INTERROGATORIES. 



IN KLIN. 



definition b laid down, there i frequently some restriction Implied in 

 th manner of nuking the definition, o that the process to which it 

 lead* presents mure cssos than can be explained by it, or were con- 

 template) when it was made. For example, the abbreviation of a, aa, 

 , 4c. [ExroSKxr] into a, a*, a 5 , and the rules which spring from it, 

 soon lead to tuch results as 



a-*, a, o, o-l; 



which, though they follow from algebraical processes, yet when they 

 finrt arrive, are without algebraical meaning. In such a case, the pro- 

 oea* of interpretation enters ; the question is, What should such symbols 

 mean f hare they a necessary meaning 1 if not, is there any meaning 

 which will be more convenient than another ! A definition has been 

 laid down, leading to results which cannot be explained by it : re- 

 quired the extension of the definition which will enable it to explain 

 its own results. 



Examples are found in all works which explain the principles of 

 algebra. The rule always is, let the interpreted meaning of the new 

 symbols be such as will make the whole of the process true by which 

 they were obtained. Now as they must have been obtained by the 

 application of those formula; which are true of the intelligible results 

 of the definition, the rule just mentioned leads to the following : let 

 the meaning of the unintelligible results be such as will make the 

 formula) of the intelligible ones true of them. Thus, in the preceding 

 instance, the fundamental formula which connects the terms of the 

 series a, a 1 , of, a 4 , Ac., is 



which is intelligible when M and are positive whole numbers, 

 Suppose it now required to interpret a : that is, to give it a meaning 

 which shall make the preceding formula true of it. Write instead 

 of stand we have a* x o" =o 0l - m =o M ,oro must stand for 1. Again, 

 suppose it required to interpret o ' . In order that the preceding 

 formula may be true of the meaning of a ' , we must have 



a i xal 



whence a * must stand for V"- And similarly for other cases. 



It is interpretation which creates the distinction between algebra, 

 as now known, and arithmetic with general symbols of number, or 

 universal arithmetic. This we shall see in the article NEGATIVE AND 

 IMPOSSIBLE QUANTITIES.' 



IXTKKROGATORIES. [EQUITY.] 



INTERVAL, in Music, is described by Dr. Robert Smith, in his 

 ' Harmonics,' as " a quantity of a certain kind, terminated by a graver 

 and an acuter sound." Brossard has said the same thing in other 

 words : " C'est la difference, ou distance, qu'il y a d'un son grave a un 

 son aigu." Agreeing in this definition, from c to D is an interval of a 

 2nd ; from c to o an interval of a 5th ; from c to BS an interval of a 

 flat 7th, tc. [ScALE.1 



Intermit are ample when confined within the octave, compound 

 when they exceed it, and are named according to the distance of the 

 two boundary notes. Thus the interval of a whole tone (o D) is called 

 a 2nd ; of a whole tone and a semitone (c E ft), a minor 3rd, &c. 

 Intervals, therefore, are considered as sounds, and hence are either 

 consonant or dissonant; that is, concords or discords. [CONCORD; 

 DISCORD.] 



Efamplet of Simple fntervali. 

 Ofaftui Ofisrt. OfaSSrd. Ofa{4th. OfaBSth. Of an Sth. 



Example* of Compound lntcrva.lt. 



Of a Mb. or an 8th 

 and tod. 



Of 12th, or an gth 

 and a Sth. 



Of a 16th, or of two 

 octaves. 



INTESTACY is either the dying without a will, or leaving a win 

 which does not dispose of the whole of the real or personal estate. 

 There may therefore be either a general or a partial intestacy. 



I \ToNATIoX, in Vocal Music, is the tuning of the voice the 

 singing true or false in time or out of tune. Correct intonation is the 

 first requisite in a singer; this wanting, all his other musical qualities, 

 however good, are unavailing. 



IXTRADOSand EXTRADOS, the lower and higher curves of an 

 arch. The intrados of an arch is also called the mffii. The intrados 

 and cxtrados are measured respectively along the inside and outside of 

 the vmusnirs. [ARCH.] 



INTUTI'iN (m/fn), the most simple act of the reason or intellect, 

 on which, according to Locke, " depends all the certainty and evidence 

 of all our knowledge ; which certainty every one finds to be so great, 

 that he cannot imagine, and therefore cannot require, a greater. For 

 a man cannot conceive of a greater certainty than that any idea in his 

 mind U such as be perceives it to be, and that two ideas, wherein be 

 perceives a difference, are different and not precisely the same." 

 Hi* definition, or rather explanation, of intuition is as follows : 

 " Sometimes the mind perceives the agreement or disagreement of two 



idess immediately by themselves, and this, I think, we may call intui- 

 tive-knowledge. In this the mind is at no pains of proving or exan 

 but perceives the truth as the eye does the light, only by being directed 

 t<> it." ('Essay on Human Understanding,' b. iv.,c. ii.. g 1.) > 

 Hamilton (' Lectures on Metaphysics,' loot, xxiii.) observes that " an 

 intuitive cognition, as an act, is complete and absolute, as irrespective 

 of aught beyond the dominion of consciousness ; whereas a representa- 

 tive cognition, as an act, is incomplete, being relative to and vicarious 

 of an existence beyond the sphere of actual knowledge." 



The nature of the relation which subsists between intuition and 

 reasoning has been strongly contested. While Beattie maintains that 

 the connection between them, how closely soever they are foun.l in 

 general to be connected, is not necessary, but, on the contrary, a being 

 endued with one may be destitute of the other ; Dugald Stewart, on 

 the other hand, insists that the two are not radically distinct, although 

 by most writers they are considered to be different faculties. Locke 

 having rightly maintained that every step which the reason makes in 

 demonstrative knowledge has intuitive certainty, and that, conse- 

 quently, the power of reasoning presupposes that of intuition, Stewart 

 thinks that the intuition of Locke implies the power of reasoning ; or, 

 at least, that intuition combined with memory explains reasoning. 

 Here his usual sagacity appears to have failed Stewart. While the 

 mind itself is perfectly simple, it has been, for the purpose of attaining 

 accuracy of language and distinctness of theory, supposed to be multiple ; 

 and distinct faculties have been ascribed to it according as its several 

 operations comprise more or fewer elements. According, therefore, 

 to his own account, reason, which involves the element of time, must 

 be kept distinct from intuition, which does not involve that element. 



The proper objects of intuitive certainty ore identical propositions. 

 This, of course, does not mean propositions verbally identical ; such as 

 " a man is a man." But while the object of thought is perfectly and 

 always one, it may present itself to the thought under a van 

 aspects, either dissolved into ita elements or as combined into a whole. 

 It is this identity under an appu-ent diversity that constitut. 

 original and primary evidence which makes en' nn piujiositions, as 

 soon 03 the respective terms ore understood, to be perceived intu 

 On the other hand, the apparent identity of a real diversity is the 

 ground of all sophistical argument. The ultimate form of legitimate 

 argumentation is, = 6, 4 = c, . . a = e. But every fallacy, \vlim 

 detected, will invariably be found to be a = 6 + r, 4 = e, . . a = c. The 

 sophistry consists in the suppression of the element r, either positive 

 or negative. 



INULA HELENIUM (Elecampane), an indigenous perennial herba- 

 ceous plant, found in most meadows, the root of which is used in 

 medicine. This port is thick and branching, brown externally, white 

 internally, with an aromatic odour and a mucilaginous taste, at first 

 bitter, afterwards sharp and camphor-like. In addition to mucilage 

 it contains a large quantity of a variety of starch termed inn I in. 

 Inulin exists in many other plants, and goes by a variety of names, 

 Alantin, Menzanthin, Elecampanin, Dahlin, Datiscin. Inulu /', 

 also contains a volatile oil, a portion of which when crystallised con- 

 stitutes the stcoropten called Elecampane camphor; a bitter ex- 

 tractive ; an acrid resin ; some salts of lime, Ac. 



These ingredients give it a tonic and stimulating property, and it is 

 employed in debility of the stomach and other diseases of mucous 

 surfaces unattended with inflammation. It is, however, not much 

 used. Having kept its place in popular favour from the time of the 

 earliest Greek writers, it cannot be deemed altogether useless. It 

 affords a ready substitute for senega, the virtues of which are greatly 

 lessened by age, and can rarely be had fresh. The Inula canyta, 

 formerly Conyza iquarrota, a plant not uncommon by the sides of 

 fields or roads in chalky districts, is deservedly esteemed in the east of 

 Europe as an antidote against the bites of vipers. It is remarkable 

 that such an antidote has, in different parts of the world, been sup- 

 posed to be found in the tribe of Componia-, such as Mikania guaco, 

 Kupatorium agapana, Inula ritcuta, Prenanthet terptntaria, Venunua 

 altiiaima, Ac. 



INULIN, Dahlin, Alantin, Mtnuinthin, Datacin (C,,H 10 10 1 ), a 

 neutral vegetable principle, resembling starch in many of its properties; 

 it exists in the root of elecampane (Inula heltnium), the fftlinnlhia 

 tuberoiut, the dahlia, and some other plants. The roots ore reduced 

 to a pulp, which is to be placed on a very fine sieve, and a stream of 

 water is to be poured upon it as long as the latter is rendered milky; 

 the inulin is then allowed to deposit ; the supernatant liquor being 

 poured off, the deposit is to be repeatedly washed with water till it 

 comes off perfectly limpid. 



Inulin when dry has the following properties : It is a white brittle 

 mass composed of crystalline grains, or else a fine and white powder, 

 which adheres to the teeth. It is insipid, insoluble in cold water, but 

 very soluble in boiling water; the solution is fluid, and not gelatinoun 

 like that of starch. When it is very dilute, it does not become t\n bid 

 on cooling; but alcohol, not being a solvent of Inulin, precipitates ft 

 from this solution. When heated to above 212*, it melts, and U 

 converted into a sweetish mars which is very soluble in cohl 



nulin). Cold sulphuric or nitric acid converts it into the same 

 substance. 



Iodine renders inulin of a brown tint, which is fugitive. Lime- 

 water, solution of tin, subocetate of lead, tincture of galls, protosalts 



