

 a brother or sister, 3/. per cent ; where a brother or sister of th< 

 or mother, or a descendant of the brother or sister of the father or 

 mother of the predecessor, 51. per cent. ; where a brother or sister of 

 the grandfather or grandmother, or a descendant of the brother or 

 sister of the grandfather or grandmother of the predecessor, til. per 

 cent. ; and where the successor is in any other degree of collateral con- 

 sanguinity to the predecessor, or is a stranger in blood to him, ] 

 cent. The value of the succession, if it be to real property, is 

 ascertained by considering the interest of the successor as of the value 

 of an annuity equal to the annual value of the property, estimated as 

 the act directs ; and the duty may be paid by eight equal half-yearly 

 instalments, or at once, according to the wish of the i>arty liable 

 thereto. 



SUCCESSIVE SUBSTITUTION. [SI-BSTITUTION.] 



SUCCINAMIC ACID. [Succituc GROUP.] 



SUCC1NAMIDE. [SUCCINIC GROUP.] 



SUCCINAMILIC ACID. |Si OOJWC Gnorp.1 



M I'CINALIDE. [Suci IMC Unoup.1 



8UCCINANILE. [Buoonno GBO0F.1 



SUCCINIC ACID. [Si r, ,M. GROUP.] 



SUCCINIC ETHER. [ETHYL.] 



SUCCINIC GROUP. The generic name of succinic acid ami it., 

 derivatives. 



nit acid (2 HO, C.H.O.) exists naturally in AMHKH (<irri,,u,), 

 from which resin it was first obtained as one of the products of de- 

 structive distillation. In combination with potash it also ocei 

 the milky juice of the leaves and stems of wormwood (Art, 

 ulisinihinm \. It may be artificially prepared from stearic acid or other 

 fatty matter by oxidation with nitric acid : in this reaction, pimelic 

 and adipic acids ore also formed, as well as, a body that was at first 

 thought to be a distinct acid (lipic acid), but which has since 

 shown to be identical with succinic acid. i h most advantageous 

 method of forming succimc acid is that known as Dessaignes, and con- 

 sists in fermenting crude malatc of lime with eight or nine 

 decayed cheese and three times its weight of water. The mixture 

 ' kept at a temperature of 100 Fahr. for about a week, when 

 the inalato will be found to be changed to a i Aliment of 



.-uei mato and carbonate of lime, acetate of Him- remaining in soluti.'n. 

 The precipitate decomposed by boiling dilute sulphuric acid, and the 

 aolaUoo evaporated and treated with animal charcoal furnishes the acid 

 in rhombic! prisms or tai 



