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cumstances most favourable to oxidation, and still no oxidation operations, the cupels are frequently no less than five, six, or
Exemplification of the Properties f Bone Ash in reference to cation of a fame externally.. In practice this system could
Fuse together on a charcoal support a small leaden shot
This muffle is made of refractory clay ware, and its sides, as
air necessary to cause oxidation. flame. Presently the bead will begin to oxidise; the oxide into a furnace in readiness for the cupelling operation. It
The accompanying sketch, fig. 30, represents a muffle inserted will fuse into a thin transparent liquid, which immediately on its generation is absorbed into the substance of the bone earth
Fig. 30. 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 metuls has been effected, : So long as the operation of oxidation procecds, the compound bead will not only have a dull surface, but fumes of oxide will be seen to arise bodily in yapour. Immediately, however, that the last particle of lead has become removed, then the remaining bead will become clean-luoking, 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, howerer, 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, should be remarked, however, that for the sake of greater and technically denominated a cupel.
clearness of illustration, the muffle is not inserted quite so far Fig. 28.
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, In practice the size of these cupels varies, the usual dimen- and hy far the larger portion, is absorbed by the porous bune sions ranging from half an inch to an inch and a half in dia- earth, which acts just like a sponge.
Not the least difficulty can arise as to knowing when the come what less. I allude
, it need scarcely be indicated, to the operation has come to a conclusion, the evidences of this ! hint or :ssaying cupels. For the purpose of large metallurgie most striking. so long as the change of oxidation gocs
the muflle is pervaded with a peculiar smoke, by observing the mantissa prefix the index in the manner described in the
right, and under 0 at the top, the mantissa •8921; to this
number 7.8 were required, the mantissa would be the same, MATHEMATICAL ILLUSTRATIONS.-No. VI. but the index would be 0, and the logarithm 0.8921. If the
logarithm of the number •78 were required, the_mantissa "ARITHMETICAL LOGARITHMS.
would still be the same; but the index would be 7, and the
logarithm 78921; and so on. (Continued from p. 61.)
If the logarithm of a number be required which consists of TABLES OF LOGARITHMS AND ANTILOGARITHMS.
three figures, as of all numbers between 100 and 999, seek for
the first two figures of the number as in the preceding case, Tue following is one of the tables promised in our last Lesson; that is, in the first column of the table; and when these are it will be found very useful, not only to our students who found, you will then find the mantissa of its logarithm in the are endeavouring to make themselves acq'uainted with loga the right, under the third figure of the number at the top. To
same horizontal line in one of the ten adjoining columns on rithms, but also to persons who are desirous of abridging cal. this piefix the proper index, and you will have the logarithm culations of any description, especially those connected with required. Thus, let the logarithm of 476 be required. Here, the Mathematical and Philosophical Sciences. The first looking for 47 in the first column of the table, you find in one table, called the Table of Logarithms, contains the logarithms, of the ten adjoining columns on the right, and under 6 at the or rather the mantisse of the logarithms, of all numbers from i top, the mantissa 6776 ; to this prefix 2, which is the index
for hundreds or for a number consisting of three integer to 10,000, according to the common system, of which the base figures, and you have 2 6776 for the logarithm of the number is 10. The decimal part of a logarithm is called its mantissa, 476. If the logarithms of the numbers 47:6, 4.76, 476, or and the integral part is called its index or characteristic. Thus 0476 were required, the operation for finding the mantissa of in the logarithms 0.477121, 1:041393, and 3·005609, the decis sach would be the same, and they would be, on the pricmal parts ·477121, 041393, and. -005609, are the man I 11,776, and 7 6776 respectively,
les now fully explained to our students, 1.6776, 0.6776, and the integral parts 0, 1, and 3 are the indices or chulao
If the logarithm of a number be required which consists of teristics.
tour figures, as of all numbers be.ween 1000 and 9999, scek The mantissæ of the logarithms in the first table extend tor the mintissa corresponding to the first three figures, as in only to four decimal places; but these are reckoned suffin the preceding case, and in the same horizontal line in one of cient for ordinary purposes. If, however, a greater degree of the fourth figure at the top, a number which is to be added to
the nine columns, headed Fourth Figure, you will find, under accuracy be required than can be obtained from this table, the mantissa, in order to make it the complete mantissa rerecourse must be had to more extensive tables ; of these the quired; to this prefix the index as before, and you will have best are Hutton's or Babbage's Tables of Logarithms. Let the logarithm sought. For example, let it be required to find us now proceed to explain our own tables contained in the the ligarithm of the number 5768. Here, looking for the two following pages.
mantissa of the first three figures 576, as in the preceding
case, you find 7604; and in the same horizontal line with it, In the first vertical column of the table are contained the under the fourth figure 8, you find the number 6, which is to first two figures of any given number, whose logarithm is be added to ·7604; this being done, you have 7610 for the required, within the range above mentioned; and this column complete mantissa; prefixing the index 3, according to preso is headed, First Two Figures
. In the next ten vertical columns vious directions, you have 3.7610 for the complete logarithm is contained the third figure of any such number; these required. If the logarithms of 57680, 576-8, 5.768 or -005768 ten columns are headed, Third Figure. In the next nine were required, the operation for finding the mantissa would vertical columns is contained the fourth figure of any such still be the same; but the indices, according to the previous number; and these nine columns are headed, Fourth Figure. rules, would be different, the logarithms being respectively
If the logarithms of a number be required, which consists of 4.7610, 2:7610, 0.7610, and 3.7610.
of the table; and of numbers from the table, we ought now to show how to when it is found, then you will find the mantissa of its loga- perform arithmetical calculations by their means ; but we rithm in the same horizontal line in the adjoining column on delay doing so till our next Lesson, when we shall also give the right, under the figure marked 0 at the top. To this and explain our Table of Antilogarithms.
50 51 52 63 54
6990 6998 7007 7076 7084 7093 7160 | 7168 7177 7243 7251 7259 73247332 7340
7016 7101 7185 7267 7348
7024 7110 7193 7275 7356
7033 7042 7118 7126 7202 7210 7284 7292 7364 | 7372
7050 7135 7218 7300 7380
7059 7143 7226 7308 7388
7067 7152 7235 7316 7396
1 2 1 2 1 2 1 2 1 2
3 3 2 2 2
3 3 3 3
4 4 4 4
7 7 7 6 6
8 8 7 7 7
67 58 59
7404 7412 7419 74827490 7497 7559 7566 | 7574 7634 7642 7649 7709 7716 | 7723
7427 7435 7443 75057513 7520 75827589 7597 7667 7664 7672 7731
7451 7528 7604 7679 7752
5 5 5
نن نن نن ن ن
4 4 4
5 5 5 4 4
5 5 5 5
6 6 6 6 6
60 61 62 63 64
7782 7789 7853 7860 7924 | 7931 7993 8000 8062 8069
3 3 3 3 3
4 4 3 3 3
4 4 4
6 6 6 5 5
6 6 6 6 6
ODE OV WA R.
Ilark !--the cry of death is ringing
Wildly from the reeking plain : Guilty glory, too, is flinging
Proudly forth her raunting sirain. 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 calınly sit and number
Feilow-beings one by one,
Sinking to a bloody grave?
Calling upon you to save!
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 fuintly gleaming
Through the clouds that hover o'ct; Soon the radiance of its beaming
Full upon our land will pour; 'Tis the light that tells the dawning
Of the bright millennial day, IIeralding its blessed morning
With its peace-bestowing ray.
Sign of universal peace;
And the reign of blood shall cease.
Through a sea of human gore; War shald spread its gloomy pinion
O'tr the peaceful carih rio more. - Burleigh.
Verse 9. owTiket (root ous, wtOS, TO, light), the third person LESSONS IN GREEK.-No. XXX.
singular, indicative mood, Present tense, of the transitive verb
$wriśw, I throw light on, I enlighten. Epxouevov you will surely Dy John R. BEARD, D.D.
recognise as the participle present of the verb epxouai ex
plained in verse 7. VERBS PURE, IMPURE, AND LIQUID,-UNCONTRACTED Verbs
Verse 10. Eyvw: do you not recognise this as pretty nearly PURE.
an English word ? It is our word know; the ε is the syllabic The student has now obtained some general knowledge of the augment; yow is the root of the verb, and eyvw is the third Greek verb. If he has accurately acquired what has been person singular of the second Aorist, indicative, active, he knew;
" the world knew him not. set forth, he is in a condition to construe the simpler forms of
You will, I hope, derive from this pause in our course, not the language. Let him make trial as to what he can do, and 80 test his progress, by putting into English a few verses of only information but encouragement aleo, and so be prepared
to encounter manfully “hard things that are yet before the first chapter of the Gospel according to St. John.
you. While you are passing through these, you will do well The Gospicl of St. Johni, chap. i. verse 1–10.
to make constant efforts to read the Greek New Testament, in
the first place continuing the study of the fourth Gospel. 1. Εν αρχή ην ο λογος, και ο λογος ην προς τον θεον, και You cannot too soon habituate yourself to rely on your own
doubts θεος ην ο λογος. 2. Ούτος ην εν αρχη προς τον θεον. 3. Παντα resources, and with the general impression which you i' avrov syeveto, kai xwpıs avrov eyeveto ovĉe iv • yeyovev. you will, if you labour herd and long, be able, even withont a
less have in your mind of the contents of the New Testament, 4. Ev avrau Zoon ny, kal v Swn nu to ows twv avbpw twv. 5. dictionary, to make out for yourself much of the Greek origin Και το φως εν τη σκοτισι φαινει, και η σκοτια αυτο ου κατελα. nal. Be not, however, content with merely putting the βεν. 6. Εγενετο ανθρωπος απεσταλμενος παρα θεου, ονομα | Greek words into English, but give special attention to the αυτω Ιωαννης. 7. Ούτος ηλθεν εις μαρτυρίαν, ίνα μαρτυρηση grammatical conditions and relations of all the words and senπερι του φωτος, ίνα παντες πιστεύσωσι δι' αυτου.
8. Ουκ ην
tences you attempt to understand,
I have already given you some general instructions respect. εκεινος το φως, αλλ' ίνα μαρτυρηση περι του φωτος. 9. Ην το ing the formation of the tenses of the Greek verb. I must φως το αληθινον, ο φωτιζει παντα ανθρωπον ερχομενον εις τον now ask you to accompany me while I speak in detail on the κοσμον. 10. Εν τω κοσμο ην, και ο κοσμος δι' αυτου εγενετο, point, και ο κοσμος αυτον ουκ εγνω.
Tormation of Tenses of Verbs in w.
The verbs in w are divided into two classes, according to
their characteristics, that is, the nature of the letter immeVerse 1. IIere you can have no difficulty.
diately preceding the w of the first person singular. These Verse 2. Nor here.
classcs are, Verse 3. Here eyevero may require explanation, though you
1. Pure Verbs, whose characteristic is a vowel. Pure veris have previously had the word ; cykveto, (it, he, or she became ;
are divided into two divisions : here all things,' a neuter plural with a verb in the singular,
m. the Uncontracted, whose characteristic is any vowel exaccording to rule,) they were, or they became, they were produced, the second Aorist (like eliteTO) indicative, third person
cept a, &, 0, as du.w, I loose, Bovlev-w, I advise. singular, from yeyvopai, I become, I pass from one state into b. the Contracted, whose characteristic is either a or e or another.
again o, as Tipa-w, I honour, Qide-w, I love, molo-w, I Verse 4. Here again all must be clear to you except perhaps
let for hire. wn, 95, 1, life.
2. Impure Verbs, whose characteristic is a consonant. Im.
pure verbs are divided into two divisions : Verse 5. okotia, as, , darkness : paivw, I słow, I shine, generally in the classics used transitively; palvetat, it appears.
Mute verbs, namely, 7, 6, 7, 8, 7, 8, 9, x, 0, whose chaKarelaßev; here you have an opportunity of putting your
racieristic is one of the nine mutes, as DELT-W, I leare, acquirements into practice; look at the word; you recognise
Alek-w, I weave, 7Ell-w, I persuade. kat as a shortened form of kara, down, the a being elided 3. Liquid verbs, whose characteristic is one of the liquids, before the following &; & you know to be the syllabic aug.
namely, N, P, v, p; as ayyellow, I announce, vej.W, I ment; take it away, and you have haßev to account for; v divide, paiv-w, I shoil", quelp w, I corrupt. you recognise as v ephelkusiicon, or the v that is placed at the end of a word for the sake of sound ; so that removing v you
Formation of the Tenses of the Verbs Pure. hare left λαβε; compare λαβε with λιπε, you see some 1esenblance, and are hence led to think that laße is a second Aorist; In Pure Verbs, the contracted as well as the uncontracted, it is indeed the third person singular of the second Aorist, the tense-ending in general connects itself with the unchanged indicative, actire, of the verb daußavw (e-lapov), I take; characteristic; as lv- lv-ow, ledu.kr. Pure verbs forin no compounded with kata, the verb signities I take hold of, I second, but only first tenses: the Perfect they form with a (va), apprehend, I am aware of, I recognise.
the Future and the Aorist witlι σ and θ (σω, σα, θην, θησομαι). Verse 6. ansotauevos you at once see is a participle of the The pure verbs, however, are subject to this regular change:middle voice; cut off the participial termination uevos, and
The short vowel of the Present and the Imperfect, in unFou have ancoral. You also know that uw is the preposi- contracted as well as contracted verus, is lengthened in the iion ano, from; what then is coral ? the form is the tense,
other tenses, We speak first of stem of the Perfect passive or middle of the verb otellw, I send, which is the root of the term- arootolos, an apostle ; ante
The Uncontracted. εσταλμενος therefore signifes sent.
ī into i, finvi-w, I am rexed with, f. μηνί-σω, a. ε-μηνί- σα Verse 7. n10ev, came, is the second Aorist, third person ŭ into y, Kwłð-w, I hinder, singular, indicative, active, of the irregular verb epxopar, I come:
f. κωλύ-σω, p. κε-κωλυκα μαρτυρια, ας, ή, a testimony, from μαρτυρ, υρος, o, a witness
The Tenses of kudów, I hinder. (hence our martyr), and μαρτυρ is the root of the verb μαρτυρεω, I bear witness; the form in the text, namely paprupnoy, is the
Actite. third person singular, first Aorist, subjunctive: FLOTEVOWOI, (root RIOTIS, EWS, Y, faith), the third person plural, first Aorist,
Present, kwlů.w, impf. erwlŬ-ov, – ð. subjunctive, from HOTEVW, I believe.
Future, κωλύ-σω, aor. 1, ε-κωλύ-σα, inf. κωλύ-σαι, -ύ, Verse 8. Can now present no obstacle.
Perfect, κε- κωλύ κα, plpf. ε-κε-κωλύκειν, -ύ.