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CONICAL PROJECTION. 



CONJUGATION. 



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in the case of beginners, unless it involve the foci in the definition. 

 The properties of these points do not readily show themselves either in 

 the deduction from the cone or from the general algebraic equation. 



CONICAL PROJECTION, a method of describing a representation 

 of a part of a sphere upon a plane. A sphere cannot be unrolled into a 

 plane, as can every cone or portion of a cone. If a cone be described 

 which touches a sphere in a small circle, and if the several points of 



the sphere be then projected upon the cone by lines drawn through 

 the centre, the parts adjacent to the small circle of contact will be pro- 

 jected into figures very nearly similar to the originals. If the degrees 

 of latitude, which are very nearly equal, be made actually equal, no 

 injurious effect will be produced on the map. Suppose, for instance, 

 it is required to draw the map of a country contained between two 

 given longitude circles, and two given parallels of latitude. 



Take any radius for the sphere, and let s A be the radius x cotan- 

 gent of the middle latitude of the map. From A set off AB, AC, &c., 

 equal to the arc of one degree (or whatever the distance may be 

 between the parallels which it is desired to draw) on the great circle of 

 the sphere chosen. Let L be half the total longitude contained 

 between the extremities of the map, and take the angles ASP and 

 A 8 Q, equal to L x the sine of the middle latitude. Divide the angle 

 j 8 p into as many parts as there are degrees (or other required inter- 

 vals of longitude lines) in L ; then Q K T p is the map required, and 

 V x Y z such a portion as is usually exhibited on a sheet of paper. 



If, instead of the tangent cone, it be required to project upon the 

 cone formed by the revolution of the chord which joins the two 

 extreme points of the map on the sphere, let I and I' be the least and 

 greatest latitudes, and let 



8 K = radius x coa f -s- sin 4 



8 Q = radius x cos I -=- sin J (I + 1') 



the rest is as before. 



There are two modifications of this principle which it will be 

 convenient here to notice, the projection used by Flamsteed, and 

 that adopted by the French government in their recent maps. In 

 Flamsteed's projection the degrees of latitude are equal, and the 

 parallels of latitude are perpendicular to the middle longitude circle, 

 which is a vertical right line. But the degrees of longitude are made 

 in every parallel to bear the same proportion to the degree of latitude 

 as on the globe ; so that the meridians are, in fact, curves, the ordinatea 

 of which are as the cosines of the abscissa). 



In the French government maps the same plan is adopted, with this 

 exception, that the parallels of latitude are the circles of the conical 

 projection, and the degrees of latitude are all equal (the oblateness of 



i rth may be allowed for, if thought necessary) ; the degrees of 

 longitude are then set off on the parallels of latitude in the same 

 proportion as in Flamsteed's projection. 



VINE, C'onicine, Conia, Conicina (C !0 H 1S N). An alkaloid obtained 

 from hemlock (Conium macnlatum). It is procured from the seeds or 

 fresh leaves of the plant by distillation with water holding some potash 

 in solution. When pure it has the following properties : It has the 

 appearance of a colourless volatile oil, and in lighter than water, 



its specific gravity being 0'89. Its odour is powerful, diffusible, and 

 repulsive, somewhat like that of hemlock itself. It is intensely acrid 

 to the taste. It has a strong alkaline reaction on turmeric paper. It 

 combines readily with and neutralises acids ; and some of the salts 

 which it forms with them have been obtained in a crystalline state. It 

 is sparingly soluble in water, and what is remarkable is, that it is more 

 soluble in cold water than in hot. It imparts its odour and taste to 

 water. Alcohol mixes with it in all proportions ; and it also dissolves 

 readily in ether. With about one-fourth of its weight of water it forms 

 a hydrate. By exposure to the air it quickly becomes of a dark 

 colour, and spontaneously decomposes with the evolution of ammonia. 

 Its boiling-point is 370 Fahr. It distils, however, with boiling water, 

 but suffers partial decomposition. 



It is one of the most virulent poisons known, destroying small 

 animals by a very small quantity and in a very short time. 



Hemlock also appears to contain a second base, -methyl-canine 

 (C 15 H 17 N) ; whilst, by acting upon conine with iodide of ethyl, a third 

 base, ethyl-conine (C,, H I() N), may be obtained. 



CONJUGATE. This word is used in several branches of mathe- 

 matics in a sense which (with one exception, and that might easily be 

 abolished) may be described as follows : Two points, lines, &c., are 

 called conjugate, when they are considered together in any property in 

 such a manner that they may be interchanged without altering the 

 way of enunciating the property. Thus, if AC be to B as A D to 

 D B, c and D are conjugate points with regard to this property. 



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If we write D where c now is, and c for D, the property is still 

 expressed in exactly the same way. We have other instances in 

 conjugate diameters, conjugate hyperbolas [ELLIPSE ; HYPERBOLA], 

 conjugate foci [LESS ; MIRROR]. 



The instance of exception is the conjugate point of a curve, meaning 

 a single point lying by itself, whose co-ordinates satisfy the equation of 

 the curve, without its actually being on any continuous branch of the 

 curve. [CURVES, THEORY OF.] It would be better to call this point 

 ronjuHct than use a term which destroys the generality of language. 

 But the best term, in our opinion, would be evanescent oval. [See the 

 article already cited.] 



CONJUGATION of a verb is a term in Grammar, denoting the 

 addition of suffixes or prefixes to the crude, or elementary form of a 

 verb, for the purpose of denoting respectively, person, number, time, 

 state, mood, and what is generally understood by voice. In the 

 English language prefixes are commonly used for these purposes, and 

 these prefixes are not printed in connection with the verb, though the 

 voice presents them in one mass. Thus, 7 shall hare heard, as pro- 

 nounced, is not less one word than the Latin audi-v-er-o. In this 

 example, therefore, 7, shall, have, are virtually prefixes, and the letter 

 d, a contraction from ed, or rather de, is a suffix attached to the 

 simple verb or crude form hear. In the ancient languages, such as 

 Greek, Latin, and Sanscrit, suffixes are commonly but not exclusively 

 preferred. 



The suffixes which denote the permmt are the personal pronouns 

 more or less corrupted. Thus, in Latin, (garnet is the full form of the 

 pronoun which signifies 7; but as three syllables would be too long 

 for a term in such frequent use, and this inconvenience in the present 

 instance would be aggravated by an appearance of egotism, the word 

 was shorn of its exterior letters, and at the utmost the three middle 

 letters, ome, were attached to the verb. We see them in the Greek 

 form tupt-ome-s, or tupt-ume-n, " we strike." In the Latin, the vowels 

 were corrupted, so that instead of time, either umu or imu occur, as in 

 -unlit-*, "we are;" jtoss-umu-s, " we are able;" tcrib-imu-t, "we write." 

 The old German has nearly the same suffix in war-mne-s, " we were ; " 

 bir-umc-s, " we be." Again, the three letters, ome, deprived of the last 

 vowel, became om, as Greek, tupt-om-ai, " I strike myself ; " am, as 

 Latin, s-um, " I am ; " poss-um, " I am able ; " also am, as seen in inqu- 

 am," I say ; " and on, as Greek, e-tuft-mi , " I was striking." But the 

 first vowel might disappear instead of the last. Thus, me is the form 

 which appears in the Greek es-me-n, or es-me-s, " we are ; " mi is used in 

 es-ml, ei-mi, " I am ; " di-do-mi, " I give," &c. Sometimes the m is all 

 that appears, as scribeba-m, " I was writing." In Greek, this final m, 

 by a principle constantly observed in that language, becomes an n, as 

 i-n, " I was ; " etetuphei-n, " I had struck." Another form of the suffix 

 is o, instead of om, which is common both in the Greek and Latin, as 

 Greek, tupt-o, " I strike ; " Latin, scrib-o, " I write." Finally, all trace 

 of the pronoun at times disappears, and the defect ceases to mislead 

 because the other persons have their characteristic terminations. Thus 

 the Greek tenses, etupsa, " I struck," telupha, " I have struck," and 

 etetupheu, " I had struck," contain no remnant of the pronoun. In the 

 English language there are some slight traces of the personal suffixes, 

 which existed in full perfection in some of the older forms of the 

 Teutonic languages. The word am, for example, has a remnant of the 

 first person suffix in its final m. 



The second person in the Greek and Latin languages was s or tu ; 

 in German, rf ; and in English, " thou." Accordingly, we find a 

 sibilant attached to the verb to denote the second person, as in the 

 Greek, es-si, " thou art ; " oit-tha, " thou knowest ; " tupt-es-ai, " thou 

 strikeat thyself;" in the Lathi, scrib-is, "thou writest;" and in the 



