HYMN. 



HYPERBOLA. 



who bad been carried to Eleusis by Pelaagian pirates. For this service 

 be was rewarded with a maiden of whom he was deeply enamoured ; 

 and on account of hi* conduct, and the happiness of hi* muriage, he 

 was mvokcd m bridal songs, theixK called hymeneal song*. But aflvenil 

 other legends are rrlated. which account for hit apotheosis in a some- 

 what different manlier. In ancient art he is represented as a tall aiul 

 ilaynt, but somewhat effeminate youth a larger and more serious 

 Eros. He usually carries in his hand the bridal torch, and sometimes 

 wean on hi* head, or around his neck, a wreath of flowers. 



HYMN (fern), a song of praise and adoration, in honour of a Deity, 

 and by the Hebrews, as well as the Greeks, accompanied on some 

 musical instrument The Te Dmm and Hfxtiiinm are, in our liturgy, 

 both called hymns : the former is supposed to have been written by 

 St. Ambrose ; though St. Hilary, bishop of Poitiers, is said to have 

 bean the first who composed hymns for the church. To Pnidentius is 

 ascribed most of those which appear in the Roman breviary. The 

 hymn should be a song of joy, not of lamentation, as is too often the 

 ease in the present day. Such was the opinion of St. Isidore, who gave 

 to the song of complaint and sorrow the name of Ihrrna, from threnos 

 (Jjripwf), "lamentation." 



The term is now applied to any short religious poem sung in places 

 of public worship, not being a version of a psalm, or taken directly 

 from any of the canonical books of Scripture. 



HYOCHOLALIC ACID (C W H W O.). A peculiar crystalline acid, 

 produced along with sugar of gelatin by the action of potash upon 

 hyocholic add. 



HYOCHOLIC ACID (C..H U KO )0 ). This acid, in combination 

 with soda, constitutes the chief portion of the bile of the pig. It is a 

 white resinous body, fusible in hot water, and then presenting a silky 

 appearance. It is very slightly soluble in water, by which it is dis- 

 tinguished from cholic acid. It gives insoluble precipitates with lime 

 and baryta. 



HYOCHOLOIDIC ACID. [HYODTSLTSIN.] 



HYODYSLYSIN (C^H^O,). An homologue of dyalysin, produced 

 by the action of boiling hydrochloric acid upon hyocholic acid. It ia 

 insoluble in water, ammonia, and potash, tolerably soluble in ether, 

 and but slightly soluble in alcohol. Its formation is preceded by that 

 of a peculiar resinous acid, termed hyocholeidic acid. 



HYOSCYAMINE, J/yotcyama, the active and alkaline principle of 

 the Jfyotryamitt niyer and other varieties of henbane, from which it ia 

 obtained by a very complex and tedious process. 



The properties of hyoscyamine are : It crystallises in stellated 

 groups, which have a silky lustre ; and it is often obtained in the state 

 of a colourless, viscid, adhesive mass. When perfectly dry it is 

 inodorous; but when moist, especially if impure, it has a disagreeable 

 stupefying smell, resembling that of tobacco. When anhydrous, hyos- 

 cyamine has not an alkaline reaction ; but when mixed with water it 

 has, on the contrary, very permanently alkaline properties. It is not 

 volatile at common temperatures, and undergoes no change by exposure 

 to the air. It melts at a low temperature, flowing like oil, and is volati- 

 lised at a high temperature ; a large portion of it is then decomposed, 

 becoming carbonised and yielding ammonkcal vapour. It is also partly 

 volatilised by the vapour of boiling water, and communicates to the 

 distilled water the properties of a narcotic poison. It is readily 

 soluble in water, and iodine added to the solution gives a kermes- 

 coloured precipitate ; tincture of galls gives a white precipitate ; 

 chloride of gold precipitates whitish flocculi ; solution of chloride of 

 platinum gives no precipitate whatever. It dissolves also in alcohol 

 and in ether. 



Hyoscyamine burns with a sooty flame ; concentrated nitric acid 

 dissolves it without acquiring colour, and sulphuric acid renders it 

 i V| 



Hyoscyamine exists in combination with an acid ; it neutralises acids 

 perfectly, and its power of saturation is great. The salts which it forms 

 by direct combination with dilute acid mostly crystallise, are inodorous, 

 bat have an acrid nauseous taste, are unalterable in the air, and are 

 extremely poisonous. 



Hyoscyamine is a narcotic poison, like narcotine, and proves fatal ax 

 quickly as coninr. 



H YOSCYAMU8 NIGER. The medical uses of Ifyotcyamiu niger, 

 or henbane, have been detailed at the end of the article HYOSCYAMUB, in 

 NAT. HIST. Div. 



HVP..CTHRAL. [TEMPLE.] 



H YPE'RBOLA. In connection with this article see CONIC SECTIONS ; 

 Emm; PABABOLA. 



The hyperbola is one of the curves known by the name of conic 

 section*. It is hi the application of mathematics the least useful of the 

 three ; indeed, so very rarely does the necessity of using it occur, that 

 H may be a question whether the study of it should form a part of a 

 course of practical mathematics. But there are in pure analysis so 

 many analogies which are illustrated by distinctions existing between 

 the properties of the ellipse and hyperbola, that the student who 

 aspires to more than elementary knowledge cannot dispense with the 

 comparison of the two curves. 



The two branches rarring through A and M form a complete hyper- 

 bola, derived from the cone, or from the general equation of the second 

 degree. [Coxic SKCTIOXS.] There is a pair of straight lines passing 

 through the CENTRE c, namely, i.'c L and K'c K, which are ASYMPTOTES to 



the curve. There are two foci (as in the ellipse) 8 and H, the position 

 of which may be thus found when the principal axis AM and the 

 asymptotes are given : from A draw A v perpendicular to the axis ; then 

 c s and c H are both equal to r v. 



The difference of the focal distances H P and 8 P is always equal to the 

 axis major A M : in the branch passing through A, H P is greater than 

 s p, and vice vend. The tangent r T always bisects the angle s p H ; and 

 p N, the ordinate perpendicular to the axis, being drawn, c A is always a 

 mean proportional between c T and c s. There is also a directrix, as in 

 the ellipse, found by taking on the line c s, c K, a third proportional to 

 cs and c A, and drawing through K a perpendicular to the axis ; and, as 

 in the ellipse, s p always bears the game proportion to p R, namely, t li .1 

 of c 8 to c A. And c 8 divided by C A is called the eccentricity, the dis- 

 tinction between the ellipse and hyperbola being that in the former the 

 excentricity U less than unity, and in the latter greater. The double 

 ordinate drawn through s or H is called the latui rectum of the hyper- 

 bola, and its half tho semi-ktus rectum. Thus far the resemblance 

 between the ELLIPSE and hyperbola is very visible : at the same time 

 it is obvious that there is nothing in the latter which answers to the 

 minor axis of the ellipse, or to conjugate semidiameters. But if anothat 

 hyperbola be described in the manner immediately to be pointed out, 

 a figure will be obtained which will enable us to point out properties 

 answering in all respects to those of the ellipse. Complete the rectangle 

 c A v B, and describe another hyperbola of which c u is the semi-axis, 

 and the same lines as before the asymptotes. This hyperbola is said 

 to be conjugate to the former one; and its foci ' and H' are at tho 

 same distance from the common centre as 8 and H. 



In the ellipse, c A was colled the major semi-axis, as being greater 

 than c B, the minor semi-axis. Let the words major and minor refer 

 to the importance of the several axes, and not to their magnitude. 

 Then c A is called the major semi-axis (or the semi-major axis) of the 

 hyperbola passing through A and M, and c B its semi-minor axis. Con- 

 versely, c B U the semi-major axis of the hyperbola passing through 

 B and B', and c A is its semi-minor axis. Generally, the major axis of 

 an hyperbola is that which cuts it, and the minor axis that which cuU 

 the conjugate hyperbola. 



As in the ellipse, the square on the ordinate p N is to the rectangle 

 of M s aud N A (which is the excess of the square of c R over that on 

 c A) in the proportion of the square on c B to the square on c A. If c D 

 be drawn parallel to the tangent p T, D is said to be conjugate to P, and 

 the semi-diameter c D conjugate to the semi-diameter c p. If the 

 gnrallelogram P c D K be completed, the point K will always fall on the 

 asymptote, and the other diagonal DP will be parallel to the ..'!.. r 

 asymptote. And c P, any semidiometer falling in the acute angle of 

 the asymptotes, always exceeds its aemiconjugate c D ; and the excess 

 of the square on c P over that on c D is equal to the excess of the 

 square on c A over that on c B. The area of the parallelogram c D K P 

 always remains of one magnitude, namely, equal to c A v B. Tho 

 rectangle of c w and w p always remains the same, namely, equal to 

 the square on half the line joining A and B. Any part of a tangent 

 K L, intercepted between the two asymptotes, is bisected by p, the 

 point of contact ; and if E c' be drawn parallel to K L, the interceptions 

 EF and E'r' are equal, and the rectangle of F. F and rx' is always 

 equal to the square on PK or PL. And the rectangle of the focal 

 distances H P and 8 P is always equal to the square of the semicon jugate 

 diameter c p. 



Any ordinate z I drawn parallel to a tangent o L is bisected by the 

 diameter c a drawn through the point of contact And the square on 

 T X is to the rectangle of D T and T a (or the difference of the squares 

 on c Y and o o) in the proportion of the square on c p to the square 

 on CD. 



A perpendicular let fall from a focus 8 upon a tangent P T meets the 

 tangent in a point of the circle whose centre is o and radius c A. 



If any number of hyperbolas be drawn having the same centre c 

 and the same major axis C A, and ordinatrs N P, s P', 4c., )>< drawn t" 



