THEIUACA. 



THERMO-ELECTRICITY. 



lie 



on to the xL The la.it value of x \tscd U greater than any root of 

 the equation : and the first value of r. A, U vary often the lat also. 



Jl . If each eo-t'flu-itfut which differs in sign from the Brat term, be 

 divided by the cum of all which precede and agree with the first term 

 (the first term iUelf included), the greatest resulting fraction, increased 

 by unity, i* greater than any positive root of the equation. 



Newton's method of finding a limit greater than the greatest 

 positive root of any equation now merges in Fourier's theorem. It 

 consists in finding a by inspection and trial, so that $a, <f>'a, f"a, 4c., 

 shall all be positive. 



Any mode of ascertaining a limit greater than the greatest posi- 

 tive root of an equation may be thus treated. Apply it to the reci- 

 procal equation ( 17>, and the reciprocal of the result attained is less 

 than the least positive root of the original. Apply both to the equa- 

 tion of roots with signs changed, and the results give limit* for the 

 negative roots of the original. 



V celebrated mode of examining the roots of equations, but too 

 complicated for ordinary use, consists in forming the equation whose 

 roots are the squares of the difference* of the roots of the original. 

 Any quantity being found less than the least positive root of thin new 

 equation, iu square root is less than the difference of any two roots of 

 the original. If such a quantity could be readily found, the theoretical 

 imperfection of Fourier's theorem would be greatly diminished, and, 

 practically speaking, much advantage would be gained in numerical 

 solution. What is wanted to add to both Fourier's and Homer's 

 method, is a ready mode of finding out when two roots are nearly 

 equal 



25. Lagrange's mode of approximation is as follows : Having found 

 that a root of an equation lies between the integers a and a + 1 , 

 diminish all the roots of that equation by a, and take the reciprocal 

 equation to the result. Find a root of the last lying between the 

 integers k and 6 + 1 , diminish all the roota by b, and take the reciprocal 

 equation of the result. Find a root of this last between c and c+l, 

 and proceed in the same way. Then the continued fraction 



1 1 1 



JTT frT JT' &c> 



is a root of the original. The details of the work are much abridged 



of Homer's process. 



26. When on equation has equal roots, those roots can be found by 

 on equation depending entirely on the different sets of equal roots. 

 If $x have m roots equal to a, <t>'.r lias m 1 of them, 4>"x has m 2 of 

 them, and so on ; finally, ^"-"x has one of them. If then <^c and 

 q>'x be found to have a common measure, every root of that common 

 measure enters in $x one time more than in the common measure 



tts*ie 



J7. When an equation has an integer root, which must bo one of 

 the divisors of the last co-efficient, it may be discovered by successive 

 trial, as follows : Suppose a.x' + a l x* + <i t x' + a l x + a t = 0, o,,, &c., 

 being integers. Let k be a divisor of o., and let a. : 1=1, an integer. 

 Then if k be a root, we have aJP + aJ? + aji + o, + /=0, and o s + i U 

 divmible by t, giving m, an integer. Hence ajc 1 + a,* + a +m = 0, and 

 a, + m divided by t gives an integer, say n. Hence o l- + o,-t- = 0, 

 and o, -m divided by Is gives a v If all these conditions be fulfilled, 

 t is a root. All the divisors of a, being tried in this manner, settle 

 the question of the integer roots entirely. 



28. If the co-efficients of an equation read backwards and forwards 

 be the same, both in sign and magnitude, every root has its reciprocal 

 also among the roots. By reducing it to the form 



namely the JtiOkridatuut (MifloiWr.wK, or 'Am'JoTos Mi/nSaTu>i) and 

 the Thrriant A nilromadti. 



The Miihnd.itiiim received its name from the great Mithridstea, 

 king of Pontus, who had a strange affectation of superior skill in the 

 powers of simples. He tried the effects of these upon condemned 

 malefactors, and, finding that different drugs counteracted different 

 poisons, he thought that, by putting all of them together, he should 

 be able to make a compound that would render him secure against any 

 poison that could be given him. (Galen, ' Do Antid.,' p. 2.) A- 

 ingly he is commonly said to have so fortified his own body by the 

 constant use of this antidote, that he afterwards tried in vain to 

 put an end to his life ; but this, if true, " was probably," as Dr. 1 1 

 den says (' Antither.,' p. 10), "less owing to the strength of his 

 antidote than to the weakness of his poison. 



AndromachtiH the Elder (who was physician to the emperor Nero, 

 and the first person who is known to have received the title of A rrfila- 

 ler) made considerable alterations in the Mitlmdatium by omitting 

 some of the ingredients, adding others (especially the dried flesh of 

 vipers), and by increasing the proportion of opium. His receipt was 

 embodied in a Greek elegiac poem, in order that it might be the more 

 easily preserved without alteration; and this has been insert*. 1 l-y 

 Galen in two of his works; (' De Antid.,' lib. i., cap. vi., et ' De Ther. 

 ad Pison.,' c. 6), and has been frequently published in a separate form. 

 Androiuachus likewise changed the name of the Mithridatium thus re- 

 formed to TOA^M) ; but in Trajan's time it obtained that of ' Theriaca,' 

 either from the vipers in it, or from its good effects in curing the bites 

 of venomous animals. (Galen, ' De Antid.,' lib. i., cap. 6 ; ' De T! 

 Pison.,' cap. 5., torn, xiv., pp. 82, 232.) The formula for the Th- 

 of Andromachus, as well as for others, is to be found in Geiger's 

 ' Pharmac. Universalis. Pars. Posterior,' p. 281. 



It is much to be regretted that the word ' Theriaca ' is applied to the 

 uncrystollisable juice which flows from sugar in the process of refining ; 

 for distinction's sake this should always be termed " Faex Sacchari," 

 or " Syrupus Empyreumaticus," anglicd, " Molasses," as in the I luMiu 

 ' Pharmacopoeia.' The uses of molasses (or melasses) ore well known. 



THEIiM/E. [BATHS.] 



THERMOCHB08IS. [RADIATION OP HEAT.] 



THERMO-ELECTRICITY. It has been shown, under GALVANISM, 

 that any obstruction to the passage of an electric current produces heat 

 in the conductor ; so conversely it has been found that any obstr 

 to the equal propagation of heat in a conducting circuit produces a 

 currrcnt of electricity. The discovery of this principle was in 

 1822, by Dr. Seebeck of Berlin, while engaged in researches concernin;,' 

 electro-magnetism, which but two years before had been discovert-'! >> 

 Professor Oersted of Copenhagen ; and the name thermo-electricity 

 was given to the fluid by the latter philosopher in order to distinguish 

 it from that which is produced by the usual galvanic apparatus, which 

 he proposed to call Ayi/ro-electricity. 



Some of the most simple experiments by which the effects of thermo- 



which can always be done by division, when the dimension in even, 

 and assuming y x + x', an equation of the 2nth degree can be re- 

 duced to one of the nth and n quadratics. But when the dimension 

 is odd, either 1 or +1 must be a root, and the equation can be 

 depressed to an even degree by division by z+1 or x1. 



The student who is acquainted with the preceding results, namely, 



such as are either stated or referred to in this article, will find no 



difficulty either in reading on the history of this subject, or in it* 



.'ion. It is peculiarly a subject on which selection should be 



made for the beginner. 



THKIUACA (eipuunl) was the name given orginally by the ancients 

 to all those medicines which were intended as antidote* to the bite of 

 venomous animals (fypia), as those which counteracted poisonous drugs 

 were called iAt(i$4tyioxa (Galen,' Comment, in Hippocr.' ' De Alim.,' 

 lili. iii., cap. 7, torn, xv., p. 279, ed. Kuhn ; id., ' Comment in Hippocr.' 

 De Morb. Vulgar. VI.,' lib. vt, cap. 5, torn, xvii., pt. ii., ] 

 afterwards, however, the word seems to have been soinuwh.it restricted 

 in its signification, or at least Vt)f>uur4(in the singular number) is applied 

 to one particular compound, while at the same time this one drug was 

 considered to be s safeguard not only against the bites of venomous 

 animal", but also against poisonous drugs and unwholesome food. 

 (Galen, ' De Antid.,' lib. i., c. 1, torn, xiv., p. 1.) Many of these old 

 preparations are preserved in the writings of the ancient physicians, 

 but of these it will be enough to mention here the two most famous, 



was attached (in close contact), at its extremities, to the ends of a bar 

 of antimony about 15 inches long; .mil the bar being laid in the 

 direction of the magnetic meridian with the wire above it, a small 

 compass needle was suspended, or supported on a pivot between tin -m. 

 On heating the northern extremity of the bar by the flame of a lamp, 

 the north end of the needle was observed to deviate towards the west. 

 Again, when a slip of zinc and one of copper were bent so that, on the 

 extremities being applied together, there was formed a parallelogram 

 having the junctions of the slips in the middle of the shorter sid 

 a compass needle was suspended within the circuit, on placing the 

 apparatus in a plane coinciding with the magnetic mrridian, with tin- 

 longer sides parallel to the horizon (the copper slip beiiif,' upp< 

 :uni heating the northern point of junction, the needle deviated t.. 

 the west : the apparatus being inverted so that the zinc slip was \ 

 most, on heating the northern junction as before, the needle d 

 towards the east. It follows from these experiments that the ilni.l 

 current, if such it be, which affects the magnetism of the needle, i-ii.-u- 

 lates about the copper slip in such a manner that when the latter 

 horizontal position its direction is from west to east, passing above t h 

 in a plane perpendicular to its length : this effect is similar to that v Im-h 

 takes place, though in a contrary direction, when a magnetised i 

 U brought near a conducting wire joining the poles of an ordinary 

 galvanic apparatus ; for if the conducting wire be placed in a hori- 

 zontal position in the direction of the magnetic meridian, with the 

 copper, or the negative end of the apparatus towards the north, and the 

 needle be below the wire, the north end of the needle deviates t< 

 the east ; if above the wire, towards the west. 



Effects similar to those which result from the application of heat 

 take place when one extremity of the bar of antimony, or one of the 

 junctions of the zinc and copper, is made colder than the other i,\- 

 means of ice. 



When both ends of the bar were heated, no deviation was produced 

 in the needle ; and after deviation had taken place by heating one end 

 only of the- bar, in proportion as the heat tended to a uniform diffusion, 

 the needle gradually returned to the direction of the magnetic 

 meridian. 



