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cumstances most favourable to oxidation, and still no oxidation ensue; hence the appellation "noble" metals, by which they are frequently designated. For the present, we will solely direct our attention to silver, that metal having already come under our consideration, whereas gold has not. Supposing, then, the previously-described blowpipe operation to have been prosecuted, not on a piece of mere lead but on a compound or alloy of lead and silver, it should follow theoretically from what we have already stated, that separation of the two might have been effected had our charcoal been sufficiently absorbent of the fused oxide of lead. Practically, charcoal is not sufficiently absorbent, therefore another material possessing the necessary quality has to be found,-that material is bone ash. Exemplification of the Properties f Bone Ash in reference to Cupellation. Having procured a tobacco-pipe, ram into the bowl some bone earth moistened with water, or still better with a little beer. When rammed full, make a small excavation on the surface, and then place the filled pipe aside in a hot place, say an oven, and there allow it to remain until the contents are quite dry; the apparatus will then be ready for the use to which we shall apply it.

Fuse together on a charcoal support a small leaden shot with a still smaller bead of silver. The fusion can be readily effected by means of a blowpipe-jet, even though the flame employed be that of an ordinary candle; nevertheless, if the student experience any difficulty, he may employ instead of the candle a spirit lamp. When fused, allow it to cool, and when cold, deposit it in the little cavity already excavated on the surface of the compact bone earth rammed into the tobaccopipe bowl. These directions having been followed, let the operation of fusion be repeated by directing down upon the flame. Presently the bead will begin to oxidise; the oxide compound bead the outer or oxidising jet of the blowpipe will fuse into a thin transparent liquid, which immediately on its generation is absorbed into the substance of the bone earth and disappears. In this manner the operation will proceed until every particle of the lead becomes dissipated, and the pure silver remains. There will be no difficulty experienced in determining the period when the total separation of the two metals has been effected. So long as the operation of oxidation proceeds, the compound bead will not only have a dull surface, but fumes of oxide will be seen to arise bodily in vapour. Immediately, however, that the last particle of lead has become removed, then the remaining bead will become clean-looking, white, and resplendent, an appearance technically known as the "brightening;" it must now be removed from the source of heat gradually (for reasons hereafter to be described), and allowed to cool. The process of cupellation, by means of which the separation of lead from silver and gold is effected both on the large and the small scale, is an obvious application of the principles just explained. I will describe the process in detail as followed by assayers, and in our English Mint, as well as the Prussian and several foreign Mints,-not the French, however, the authorities of which preferring the moist process of analysis as being more correct, although far less expeditious. The term "cupellation" originates in the circumstance that the bone earth employed in the separative process, instead of being rammed into a containing vessel, the representative of our tobacco-pipe-bowl, is fashioned into a sort of thick-sided cup, or crucible of the shape represented in fig.28, and technically denominated a cupel.

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should be remarked, however, that for the sake of greater clearness of illustration, the muffle is not inserted quite so far as it would be in practice. Assuming the muffle to be in its place, and the fire lighted, the various stages of the assaying operation are as follow: the cupels being placed mouth downwards are gradually thrust into the muffle, and the muffle-door closed. The fire is now urged until the cupels are brought to a bright red heat. The muffle-door is no v opened, the button of alloy dropped in, and the muffle-door closed once more, until the alloy becomes completely fused. From time to time the door is opened, or partially opened, for the purpose of watching the progress of the operation and of admitting a flow of air. Presently the lead becomes oxidised, the oxide fuses, part of it volatilises and passes away in vapour, whilst another,

tions ranging from half an inch to an inch and a half in dia- earth, which acts just like a sponge. practice, the size of these cupels varies, the usual dimen- and by far the larger portion, is absorbed by the porous bone meter, and the respective thickness or depth of each being mint or assaying cupels. For the purpose of large metallurgic most striking. So long as the change of oxidation goes omewhat less. I allude, it need scarcely be indicated, to the operation has come to a conclusion, the evidences of this t Not the least difficulty can arise as to knowing when the

the muffle is pervaded with a peculiar smoke, by observing the colour of which the metals contained in the alloy may be frequently determined. For example, pure lead tinges the cupel, straw yellow verging towards lemon colour; bismuth, straw yellow passing into orange; copper, a grey dirty red or brown according to the proportion in which it is present; iron yields black scoria; tin a grey slag; zinc leaves a yellowish hue upon the cupel and generates a very luminous flame; antimony furnishes yellow scoriace, and causes the surface of the alloy to assume iridescent hues. So soon as the process of oxidation is completed, all smoke and vapours disappear, as well as the phenomena of iridescence. The silver acquires a peculiar spinning motion, and emits a sort of flash constituting an appearance termed "the brightening." The operation may now be regarded as at an end, but the purified silver must not be immediately removed from the muffle, inasmuch as it is subject whilst in the fused condition to throw off portions of its substance in all directions, constituting what is denominated in practice the phenomena of "spitting." For the purpose of guarding against this spit ing, which, if it take place, causes a portion of the silver to be lost, the cupel must not be suddenly withdrawn altogether from the muffle, but removed nearer and nearer to the mouth of the latter by degrees, the fire during the withdrawal being gradually damped.

MATHEMATICAL ILLUSTRATIONS.-No. VI.

ARITHMETICAL LOGARITHMS.
(Continued from p. 61.)

mantissa prefix the index in the manner described in the preceding Lessons, and you will have the required logarithm. Example, required the logarithm of the number 4. Here, looking for 40 in the first column of the table, you find in the same horizontal line, in the adjoining column on the right, and under 0 at " top, the mantissa 6021; to this mantissa prefix 0, which is the index for units, and you have 06021 for the logarithm of the number 4. If the logarithm of the number 40 were required, the mantissa would be the same; but the index would be 1, and the logarithm 1.6021. If the logarithm of 400 were required, the mantissa would still be the same; but the index would be 2, and the logarithm 2-6021; and so on.

If the logarithm of a number be required which consists of two figures only, as of all numbers between 10 and 99, seek for that number in the first column of the table; and when you have found it, the mantissa of its logarithm you will find in the same horizontal line in the adjoining column on the right, under the figure marked 0 at the top. To this mantissa prefix the index as before, and you will have the complete logarithm. Thus; required the logarithm of the number 78. Here, looking for 78 in the first column of the table, you find in the same horizontal line, in the adjoining column on the right, and under 0 at the top, the mantissa 8921; to this mantissa prefix 1, which is the index for tens, or for a number consisting of two integer figures, and you have 1.8921 for the logarithm of the number 78. If the logarithm of the number 78 were required, the mantissa would be the same, but the index would be 0, and the logarithm 0-8921. If the logarithm of the number 78 were required, the mantissa would still be the same; but the index would be 1, and the logarithm T-8921; and so on.

If the logarithm of a number be required which consists of three figures, as of all numbers between 100 and 999, seek for the first two figures of the number as in the preceding case, that is, in the first column of the table; and when these are found, you will then find the mantissa of its logarithm in the the right, under the third figure of the number at the top. To same horizontal line in one of the ten adjoining columns on this prefix the proper index, and you will have the logarithm required. Thus, let the logarithm of 476 be required. Here, looking for 47 in the first column of the table, you find in one of the ten adjoining columns on the right, and under 6 at the top, the mantissa 6776; to this prefix 2, which is the index for hundreds or for a number consisting of three integer figures, and you have 2 6776 for the logarithm of the number 476. If the logarithms of the numbers 47.6, 4.76, 476, or 0476 were required, the operation for finding the mantissa of

TABLES OF LOGARITHMS AND ANTILOGARITHMS. THE following is one of the tables promised in our last Lesson; it will be found very useful, not only to our students who are endeavouring to make themselves acquainted with logarithms, but also to persons who are desirous of abridging calculations of any description, especially those connected with the Mathematical and Philosophical Sciences. The first table, called the Table of Logarithms, contains the logarithms, or rather the mantissæ of the logarithms, of all numbers from 1 to 10,000, according to the common system, of which the base is 10. The decimal part of a logarithm is called its mantissa, and the integral part is called its index or characteristic. Thus in the logarithms 0.477121, 1041393, and 3-005609, the deri-zach would be the same, and they would be, on the prin mal parts 477121, 041393, and 005609, are the man and the integral parts 0, 1, and 3 are the indices or ch.160. teristics.

The mantisse of the logarithms in the first table extend only to four decimal places; but these are reckoned sufficient for ordinary purposes. If, however, a greater degree of accuracy be required than can be obtained from this table, recourse must be had to more extensive tables; of these the best are Hutton's or Babbage's Tables of Logarithms. Let us now proceed to explain our own tables contained in the two following pages.

In the first vertical column of the table are contained the first two figures of any given number, whose logarithm is required, within the range above mentioned; and this column is headed, First Two Figures. In the next ten vertical columns is contained the third figure of any such number; these ten columns are headed, Third Figure. In the next nine vertical columns is contained the fourth figure of any such number; and these nine columns are headed, Fourth Figure.

If the logarithms of a number be required, which consists of one figure only, as of the nine digits, seek for that figure with a cipher annexed to it in the first column of the table; and when it is found, then you will find the mantissa of its logarithm in the same horizontal line in the adjoining column on the right, under the figure marked 0 at the top. To this

les now fully explained to our students, 16776, 0-6776, 1776, and 26776 respectively.

1 If the logarithm of a number be required which consists of four figures, as of all numbers be.ween 1000 and 9999, seek for the mintissa corresponding to the first three figures, as in the preceding case, and in the same horizontal line in one of the nine columns, headed Fourth Figure, you will find, under the fourth figure at the top, a number which is to be added to the mantissa, in order to make it the complete mantissa required; to this prefix the index as before, and you will have the logarithm sought. For example, let it be required to find the logarithm of the number 5768. Here, looking for the mantissa of the first three figures 576, as in the preceding case, you find 7604; and in the same horizontal line with it, under the fourth figure 8, you find the number 6, which is to be added to 7604; this being done, you have 7610 for the complete mantissa; prefixing the index 3, according to previous directions, you have 3-7610 for the complete logarithm required. If the logarithms of 57680, 576-8, 5.768 or 005768 were required, the operation for finding the mantissa would still be the same; but the indices, according to the previous rules, would be different, the logarithms being respectively 4-7610, 2-7610, 0-7610, and 3-7610.

Having thus explained the method of finding the logarithms of numbers from the table, we ought now to show how to perform arithmetical calculations by their means; but we delay doing so till our next Lesson, when we shall also give and explain our Table of Antilogarithms.

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ODE ON WAR.

Hark! the cry of death is ringing Wildly from the reeking plain : Guilty glory, too, is flinging

Proudly forth her vaunting strain. Thousands on the field are lying, Slaughtered in the ruthless strife; Wildly mingled, dead and dying Show the waste of human life!

Christian! can you idly slumber,
While this work of hell goes on?
Can you calmly sit and number
Fellow-beings one by one,
On the field of battle falling,
Sinking to a bloody grave?
Up! the God of peace is calling-
Calling upon you to save!

Listen to the supplications

Of the widowed ones of earth;

Listen to the cry of nations,
Ringing loudly, wildly forth,-
Nations bruised and crushed for ever
By the iron heel of War!
God of mercy, wilt thou never
Send deliverance from afar?

Yes! a light is faintly gleaming

Through the clouds that hover o'cr;
Soon the radiance of its beaming
Full upon our land will pour;
'Tis the light that tells the dawning
Of the bright millennial day,
Heralding its blessed morning

With its peace-bestowing ray.
God shall spread abroad his banner,
Sign of universal peace;
And the earth shall shout hosanna,
And the reign of blood shall cease.
Man no more shall seek dominion
Through a sea of human gore;
War shall spread its gloomy pinion
O'er the peaceful earth no more.- Burleigh,

LESSONS IN GREEK.-No. XXX.

BY JOHN R. BEARD, D.D.

VERBS PURE, IMPURE, AND LIQUID,-UNCONTRACTED VERBS
PURE.

THE student has now obtained some general knowledge of the
Greek verb. If he has accurately acquired what has been
set forth, he is in a condition to construe the simpler forms of
the language. Let him make trial as to what he can do, and
so test his progress, by putting into English a few verses of
the first chapter of the Gospel according to St. John.

The Gospel of St. John, chap. i. verse 1—10. ̧

1. Εν αρχή ην ο λογος, καὶ ὁ λογος ην προς τον Θεον, και θεος ην ὁ λογος. 2. Ούτος ην εν αρχή προς τον Θεόν. 3. Παντα δι' αυτού εγενετο, και χωρίς αυτού εγενετο ουδε ἐν ὁ γεγονεν. 4. Εν αυτῳ ζωή ην, και ἡ ζωή ην το φως των ανθρώπων. 5. Και το φως εν τη σκοτία φαίνει, και ή σκοτια αυτο ου κατελαβεν. 6. Εγένετο ανθρωπος απεσταλμένος παρα Θεου, ονομα αυτῷ Ιωάννης. 7. Ούτος ήλθεν εις μαρτυρίαν, ίνα μαρτυρηση περι του φωτος, ἵνα παντες πιστευσωσι δι' αυτου. 8. Ουκ ην εκείνος το φως, αλλ' ίνα μαρτυρήση περί του φωτος. 9. Ην το φως το αληθινον, ὁ φωτίζει παντα ανθρωπον ερχόμενον εις τον κόσμον. 10. Εν τῷ κόσμῳ ην, και ο κόσμος δι' αυτού εγένετο, καὶ ὁ κόσμος αυτόν ουκ έγνω.

I will now go over the verses separately, and give aid when
I think you may justifiably need aid.

Verse 1. Here you can have no difficulty.
Verse 2. Nor here.

Verse 3. Here EyeVero may require explanation, though you have previously had the word; eyevero, (it, he, or she became; here all things,' a neuter plural with a verb in the singular, according to rule,) they were, or they became, they were produced, the second Aorist (like EXTETO) indicative, third person singular, from yiyvoμai, Ì become, I pass from one state into another.

Verse 4. Here again all must be clear to you except perhaps Lwn, us, i, life.

Verse 5. okоria, as, i, darkness: pairw, I show, I shine, generally in the classics used transitively; paverat, it appears. Karelaßev; here you have an opportunity of putting your acquirements into practice; look at the word; you recognise kar as a shortened form of rara, down, the a being elided before the following ; you know to be the syllabic augment; take it away, and you have λaßer to account for; v you recognise as v phelkusticon, or the that is placed at the end of a word for the sake of sound; so that removing you have left λαβε; compare λαβε with λιπε, you see some resemblance, and are hence led to think that λaße is a second Aorist; it is indeed the third person singular of the second Aorist, indicative, active, of the verb λαμβάνω (ε-λαβ ον), I take; compounded with kara, the verb signifies I take hold of, I apprehend, I am aware of, I recognise.

Verse 6. ameσraλμevoç you at once see is a participle of the middle voice; cut off the participial termination uevos, and you have areoral. You also know that an is the preposition amo, from; what then is oral? the form is the tense, stem of the Perfect passive or middle of the verb orɛλλw, I send, which is the root of the term- añoσтoλos, an apostle; aπGraμEvoc therefore signifies sent.

Verse 7. nλ0ev, came, is the second Aorist, third person singular, indicative, active, of the irregular verb eoxoμai, I come: μαρτυρία, ας, ή, a testimony, from μαρτυρ, υρος, ό, a witness (hence our martyr), and μαρτυρ is the root of the verb μαρτυρέω, I bear witness; the form in the text, namely μaprupnoy, is the third person singular, first Aorist, subjunctive: TOTEVOWOL, (root moris, Ews, n, faith), the third person plural, first Aorist, subjunctive, from TIGTEVW, I believe.

Verse 8. Can now present no obstacle.

Verse 9. pwrite (root pws, wros, To, light), the third person singular, indicative mood, Present tense, of the transitive verb φωτίζω, I throw light on, I enlighten. Ερχομενον you will surely recognise as the participle present of the verb ɛpxoμaι explained in verse 7.

Verse 10. Eyvw do you not recognise this as pretty nearly an English word? It is our word know; the ɛ is the syllabic augment; yvw is the root of the verb, and yvw is the third person singular of the second Aorist, indicative, active, he knew;

"the world knew him not."

only information but encouragement aleo, and so be prepared You will, I hope, derive from this pause in our course, not to encounter manfully "hard things" that are yet before you. While you are passing through these, you will do well to make constant efforts to read the Greek New Testament, in the first place continuing the study of the fourth Gospel. You cannot too soon habituate yourself to rely on your own resources, and with the general impression which you doubtless have in your mind of the contents of the New Testament, you will, if you labour hard and long, be able, even without a dictionary, to make out for yourself much of the Greek origi nal. Be not, however, content with merely putting the Greek words into English, but give special attention to the grammatical conditions and relations of all the words and sentences you attempt to understand.

I have already given you some general instructions respecting the formation of the tenses of the Greek verb. I must now ask you to accompany me while I speak in detail on the point.

Formation of Tenses of Verbs in w.

The verbs in @ are divided into two classes, according to their characteristics, that is, the nature of the letter immediately preceding the w of the first person singular. These

classes are,

1. Pure Verbs, whose characteristic is a vowel. Pure verl s are divided into two divisions:

the Uncontracted, whose characteristic is any vowel except a, ε, o, as λv-w, I loose, ẞovλev-w, I advise.

b. the Contracted, whose characteristic is either a or ɛ or
again o, as ripa-w, I honour, pide-w, I love, puiolo-w, I
let for hire.

2. Impure Verbs, whose characteristic is a consonant.
pure verbs are divided into two divisions:

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Im

Mute verbs, namely, T, K, T, ß, y, d, p, x, e, whose characteristic is one of the nine mutes, as A-w, I leave, TλEK-W, I weave, πɛd-w, I persuade.

ɔ. Liquid verbs, whose characteristic is one of the liquids, namely, λ, μ, ν, ρ; as αγγελλ-ω, I announce, νεμ-ω, 1 divide, pair-w, I show, beip w, I corrupt.

Formation of the Tenses of the Verbs Pure.

In Pure Verbs, the contracted as well as the uncontracted, the tense-ending in general connects itself with the unchanged characteristic; us λυ- λυ-σω, λελυ και Pure verbs form no second, but only first tenses: the Perfect they form with œ (xa), the Future and the Aorist with a and θ (σω, σα, θην, θησομαι). The pure verbs, however, are subject to this regular change:

The short vowel of the Present and the Imperfect, in uncontracted as well as contracted verbs, is lengthened in the other tenses. We speak first of

The Uncontracted.

ĭ into i, unvi-w, I am vexed with, f. μηνῖ-σω, a. ε-μηνῖ. σα
into , kwλň-w, I hinder,
f. κωλύσω, p. κε-κωλύ κα

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