in botany, called by the Dutch Kooker-boom or Quiver-tree, is a native of the southern parts of Africa, and seems to be a species of the Agave or American aloe (see Agave, Encycl.). It is thus described by Le Vaillant in his New Travels into the Interior Parts of Africa: "The aloe dichotoma rises to the height of 25 or 30 feet; its trunk is smooth, and the bark white. When young, and the trunk not more than four or five feet long, it terminates with a single tuft of leaves, which, like those of the ananas, spread and form a crown, from the midst of which all its flowers issue. As it grows older, it puts out lateral branches, perfectly regular and symmetrical, each of which has at its extremity a crown similar to that of the young plant." The kooker-boom thrives much better on mountains than in the plains. Instead of long roots penetrating deep into the earth, like those of other trees, it has but a very slight one by which it is fixed to the soil. Accordingly, three inches of mould are sufficient. ALPHONSUS X. king of Leon and Castile (see Encycl.). This prince undertook astronomy, philosophy, and history, as if he had been only a man of letters; and composed books upon the motions of the heavens, and on the history of Spain, which are highly commended. "What can be more surprising (says Mariana), than that a prince, educated in a camp, and handling arms from his childhood, should have such a knowledge of the stars, of philosophy, and the transactions of the world, as men of leisure can scarcely acquire in their retirements? There are extant some books of Alphonso on the motions of the stars, and the history of Spain, written with great skill and incredible care." In his astronomical pursuits he discovered that the tables of Ptolemy were full of errors; and thence he conceived the first of any the refutation of correcting them. For this purpose, about the year 1240, and during the life of his father, he assembled at Toledo the most skilful astronomers of his time, Christians, Moors, and Jews, when a plan was formed for constructing new tables. This task was accomplished about 1252, the first year of his reign; the tables being drawn up chiefly by the skill and pains of Rabbi Isaac Hazan, a learned Jew, and the work called the Alphonsine Tables, in honour of the prince, who was at vast expenses concerning them. He fixed the epoch of the tables to the 30th of May 1252, being the day of his accession to the throne. They were printed for the first time in 1483, at Venice, by Radtoldt, who excelled in printing at that time. This edition is extremely rare: there are others of 1492, 1521, 1545, &c.
In the Encyclopaedia it is said, that the charge of impiety brought against this prince was unjust. This was said too confidently, because we know not of any direct proof of his innocence. All that has been said Alphonso for him by Dr Hutton, one of his ablest apologists, amounts to nothing more than a high degree of probability that the charge was carried by much too far. The charge itself was, that Alphonso affirmed, "that if he had been of God's privy council when he made the world, he would have advised him better." Mariana, however, says only in general, that Alphonso was so bold as to blame the works of Providence, and the construction of our bodies; and he says that this glory concerning him rested only upon a vulgar tradition. The Jesuit's words are curious: "Emanuel, the uncle of Sanchez (the son of Alphonso), in his own name, and in the name of other nobles, deprived Alphonso of his kingdom by a public sentence; which that prince merited, for daring feverishly and boldly to censure the works of Divine Providence, and the construction of the human body, as tradition says he did. Heaven most justly punished the folly of his tongue." Though the silence of such an historian as Mariana, in regard to Ptolemy's system, ought to be of some weight, yet we cannot think it improbable, that if Alphonso did pass so bold a censure on any part of the universe, it was on the celestial sphere, and meant to glance upon the contrivers and supporters of that system. For, besides that he studied nothing more, it is certain that at that time astronomers explained the motions of the heavens by intricate and confused hypotheses, which did no honour to God, nor any wise answered the idea of an able workman. So that, from considering the multitude of spheres composing the system of Ptolemy, and those numerous eccentric cycles and epicycles with which it is embarrassed, if we suppose Alphonso to have said, "that if God had asked his advice when he made the world, he would have given him better counsel," the boldness and impiety of the censure will be greatly diminished.
Such is the apology made by Dr Hutton for this royal astronomer of Spain; and we hope, for the honour of science, that it is well founded. Still it leaves Alphonso guilty of great irreverence of language, which is to us wholly unaccountable, if it be really true that he read the Bible fourteen times. We have seen impiety indeed break out lately from very eminent astronomers of a neighbouring nation; but these men read not the Bible, nor any thing else, but the dreams of the eternal sleepers.
**ALTERNATE ANGLES.** See Geometry (Encycl.), Part I. 35.
**Alternate Ratio, or Proportion,** is the ratio of the one antecedent to the other, or of one consequent to the other, in any proportion, in which the quantities are of the same kind. So if $A : B :: C : D$, then alternately, or by alternation $A : C :: B : D$.
**Altitude, Parallax of,** is an arch of a vertical circle, by which the true altitude, observed at the centre of the earth, exceeds that which is observed on the surface. See Parallax (Encycl.) and Astronomy (Suppl.)
**Altitude of the Nonagecimal,** is the altitude of the 90th degree of the ecliptic, counted upon it from where it cuts the horizon, or of the middle or highest point of it which is above the horizon, at any time; and is equal to the angle made by the ecliptic and horizon where they intersect at that time. Altitude, Altitude of the Cone of the Earth's or Moon's Shadow, the height of the shadow of the body made by the sun, and measured from the centre of the body. To find it say, As the tangent of the angle of the sun's apparent semidiameter is to radius; so is 1 to a fourth proportional, which will be the height of the shadow in semidiameters of the body.
ALUM is a salt so useful in commerce and the arts, that the knowledge of its component parts, and of the best method of preparing it, must be of importance. In the article Chemistry (Encycl.), the opinions which were then held respecting its composition, and the practice which was generally followed in its preparation, have been detailed at full length; but some of these opinions have since been controverted, and if they be erroneous, it must be expedient to vary in some degree the mode of preparation. In particular, the opinion that it is merely an excess of acid which prevents the formation of alum by evaporation of the ley, has been shown to be false by Citizen Vauquelin, who contends, of course, that the addition of putrid urine to the ley is a very bad practice.
This eminent chemist had long suspected, that the crystallization of alum is not prevented by an excess of acid, and that pot-ash is not of use simply to saturate this acid, but to perform an office of more importance. To bring his suspicions to the test of experiment, he dissolved very pure Alumine in sulphuric acid of equal purity, and evaporated the solution to dryness, for the purpose of expelling the superabundant acid. He then redissolved the dry and pulverulent residue in water, and reduced the solution to different degrees of specific gravity, with a view to seize the point most favourable to crystallization; but with every possible precaution he could obtain nothing but a magma (see Magma), formed of saline plates, without concretion or solidity. This solution, however, though it constantly refused to afford crystallized alum alone, afforded it immediately by the addition of a few drops of the solution of pot-ash; and as he had employed these two substances in the requisite proportion, the rest of the solution, to the very end, afforded pure alum, without any mixture of sulphate of pot-ash.
Into another portion of the same solution of pure alumine he dropped the same quantity of carbonate of soda, as he had added of that of pot-ash to the former; but no crystallization was formed, even by the help of evaporation, nor did lime and barytes produce any better effect. But if the common opinion that pot-ash, in the formation of alum, is of use only to abstract the excess of acid, be true, soda, lime, barytes, and all the substances which by a more powerful force would take this acid from alum, ought to give the same result. Another argument presented itself, which seemed decisive: If the alkalis, pot-ash, and ammonia, do nothing more than unite to the superabundant acid of the alum, the sulphates of pot-ash and of ammonia ought not to occasion any change in pure alum in its acidulated state; whereas if these alkalis enter as a constituent part into the alum, and are necessary to its existence, they ought to produce the same effects as pure pot-ash or ammonia. He therefore added to a third portion of the solution of sulphate of alumine before-mentioned some drops of the solution of sulphate of pot-ash; immediately upon which octahedral crystals of alum were formed. The sulphate of ammonia presented the same effect.
This result gave still greater confirmation to his first notions, though it did not yet afford a demonstration perfectly without objection; for it might have happened that the two salts he made use of might determine the crystallization of the alum, simply by absorbing the superfluous acid, of which they are very greedy; but to determine this possible fact, he mixed in the uncrystallizable solution of alumine some sulphate of pot-ash with excess of acid, and obtained a crystallization no less abundant than with the neutral sulphate of pot-ash.
This last experiment leaves therefore no doubt with regard to the influence and mode of action of pot-ash and ammonia in the fabrication of alum; and this action is still more strongly confirmed by the examination of the alums which have been formed by the processes above related; for in this manner it is proved that they contain considerable quantities of the sulphates of pot-ash and ammonia.
These experiments led M. Vauquelin to an examination of the different alums of commerce, of which he found not one that did not afford sulphate of pot-ash, or of ammonia, or of both. His methods of analysis are very accurate; but to detail them at length would swell this article to little purpose. To such of our readers as are not chemists they would hardly be intelligible; and the experienced chemist will devise methods of analysis for himself. It may be proper, however, to observe, that M. Vauquelin proved, to his own satisfaction, that the sulphate of pot-ash, or of ammonia, is necessary to render alum capable of being precipitated by its earth, or to cause it to pass, as it were, to the earthy state (A). He proved likewise, that such aluminoous waters as do not contain pot-ash, may remain, as long as may be desired, on their materials, without being saturated with too great a quantity of earth, or suffering alum to precipitate.
From the whole of his experiments our author drew the following conclusions, which he considers as of importance to the arts, to chemistry, and to natural history.
1. It is not, at least in the greatest number of circumstances, the excess of acid which impedes the crystallization of alum, but it is the want of pot-ash or ammonia: For it is difficult to imagine that the sulphuric acid could remain disengaged after so long remaining upon alumine in a state of extreme division, and always superabundant. It is true that the aluminoous waters reddish the vegetable tinctures; but this property is not owing to a disengaged acid. This portion of acid is a constituent part of these waters; and it appears to have more affinity with the neutral sulphate of alumine than with a new quantity of this earth at the temperature of the atmosphere.
2. The sulphate of pot-ash may be used, as well as pure pot-ash, to cause the crystallization of alum. It
(A) It may be proper to notice, that Scheele seems to have known this long before, and that he mentions it expressly in his paper on Pyrophorus. even has the advantage over the latter salt, because if the aluminoous waters do not really contain a disengaged acid, the pot-ash, in its combination, will precipitate a portion of alumine, and diminish the product of the boiling; whereas the sulphate of pot-ash does not produce the same effect; but if the lixiviums contain disengaged acid, which must very seldom be the case, it is not converted into alum by the sulphate of pot-ash, and is lost with regard to the product. Our author therefore is of opinion, that when the waters really contain an excess of acid, or a very oxidized sulphate of iron, the use of pot-ash is preferable to that of the sulphate of pot-ash. But when economy is an object, that in many places it would be profitable to use the sulphate of pot-ash; because it is a salt indirectly produced in many manufactories, where of course it may be obtained for nothing. In particular, the residues of the distillation of aquafortis by the sulphuric acid would be excellent for this operation, and much preferable to putrid urine, because this fluid always contains phosphoric salts, which decompose a portion of the sulphate of alumine, and considerably diminish the product.
3. Alumine cannot be used in the treatment of mother waters, as Bergman proposes. This earth is incapable of favouring the crystallization of alum, besides which, it decomposes a portion of alum by the assistance of ebullition; in which circumstance it seizes the acid necessary to its solution, and precipitates it in the form of that powder which is called alum saturated with its earth.
4. Many alum ores must naturally contain pot-ash, because perfect alum is often obtained from the first crystallization of new alum waters without the addition of this alkali. It is true that an objection may be made with regard to the wood used in calcining these ores, which may be supposed to have furnished the alkali; but it is not probable that the small quantity of wood employed, in comparison to the quantity of ore and the alum it affords, could supply enough of pot-ash for the crystallization.
5. All the earths and stones which have given, or shall hereafter afford, by analysis with the sulphuric acid, perfect alum without addition of pot-ash, must contain this alkali naturally. For it is well proved, that alum cannot exist without pot-ash or ammonia; and as there is little probability that this last should be found combined in earths or stones, unless perhaps in very rare cases, we may almost certainly be assured, when alum is obtained from any of these substances, that its formation was effected by pot-ash. The quantity of alum will immediately show in what proportion this alkali existed in the substances analysed.
6. The alum of commerce ought not to be considered as a simple salt, but as a combination in the state of a triple and sometimes quadruple salt of sulphate of alumine; sulphate of pot-ash, or of ammonia. Among these last we may distinguish two species; the one without excess of acid, insoluble in water and insipid, being what is improperly called alum saturated with its own earth; and the other, which contains an excess of acid soluble in water, very rapid and astringent, is the common alum.
There is likewise a pure sulphate of alumine, very astringent, very difficult of crystallization, in the form of brilliant pearl-coloured plates without consistence, and which cannot be rendered insoluble by the addition of a new quantity of its base. This last salt may with the greatest propriety be called the sulphate of alumine.
7. It follows from the comparative analysis, and the knowledge acquired respecting the different states of the combination of alumine with the sulphuric acid united at the same time with other bases, that we must distinguish seven states in this combination, and that it is necessary to express them according to the rules of the methodical nomenclature. Here follow the series, the nature, and the names of these seven sulphates of alumine.
1. Sulphate of alumine, or the artificial combination of sulphuric acid and alumine. This salt is astringent; it crystallizes in laminae or flexible leaves, soluble in water. It has never been described nor named by chemists.
2. Acid sulphate of alumine is the foregoing salt, with excess of acid, from which it differs by reddening blue vegetable colours. It is easily made by dissolving that salt in the sulphuric acid, but it is not easy to convert this into the neutral sulphate of alumine by boiling it a long time with its earth. This salt, like the first, has not been described.
3. Saturated sulphate of alumine and of pot-ash is the alum of the chemists saturated with its earth. It is pulverulent, insipid, insoluble, not crystallizable, and is easily converted into true alum by the addition of sulphuric acid.
4. The acid sulphate of alumine and of pot-ash greatly resembles common alum, and is easily prepared chemically; but M. Vauquelin found no alum but that of La Tolfa which is exactly of the same nature with it.
5. The acid sulphate of alumine and of ammonia has all the properties of alum, and may be used for the same purposes; but though it is easily made in the laboratories, our author never found it pure in commerce.
6. The acid sulphate of alumine, pot-ash, and ammonia. It is remarkable enough, says M. Vauquelin, that this should be the nature of the alum most frequently made in the arts, and that to express its combination so many words should be necessary. This, however, may be avoided, by referring the name of alum to this substance, which will be sufficient to distinguish it perfectly.
7. The acidulous sulphate of alumine and of pot-ash, our author says, he is less acquainted with than with the preceding series. The name by which he characterizes it was suggested to him, and he thinks it proper, because by adding to the solution a small quantity of pot-ash more than is necessary to obtain octahedral crystals, it manifestly passes to the cubic form.
From these deductions, the physician, the chemist, and the manufacturer, with whom the uses of alum are greatly multiplied, will hereafter possess a knowledge of the substance they employ, and may appreciate its effects on the animal economy, and other bodies to which it is so frequently applied. See Annales de Chimie, xxiii. 258, and Nicholson's Journal, Vol. I. p. 318, &c.