326979900

328006900

We first put down the coefficients as usual, not changing the sign of the last (which is only a convenience for evolution, and does not alter any figure). The value of x being 121-23, we begin with 100, which, having two ciphers, we mark off by commas from the several coefficients 0, 2, 4, 6 places. We then proceed by Horner's process with the figure 1 (not 100), taking care to make commas fall under commas, or to use the commas as if they were decimal points (which they are in fact, though not unit-points). As soon as we have done the first process, containing all that comes before the lines A, we learn as follows. Let

px=9x3-3141x2 + 009x1427.499

then, x being 100, px, p'x, p''x, and "" are severally 8967163-401, 269371-809, 2696-859, and 9. We then write down the results again, after the lines A (which is not necessary in calculation), merely to show the new disposition of the commas. We are now to proceed with 20 (from the first 2 in 121-23), which, having one cipher, we mark off 0, 1, 2, 3 places in the several columns. Immediately before the lines B we learn that when x = 120, px, p'x, and "x are severally 15505343 181, 388046-169, and 3236-859. We then write down these results without any commas, and proceed with the second 1 in 121, from which we find that when x=121, the functions are 15896635-209, 394546 887, and 3263-859. We then begin to provide for the decimal point, by annexing one, two, and three ciphers to the working columns, and taking the second 2 in 121-23 to work with, and applying Horner's process, we find, when r=121-2, that or, o'x, and ox, are severally (remembering that all the annexed ciphers are so many additional decimal places) 15975675-212760, 395853-51060, and 3269-2590. Finally, we annex the ciphers again, and with the 3 we find that x = 121-23 gives 15987553-760654100, 396049-6904400, and 3280-06900.

Let us now compare the trouble of this process with that of any other method of doing the same. If we throw out all the figures which we have written twice over merely for explanation, and also the last two and one lines in the second and third columns, which are only wanted to go on further with, we have written down about 280 figures. The ordinary verification costs about 340 figures. It is true that every step is both a multiplication and an addition in one: but this can be done and ought to be done in the use of this method, and is not done in the ordinary method. And we have not only the advantage of a purely mechanical method, in which the first arrangement causes the succeeding steps to require nothing except a look at the successive figures of the value, but the still greater advantage of being able, at the end of the process, to make any small alteration of value with ease. If, for instance, having discovered that 121.297 would do better than 121.23, we wish to get additional accuracy, we have but to rub out the last 3-process, and proceed with 9 and 7. In the ordinary mode, we must either repeat the whole process again, or correct approximately by substituting 121·23—·003, which will require us to calculate p', and perhaps "x.

We shall now exhibit a common multiplication, and the formation of a square: not, of course, that we attach any particular value to these simple cases, but that we may show the uniformity of the process. Required 14796 × 32316, or the value of 14796x +0 when x=32316. We repeat the lines as before, which is more than is necessary, and makes this process look very long.

The process here described is one which, we venture to say positively, has neither been put in its right place, nor received its due reward. It is the natural extension of the common process of multiplication, and its inversion is as naturally and necessarily the proper mode of solving equations, as the inversion of multiplication is the same for the simple equation ax=b, or common division. The inventor of it must rank, not with the analyst or the algebraist, commonly so called, but with the discoverer of the process of multiplication and division, and the extraction of the square root.

The application of this method to the solution of pr=0 consists in finding the first figure by trial, and making use of the Newtonian approximation to find successive figures: namely, that if a be nearly a value of x, a-pa: q'a is more nearly so. This method becomes difficult when two roots are nearly equal; but the difficulty lies in what may be called Newton's part of the complete method, not in Horner's part. When the difficulty of algebra shall be conquered, the process of arithmetic may easily be amended in the trial part; but to suppose that a capital improvement in the manner of conducting computations is little worth, because it is not accompanied by a victory over difficulties of quite another kind, is unreasonable. With a little more trial, Horner's method may be applied to the case of nearly equal roots; and as it is, it is more efficacious in discovering them than any other method. To what has been said upon the method, we may add the following remarks:-1. When the last term is positive, and would in the ordinary process be made negative, it is often better, instead of changing the sign of the last coefficient only, to change the sign of all but the last. Thus in solving 3-11x+1=0, the heads of the columns, - 1, 0, 11, and 1, instead of 1, 0, - 1. Also, should be - 11, and that if at any period of the process the divisor and dividend columns should become negative, the signs of all should be immediately changed. 2. In making the contractions, it will be advisable to make the figure which comes next after the separating line correct, to continue it, in fact, till the next contraction, and to use it to carry from. This is not done in what precedes, but it is done in the instance in COMPUTATION. In that instance, the following figures, seen one over the other in the last column but one, as follows, 3, 5, 7, 6, 9, 1, -2, 2, 2, are figures cut off by the contraction, but made up from the second column to carry from into the fourth.

3. If, at the beginning of the process, all the heads of the columns be multiplied by 9, the root will not be altered, and, until the contraction begins, the verification by casting out nines is rendered easy, since every result in every column is divisible by 9. We shall now show how the process works in some equations which have equal, and nearly equal, roots.

Let x-6x+9=0, which has two roots, each equal to √3.

The existence of equal roots, or of nearly equal roots, might be here suspected from the slow increase of the divisor column; but the method cannot verify the fact of their being two absolutely equal roots. The column preceding the divisor column being large and negative, requires us to make trial of figures above, not below, those which the divisor column seems to indicate. But nearly equal roots may sometimes be detected, as in the following instance. Let 7x3-10x2-14x+ 20=0, of which it is known that one root lies between 1 and 2. The ordinary process gives

10

14

3

17

-46

75

38 (2·11111

0

-19694

28460 28440

This root may be carried on without difficulty. But at the end of the second process, when the dividend is reduced to 8000, the divisor only 8400, and the preceding column as much as 1940, it may be worth while to try another figure. This state of things gives a suspicion that there is another root in the immediate vicinity of the one in hand. If the three last columns be +a, b, and c, and if we find that pa+b is nearly c÷p, which is the trial test of p being a new figure of the root, we are sure that (p+1) a+b will not be near c(p+1): and moreover p (pa+b)=c has not two positive roots. But if the three last columns be -a, b, and c, it may very easily happen that b-pa may be nearly c÷p, and b―qa nearly c÷q; for p (b−pa)=c has two positive roots. Perfect certainty, in the absence of an easy algebraical criterion, may only be attainable by trying every figure. In the instance before us, finding 141 succeed, with a presumption of a larger root, we try 1:43, beginning with

problem, and of the controversies which have existed, and to some We shall now proceed to a short account of the history of this extent still exist. For a fuller account of it up to the time of Mr. Horner, see a paper by the writer of this article in the 'Companion to the Almanac,' for 1839.

performance of division, and extraction of the square and cube roots, in Before the time of Vieta, evolution consisted in the rules for the forms probably derived from the East. To him [VIETA, in BIOG. DIV.] we owe the first publication of a numerical method of finding the successive figures of the root of an algebraical equation by means of the value of the function equated to zero in the equation. This method of Vieta is in fact that which Horner's process now makes so easily practicable. If px=0 be the equation, and a a part of the root, it uses pa, and p (a+1) — pa as a divisor. The process is so cumbersome, that Vieta does not attempt to apply it to equations having more than two figures in the root.

This method attracted but little attention on the continent: but in England, where everything relating to numerical calculation has been always diligently studied, it was much noticed, and received extensions of power. In the posthumous work (1631) of Harriot [HARRIOT, in only so many figures of the divisor as are wanted: and he ventures upon roots of three places. In the second edition of Oughtred's 'Clavis Mathematica' (1647) Vieta's method is given without Harriot's improvements. But the first who used Vieta's method to any great extent was Briggs, in the calculation of the sines, &c., in the Trigonometria Britannica.' In the preface the method is applied to equations of the third and fifth degrees, and partially described for the seventh and higher degrees: with examples carried to fifteen and sixteen figures of the root. It is for the facilitation of these solutions that the Abacus TаYXρηOTOS is given, which some have unreasonably interpreted as giving Briggs a claim on the binomial theorem. Gellibrand tells us that Briggs formed his tables of sines by algebraic equations and differences about thirty years before his death. Now Briggs died in 1630, and Vieta's tract appeared in 1600: the former must then have received the work soon, immediately seen the importance of the method, and commenced operations by means of it. We cannot give Briggs any independent title to the invention; for it is likely enough that he was in correspondence with Vieta, whose works he certainly knew. One of his examples is the solution of what would now be written

x3-3x = 1.298896096660366

for which he gets x = 1.917639469736386. He puts down the work time: and he has got what Vieta had not, the Newtonian divisor o'x as far as...697, proceeding towards the end by several figures at a instead of p(x + 1) - px. Of course it adds materially to the historical value of this method that it was thus used in an operation of so much importance to the progress of mathematics in general. The solving equations thus suddenly acquired, which first suggested the calculation of the natural sines, &c., in the Trigonometria Britannica.'

the roots of which are 1.111..., 1.222 ..., and 1.233... Whatever common figures two roots of ox=0 may have begun with, there must be a root of 'x=0 which begins with these figures. And whatever common figures three roots may begin with, there must be two roots of p'x=0, and one root of p'x=0 which begin with those figures and so on. If there were a difficult equation having three roots nearly equal, no method of detecting them would be easier, of all those known at present, than solving contemporaneously the three equations px=0, q'x=0, p'x=0, not making any step in one till all

ARTS AND SCI. DIV. VOL. IV.

Wallis, in his Algebra (1684), gives the method of the " numerose exegesis," as he calls it (Vieta had called it potestatum adfectarum ad exegesin resolutio) with an example of the fourth degree worked to seventeen places of the root. He makes use of the method of contracting the figures towards the end. In this same Algebra appeared, for the first time, what is called Newton's method of approximation, which soon superseded the exegesis, into which however it had been virtually incorporated by Briggs. Newton's approximation, at least in the general form which it took in the hands of Taylor, is as follows. If a be a near value of x in px 0, then, except when there are two nearly equal roots, a nearer value is

The old exegesis, and especially Briggs's form of it, employs this principle; pa is calculated, and either p'a or p(a + 1) — pa. Briggs, who proceeds by several figures at a time, and uses p'a, does really use what was afterwards called Newton's method, and assists it by operations suggested by Vieta. When the exegesis was abandoned by Raphson and others, in favour of Newton's form of operation, no further improvement was made in the direct numerical solution of equations, until the time of Mr. Horner; at least no further improvement was published. Mr. Henry Atkinson, a young man of Newcastle, re-invented the whole method in 1801, ap; lying Newton's divisor, and giving rules by which one divisor was made to help in forming the next. This was read to the Philosophical Society of Newcastle in 1809, and published posthumously, as 'A new Method of extracting the Roots of Equations,' Newcastle, 1831, 4to. In our article in the Companion to the Almanac, already cited, we have supposed that no one can be shown either to have used p'a, or to have made each value of it help the next, before Mr. Atkinson: but we now find that Briggs was before him in both points. Lagrange's method of transforming the root into a continued fraction [THEORY OF EQUATIONS] does not need notice here, because it belongs to another mode of expression. But it ought to be noticed that Horner's process very much abridges the labour of Lagrange's method, as much indeed as it does that of Vieta's exegesis, and for the same reason. Mr. Exley, of Bristol, in the Imperial Encyclopædia,' article ARITHMETIC, improved (according to Horner himself) the common method of extracting the cube root, so as to precede Horner in this particular case. We believe more than one method had been given for reducing the enormous labour of the ordinary extraction of the cube root: we may mention one, which is ingenious and effective, and almost exactly a particular case of Horner's method, given by Mr. A. Ingram, in his edition of Hutton's Arithmetic,' Hawick, 1811, 8vo. : and Horner himself refers to an edition of Melrose's' Arithmetic,' by Mr. Ingram (the same, we suppose) as containing such a method. Horner's paper was read to the Royal Society on the 1st of July, 1819, and was published in the current volume of the Transactions, on the 1st of December. These dates are of importance: the publication of the above paper was the signal for more than one person to make a nibbling claim to the invention. Horner was unfortunate in two points. First, he had not sufficient knowledge of ancient algebra to be aware that his method contained the process of Vieta, and that his real claim consisted in the discovery of the beautiful process by which the labour is immensely reduced, and completely systematised: we suspect that he completely re-invented Vieta's part for himself. Secondly, he appears to desire to be the analyst rather than the arithmetician, and will not show anything except to those who can take all. It is true, beyond a doubt, that his method is adapted to every sort of equation, and that it is as great a help to the person who desires to solve tan x - ax = 0, or sina = x, as to the other who wants nothing but a common algebraical equation. So far, then, it is more than Vieta's method simplified; it is the same also extended. But if the inventor had proceeded from simple algebra to the more complicated cases, his merits would have been more rapidly appreciated. He did not well see that his mode of solution applies as well to the integer part of the root as to the fractional; nor did he fully comprehend how much of his own discovery consisted in the general mode of calculating the value of ox, as given at the beginning of this article. But that we may not do him injustice, and still more that we may enable those of our readers who have not access to the original paper to see how completely he had got hold even of the most convenient arithmetical process, we give his solution of the famous Newtonian instance x3 -2x=5. After reducing the root by 2, the heads of his columns are 1, 6, 10, and 1 (the first column, which is always vacant, he does not set down). He then annexes either dots or ciphers, and proceeds exactly as follows

*

'A new Method of Solving Equations,' by Theophilus Holdred, London, 1820 (preface dated June 1), 4to. The method is taken from Harriot; and a supplement is added, which gives Horner's method. Both are claimed as independent inventions, and Horner's name is not mentioned. Mr. Holdred asserts that, after having had his method for forty years he was led to that in the supplement by a mistake he committed in solving an equation sent him by one of his subscribers. We have given, in the article of the Companion to the Almanac,' already cited, our reasons for coming to the conclusion that Mr. Holdred took his first method from Harriot, and his second from Horner. A claim was made by Mr Peter Nicholson in various places, which is quite futile. We acquit Mr. Nicholson (a highly respectable man, eminent in the application of mathematics to the arts) of all unfair intention: and we must remind our readers of a point without the knowledge of which the various controversial writings on this subject will be full of confusion. Hardly any one knew of Vieta's Exegesis, which there is little doubt that both Horner and Atkinson reinvented. In fact, so completely had this exegesis dropped out of sight, that even Dr. Peacock, in his short account of Horner's method (Report on Analysis to the British Association') does not allude to it. Accordingly, all the re-inventors of Vieta's method speak of quite new rules discovered for the solution of equations, and treat Horner's process as a constituent part of one of the new inventions. But a person acquainted with the history of the subject finds nothing new except Horner's process. Vieta had the main system, Briggs had the Newtonian divisor, Wallis had the method of contraction, Briggs had a method of making one divisor help the rest: Horner had the method which must finally be adopted. Budan, as we shall see, had only a particular case of that method, and did not apply it to any mechanical process of numerical solution.

Mr. Nicholson claims Horner's identical process, and fairly refers to the very place in which he says it is to be found. But on looking there (see the article already cited in the Companion to the Almanac '), we find that he has been deceived by a distant resemblance, and that, though he has given a new and useful process for a useful purpose, neither the process nor the purpose is Horner's. At the same time it is but justice to Mr. Nicholson to say, that in his 'Elements of Algebra,' London, 1819,† 12mo, he made as near an approach to Horner's method as could well be done, and applied it in the case of equations of the second and third degrees. The succession of columns is seen, each column helps the next, and each step in any one column helps the next step. But the grand simplification, which the controversialists called the "non-figurate method," is wanting: so that this process of Nicholson's is perhaps hardly more than Briggs was in possession of. Mr. Nicholson had received Mr. Holdred's method, whose name he properly mentions in the preface. This method he had greatly improved; and it seems he wished that Holdred should publish his own method as amended by him; but he asserts (in the preface to his work on Involtion and Evolution) that the latter refused, alleging that his own credit would be diminished, unless he could pass them as his own.

Dr. Peacock had never seen Holdred's tract, and his result, derived from the assertions of Mr. Nicholson and from Horner's paper, is that Nicholson, by a combination of the methods of Holdred and Horner, reduced the method to its present practicable form. But any one who will solve 3-2x=5 in the systematic form we have given, will see that Horner had that form. Nicholson was, we believe, the one who first clearly saw that the method, in its simplest organisation, applies as well to the integer as to the fractional portion of a root. All Mr. Nicholson's simplifications, as given in his latest writings, consist in doing in the head some of the things which Horner put down on paper. The form we give carries this still further; and those who can do what we have recommended all arithmeticians to practise in COMPUTATION can follow us: but there is no invention in this.

Some have been disposed to give a good deal of the merit of this system to Budan; and his claim must be considered. Two editions of the Nouvelle Méthode pour la Résolution des Equations numériques,' Paris, 4to., were published in 1807 and 1822. The basis of M. Budan's operations is the simple case of Horner's process in which the root of an equation is diminished by unity. This is done exactly in the mode by which Horner afterwards proceeded. Thus to lessen the root of x3-2x-5-0 by unity, Budan proceeds thus :—

1+0-2-5 1+1-1-6

(A) 1+2+1

1+3 1

Answer 3+3x2+x-6=0

But to lessen the root by 2, Budan is never able to arrive at the

We cannot but believe that Mr. Holdred did see Mr. Horner's paper. Had he mentioned it, and the name of the subscriber, his equation, the mistake made, &c. &c., distinctly declaring when and where he first saw Mr. Horner's paper, he might have possibly established a claim to be a second inventor. †The preface is dated May 17, 1819, and the publication took place early in July, Mr. Horner's paper having been publicly read at the Royal Society on the

The same difficulty must exist in every method, as matters now stand. In the meanwhile, we think the discoverer of the process, which is now beginning to take its proper place, deserves attention to his request when he says, speaking of the antagonist claims which had started up-"All I ask of them (mathematicians) in recompense for the facilities consigned to their use in the non-figurate method, is to bear in mind that I alone am the author of it." And we have no doubt whatever, and are willing to stake our credit upon it, that when the inertia of the higher mathematicians in matters of computation is overcome, and when the mode of solving equations has reached the schoolboys, as it is rapidly doing, the name of Horner will be one of the household words of pure arithmetic, and himself looked upon as one of the greatest of its modern benefactors. Justice requires that his name should remain attached to his process.

IOD or IODO. A prefix used in chemistry to signify that the body to the name of which it is attached contains iodine substituted for some other element. Such compounds will generally be found described under the name of the body to which this prefix is attached.

IODAL (CHI,O,) Hydride of tri-iodacetyl. A body analogous to CHLORAL, said to be produced by mixing alcohol with nitric acid and then adding iodine. Its existence has not been satisfactorily established.

IODANILINE (CH.IN). A derivative of aniline. [ANILINE.] IODHYDRIN (C12HIO). A liquid compound produced by the action of hydriodic acid upon glycerin. [GLYCERIN.]

IODIC ACID. [IODINE.]

IODIDES. [IODINE. Hydrogen and Iodine.]

IODINE (I), a non-metallic, elementary, or simple solid body, discovered by M. Courtois, of Paris, in 1812. Its peculiar properties were however first ascertained by Gay-Lussac and Davy. Iodine exists in the water of the ocean and mineral springs, probably combined with sodium, or calcium, or magnesium; also in marine molluscous animals and sea-weeds; and has been met with in combination with silver. Iodine is principally obtained from kelp, or sea-weed which has been burnt for the purpose of obtaining alkali from it. When the alkaline and other salts have been separated from this ash, the residual solution is treated with sulphuric acid and binoxide of manganese, by which the iodine is set free, the decomposition being analogous to that by which chlorine is obtained by the same agency from common salt.

The process is conducted in leaden retorts of cylindrical form, and heated on a sand-bath to a temperature not exceeding 212° Fahr., a higher heat than this causing loss from the formation of chloride of iodine. At this temperature the iodine slowly vaporises, and passing off through the neck of the retort is condensed to the solid form in a series of flasks connected together by the neck of each passing through a hole in the bottom of the one preceding it.

Iodine is a soft opaque solid, of a bluish-black colour and metallic lustre. The primary form of the crystal is an acute rhombic octohedron. The crystals are usually flat. According to Gay-Lussac, its specific gravity is 4.947. When moderately heated, it rises in vapour of a violet colour, and hence its name from the Greek (úons, “violetcoloured"). On cooling, it again crystallises unchanged, nor is it altered by being subjected to very high temperatures; it has resisted all attempts to decompose it. Iodine has a strong disagreeable odour and taste, somewhat resembling bromine and chlorine; it stains the skin of a brownish colour, but not permanently. It is readily dissolved by alcohol, and the solution is of a reddish-brown colour; so little is taken up by water that a pound of that liquid will not dissolve more than a grain of iodine. It is very poisonous. Its characteristic property is that of giving an intense blue colour when added to a solution of starch. It unites with metals to form compounds, termed iodides; these are all decomposed by chlorine, or even bromine, iodine being liberated. They will be found described under the names of the respective metals. Iodine, like chlorine and bromine, forms acids both with hydrogen and oxygen.

The equivalent of iodine is 126.8; its combining volume, 2; and the specific gravity of its vapour, 8.716.

Oxygen and Iodine combine to form probably four compounds. When the vapour of iodine and oxygen gas are mixed at rather a high temperature, the violet tint of the iodine disappears, and a yellow soft substance is formed, which is regarded by Sementini as oxide of iodine; if this be subjected to the action of more oxygen gas, converted into a yellow liquid, which the same chemist supposes to be iodous acid; but the composition and properties of these compounds have not been accurately determined.

it is

lodic Acid (10).-This compound was first obtained by Davy by the action of iodine upon what he called euchlorine gas. A better process however consists in heating the iodine in the strongest nitric acid. For this purpose the acid should be introduced with about a fifth of its weight of iodine into a capacious retort, and kept boiling for 12 hours; the iodine which rises and condenses on the sides of the retort is to be returned to the acid either by a glass tube or by agitation; when the iodine disappears, the excess of nitric acid is to be got rid of by evapo

ration. Iodic acid is a white semi-transparent solid substance, which may, however, be obtained in crystals containing one equivalent of water (HO, IO,). It is inodorous, but has an astringent sour taste. It is so dense as to sink in sulphuric acid, and it deliquesces in a moist atmosphere. It is very soluble in water; the solution reddens vegetable blue colours; it detonates when mixed and heated with charcoal, sugar, and sulphur. When crystals of iodic acid are heated to 360° Fahr., they become anhydrous, and at about 700° are decomposed into iodine and oxygen. Iodic acid combines with metallic oxides to form salts, which are termed iodates, containing one, two, or three atoms of acid to one of base, and these, like the chlorates, yield oxygen when heated; an iodide remaining.

Periodic Acid (IO,).-When chlorine is added to saturation to a solution of iodate of soda with excess of the alkali and concentrated by evaporation, a sparingly soluble white salt is obtained, which is periodate of soda; when this is dissolved in dilute nitric acid and mixed with nitrate of silver, a yellow precipitate falls, which, dissolved in hot nitric acid and evaporated, yields orange-coloured crystals of periodate of silver; these are decomposed by cold water, and an aqueous solution of pure periodic acid formed; this by cautious evaporation yields crystals, containing five equivalents of water of hydration. When heated to 212°, they are resolved into oxygen and iodic acid. Nitrogen and Iodine appear to form three distinct compounds, containing respectively NHI, NHI,, and NI,, derived no doubt from ammonia (NH) by the substitution of hydrogen by iodine, thus:

Iodide of nitrogen, or probably, a mixture of the iodides, is best prepared by dissolving iodine in aqua regia, and pouring the mixture into strong solution of ammonia; it then precipitates as a pucecoloured powder; or iodine may simply be powdered and digested at once in the ammonia, when an iodide remains insoluble in the state of a dark brown powder. This compound is very explosive, especially when dry: the best method of exhibiting its power is that of allowing it to dry in small portions on bibulous paper, and then simply letting it fall on the ground or merely touching it, when it detonates with a sharp noise, heat and light being emitted, and the vapour of iodine and nitrogen gas evolved. It is not dangerously explosive in quantities of 3 or 4 grains.

Hydrogen and Iodine form hydriodic acid (HI), which may be prepared by the direct combination of its elements. When a mixture of iodine in vapour and hydrogen gas is passed through a red-hot porcelain tube, they combine to form this acid. It is however much more conveniently formed by heating in a retort ten parts of iodide of potassium, five of water, and twenty of iodine, and cautiously dropping in one part of phosphorus cut into small pieces; hydriodic acid then passes over in the state of a colourless gas, and may be collected by displacement in dry bottles. This acid has a sour taste, reddens vegetable blues, and when mixed with atmospheric air forms dense white fumes with its moisture: its odour resembles that of hydrochloric acid gas.. It is soluble in water. The salts which it forms are termed iodides. When it is acted upon by metals, hydrogen is evolved, and when by metallic oxides, water is formed, and in both cases iodides result.

It is decomposed by oxygen when they are heated together; water is formed, and iodine evolved. It is also immediately decomposed by chlorine, which unites with its hydrogen to form hydrochloric acid, and iodine is set free.

Chlorine and Iodine form two chlorides. The protochloride (ICI) may be obtained by passing a current of chlorine gas into water in which iodine is suspended. A deep reddish solution is formed that yields irritating fumes possessing the smell of both the elements: it first reddens and then bleaches litmus paper. The terchloride (ICI) is best formed by acting upon iodine with excess of dry chlorine gas. It forms fine ruby-red crystals.

Bromine and Iodine form compounds corresponding with the chlorides.

Sulphur and Iodine.-Four parts of iodine and one of sulphur combine on the application of gentle heat, and yield a product of dark colour and radiated crystalline structure. It is easily decomposed by heat.

Phosphorus and Iodine unite in two proportions. The biniodide (PI) is formed by dissolving one equivalent of phosphorus in bisulphide of carbon, and adding two equivalents of iodine. On cooling the mixture to a very low temperature, acicular crystals of orange colour are deposited. The teriodide (PI) is produced in a similar manner to the last, three equivalents of iodine being used instead of two. It forms dark red tabular crystals.

Carbon and Iodine appear to form no true compound. IODINE, Medicinal Properties of. Iodine, though only obtained in an isolated state in the year 1811, has been long employed as the efficient principle of other preparations and therapeutic agents, namely, burnt sponge and certain mineral waters. [WATER, subsect. Mineral, in NAT. HIST. DIV.] It is only since it has been procured as a distinct principle that its action has been ascertained with precision. In the present day it is administered rather in some artificial compound than as pure iodine, owing to its very sparing solubility in water. Iodine in substance,