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THIRD FIGURE.

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45 2818 2825 2831 2838 2844 2851 2858 2864 2871 2877
46 2884 2891 2897 2904 2911 2917 2924 2931 2938 2944
47 2951 2958 2965 2972 2979 2985 2992 2999 3006 3013
48 3020 30273034 3041 3048 3055 3062 3069 3076 3083
49 3090 3097 3105 3112 311931263133 3141 3148 3155

FOURTH FIGURE

123 4 5 6 7 8 9

1 1 2 3 II 2 3 1 1 2 3 1 1 2 3 I 1 2 3

answering to any given logarithm. It is as follows:-Look for
the first two figures of the mantissa of the given logarithm in
the first column of the Table of Antilogarithms, and in the same
horizontal line with these two figures, in one of the ten adjoin-
ing columns on the right, under the third figure of the mantissa
at the top, you will find the antilogarithm answering to the
first three figures of the mantissa. Next, in the same horizontal
line with this number, in one of the nine other columns, headed
Fourth Figure, and under the fourth figure of the mantissa at
the top, you will find a number which is to be added to the
antilogarithm already found, in order to make it the complete 523311 3319 3327 3334 3342 3350 3357 3365 3373 3381 1 2 2 3
antilogarithm required. Now, according to the nature of the
index of the given logarithm, by the rules laid down in our pre-
ceding lessons, point this antilogarithm—that is, mark it either
as integer or decimal or mixed number, as the case may be—
and you will have the number required.

Example.-Let it be required to find the number corresponding to the logarithm 0·1635. Here, looking for 16 in the first column of the table, you find in the same horizontal line in one of the ten adjoining columns on the right, under 3 (the third figure of the mantissa) at the top, the antilogarithm 1455; and in the same horizontal line with this antilogarithm, in one of the next nine adjoining columns, under 5 (the fourth figure of the mantissa) at the top, the number 2, which is to be added to 1455; this being done, you have 1457 for the complete antilogarithm required. Now, as the index of the given logarithm is 0, this indicates that the number must contain only one integer figure; and the antilogarithm 1457 being pointed according to this index, you have 1.457 for the number required.

Had the given logarithms been 1.1635, 2.1635, and 5.1635, the corresponding numbers would have been 14:57 145-7,

and 145709.

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201585 1589 1592 1596 1600 1603 1607 1611 1614 1618 0 1 1 I
211622 1626 1629 1633 1637 1641 1644 1648 1652 1656 0 1 1 2
1660 1663 1667 1671 1675 1679 1683 1687 1690 1694 0 1 1 2
231698 1702 1706 1710 1714 1718 1722 1726 1730 1734 0 1 1 2
24 1738 1742 1746 1750 1754 1758 1762 1766 1770 1774 O I I 2
251778 1782 1786 1791 1795 1799 1803 1807 1811 1816 0 1 I
26 1820 182 1823 1832 1837 1841 1845 1849 1854 1858 0 I I 2
*27 1862 1866 1871 1875 1879 1884 1888 1892 1897 1901 0 1 1 2
28 1905 1910 1914 1919 1923 1928 1932 1936 1941 19450II 2
29 1950 1954 1959 1963 1968 1972 1977 1982 1986 1991 o II 2

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*30 1995 2000 2004 2009 2014 2018 2023 2028 2032 20370 II 2
*31 2042 2046 2051 2056 2061 2065 2070 2075 2080 2084 0 1 1 2
32 2089 2094 2099 2104 2109 2113 2118 2123 2128 2133 0 1 1 2
33 2138 2143 2148 21532158 2163 2168 2173 2178 2183 0 1 1
34 2188 2193 2198 22032208 2213 2218 2223 2228 2234 1 1 2
*35 2239 2244 2249 2254 2259 2265 2270 2275 2280 2286 1 1 2
36 2291 2296 2301 2307 2312 2317 2323 2328 2333 2339 1 1 2
*37 2344 2350 2355 236 2366 2371 2377 2382 2388 2393 1 1 2
38 2399 2404 2410 2415 2421 2427 2432 2438 2443 2449 II 2 2 3
*39 2455 2460 2466 2472 2477 2483 2489 2495 2500 2506 1 1 2 2
*40 2512 2518 2523 25292535 2541 2547 2553 2559 2564 1 1 2
412570 2576 2582 2588 2594 2600 2606 2612 2618 2624 1 1 2
422630 2636 2642 2649 2655 2651 2667 2673 2679 2685 1 1 2
*43 2692 2698 2704 2710 2716 2723 2729 2735 2742 2748 1 1 2
44.2754 2761 2767 2773 2780 2786 2793 2799 2805 2812 1 1 2

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55 3548 3556 3565 3573 3581 3589 3597 3606 3614 3622 1 2 2 3
56 3631 3639 3648 3656 3664 3673 3681 3690 3698 3707 1 2 3 3
57 3715 3724 3733 374 3750 3758 3767 3776 3784 3793 1 2 3 3
58 3802 3811 3819 3828 3837 3846 3855 3864 38733882 1 2 3 4
59 3890 3899 3908 3917 3926 3936 3945 3954 39633972 1 2 3 4 5
60 3981 3990 3999 40094018 4027 4036 4046 4055 4064 1 2 3 4 5 6 6
61 4074 4083 4093 41024111 4121 4130 4140 4150 4159 1 2 3 4
62 4169 4178 4188 419844207 4217 42274236 4246 4256 1 2 3 4
63 4266 4276 4285 42954305 4315 4325 4335 4345 4355 1 2 3 4
64 4365 4375 4385 4395 4406 4416 4426 4436 4446 4457 1 2 3 4
65 4467 4477 4487 4498 4508 4519 4529 4539 4550 4560 1 2 3 4
66 4571 458 4592 4603 4613 4624 4634 4645 4656 4667 1 2 3 4
674677 4688 4699 4710 4721 4732 4742 4753 4764 4775 1 2 3 4
63 4786 4797 4808 4819 4831 4842 48534864 4875 4887 1 2 3 4
69 4898 49094920 4932 4943 4955 4966 4977 4989 5000 1 2 3 5
70 5012 5023 5035 5047 5058 5070 5082 5093 5105 5117 1 2 4 5
71 5129 5140 5152 5164 5176 5188 5200 5212 5224 5236 1 2 4 5 6
72 5248 5260 5272 5284 5297 5309 5321 5333 5346 5358 1 2 4 5
73 5370 5383 5395 5408 5420 5433 5445 5458 5470 5483 1 3 4 5 6
74 $495 5508 5521 5534 5546 5559 55725585 5598 5610 1 3 4 5 6

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76 5754 5768 5781 5794 5808 5821 5834 5848 5861 5875 1 3 4 5
77 5838 5902 5916 5929 5943 5957 597 5984 5998 6012 1 3 4 5
78 6026 6039 6053 6067 6081 6095 61096124 6138 6152 1 3 4 6
79 6166 6180 6194 6209 62236237 6252 6266 6281 6295 1 3 4

80 6310 6324 6339 63536368 6383 6397 6412 6427 6442 1 3 4 6
81 6457 6471 6486 6501 6516 6531 6546 6561 6577 6592 2 3 5 6 8
82 6607 6622 6637 66536668 6683 66996714 67306745 2 3 5 6 8
83 6761 6776 6792 68086823 6839 6855 6871 6887 6902 2 3 5 6 8
84 6918 6934 6950 69666982 6998 7015 7031 7047 7063 2 3 5 6

85 7079 7096 7112 7129 7145 7161 7178 7194 72117228 2 3 5 7
86 7244 7261 7278 7295 7311 7328 7345 7362 7379 7396 2 3 5 7
87 7413 7430 7447 74647482 7499 7516 7534 7551 7568 2 3 5 7
88 7586 7603 7621 7638 7656 7674 7691 7709 7727 7745 2 4 5 7
89 7762 7780 7798 7816 7834 7852 7870 7889 7907 7925 2 4 5 7

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Rule 41.-No article generally precedes the possessive pronouns when the latter are prefixed to substantives which express (1st.) kindred or relation, such as padre, madre, figlio, sorella, marito, etc.; (2nd.) the rank and quality, such as altezza, eccellenza, maestà, etc.; as

Chi è vostro padre? who is your | Egli adunque inteso il nobile atto father?

di Filippo usato a salute di suo marito, he then having heard of the noble action of Philip in favour of her husband.

Venne sua Maestà accompagnata dal Duca d' Orleano, his Majesty was accompanied by the Duke of Orleans.

Mia madre, un fratello minore, ed io, siamo restati nell' estrema miseria, my mother, a younger brother, and myself, have been left in great distress. Sua Eccellenza le baciò la mano, his Excellency kissed her hand. Rule 42.-When the possessive pronouns follow the above substantives, padre, madre, etc., or precede the same in the plural, then the article is used :—

Ho veduto la sorella vostra, I have | Finchè io possa farlo in persona, seen your sister. soffra la maestrà vostra, as long as I can do it myself, allow me, sire.

La madre mia è partita, my mother has set out.

Mi ricordo aver udito dire il padre mio, I recollect having heard my father say.

Prima che io ringrazio le loro signorie, before I thank your lordships.

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tando, I see some one who is listening to us.

Alcuni sono li quali, più che l' altre genti si credono sapere, e sanno meno, there are some people who think they know more than other folks, when they know less.

Egli è dimorato in Parigi alcun

tempo, he has remained some time in Paris.

Vi sono andato con alcuni amici, I have been there with some friends.

Rule 52.-Alquanto, meaning somewhat, several, some, rather, is sometimes used alone, and sometimes with a substantive. When it is joined to a substantive, it agrees with it in gender and number :

Ella uscita dalla camera, e stata alquanto tempo, tornò dentro piangendo, she went out of the room, and, after some time, she came in with tears in her eyes. Alquante lagrime mandate per gli occhj fuori, cominciò ad attendere quello che la gentildonna gli rispondesse, having shed a few tears, he waited for the lady's

answer.

Alquanti, che risentiti, erano all' arme corsi, n' uccisero, they murdered several, who, being awakened, had taken up arms. Dopo alquanto spazio ella a me ritornò, after a little time she

came back to me.

La Lauretta con maniera alquanto pietosa cominciò così, Lauretta thus began, in a manner rather pathetic.

Rule 53.-Altro, signifying differently, something else, another, etc., may be used alone, or with a substantive; in the latter case it agrees with the substantive in gender and number:Altro avresti detto, se tu m'avessi veduto a Roma, you would have spoken differently, had you seen me at Rome. Sembiante facendo di rider d'altro, feigning to laugh at something else. Altri tempi, altri costumi, other times, other manners.

Un altro non vi avrebbe perdonato così facilmente, come v' ho perdonato io, another would not have pardoned you as easily as I have done.

Datemi un altro bicchiere di quel buon vino, give me another glass of that good wine.

Rule 54.--Ciascheduno and ciascuno, meaning every one, each, etc., are used either alone or with substantives. When they are prefixed to substantives, they agree with them in gender, and seldom admit of a plural :—

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Rule 58.-Every verb must agree with its subject, either Abborrire, to abhor. expressed or understood, in number and person; as—

Voi parlate troppo forte, you Io scrivo, I write. speak too loud.

I sarti dicono spesso bugie, tailors often lie.

Parli da sciocco, thou speakest like a fool.

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re

Accadere, to happen.
Accennare, to show.
Accertare, to assure.
Accomandare, to
commend.
Accordare, to grant.
Accorgersi, to perceive.
Afliggersi, to grieve.
Ammonire, to admonish.
Annojarsi, to be weary.
Ardire, to dare.
Arrischiare, to venture.
Assicurare, to assure.
Astenersi, to abstain
from.

Attentarsi, to attempt.
Avvedersi, to perceive.
Avventurare, to venture.
Avvertire, to admonish.
Avvisare, to inform.
Badare, to mind.
Biasimare, to blame.
Bramare, to wish.
Cercare, to seek.
Cessare, to cease.
Chiedere, to ask.
Comandare, to com-
mand.

Commendare, to com

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Rule 63.-The future is used to event will take place at some future time :Noi lo faremo domani, we shall do | Egli ritornerà al suo paese, he Contentarsi, to consent. will return to his country. Rule 64.-The conditional present denotes that an action or event would take place, if certain conditions are fulfilled :

it to-morrow.

Se io avessi danari, comprerei un buon cavallo, if I had money, I would buy a good horse.

Tacerebbero, se potessero, they would be silent, if they could.

SUBJUNCTIVE MOOD.

Rule 65.-Verbs expressing command, desire, doubt, fear, ignorance, order, passion, surprise, uncertainty, etc., require the following verb in the subjunctive :

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Procurare, to try.

Professare, to profess. Proibire, to prohibit.

Proporre, to propose. Promettere, to promise. Ricordarsi, to remember. Ricusare, to refuse. Rimproverare, rinfacciare, to reproach. Rincrescere, to be sorry, Ringraziare, to thank. Riprendere, to reprove. Risolvere, to resolve. Scegliere, to choose. Scommettere, to bet.

Fermarsi, to stop.
Fingere, to pretend.
Finire, to finish.
Fissare, to fix.
Giudicare, to judge.
Giurare, to swear.
Gloriarsi, to pride one's
self.
Godere, to delight.
Guardarsi, to beware.
Immaginarsi, to ima-
gine.
Impedire, to hinder.
Imporre, to impose.
Increscere, to be sorry.
Incaricare, to charge.
Infingersi, to pretend.
Ingegnarsi, to endea-
[stand.
Intendere, to under-
Lamentarsi, to com- self.
plain.
Lasciare, to cease.
Lusingarsi, to flatter
one's self.
Mancare, to fail.
Meditare, to meditate.
Meritare, to deserve.
Minacciare, to threaten.
Negare, to refuse.
Mostrare, to show.
Negligentare, to neglect.
Obbligare, to oblige.

vour.

dis.

Scongiurare, to conjure.
Sconsigliare, to
suade.
Scordarsi, to forget.
Scusarsi, to cxcuse one's

Sembrare, to seem. Sospirare, to sigh. Sostenere, to support. Sperare, to hope. Svolgere, to dissuade. Supplicare, to entreat. Temere, to fear. Tentare, to try. Tremare, to tremble. Tralasciare, to desist. Vergognarsi, to be ashamed.

Here are two examples of the above rule :

Il padre cercò di dargli moglie, Non mi curo di vederlo, I do not his father sought to give him a wife.

care to see him.

RECREATIVE NATURAL HISTORY.

FIR-TREES AND PINE-CONES.

THERE is to me an inexplicable charm in the fir-needle-carpeted, cone-strewn, aromatic, and shaded glades of a pine forest; and I like to linger where the fresh breeze sings through the tufted pine needles. The crossbills, too, are in their element, when hanging, parrot-like, head downwards, amongst the ripe brown cones, they deftly wrench off scale after scale with their pincerlike mandibles, as they cull the sweet, oil-laden seed which lies hidden at the base of each plate of the cone's armour. It is not my intention here to attempt a description of the almost endless number of conifers which the labours and researches of botanists and explorers have brought to the knowledge of the scientific: I intend rather to endeavour to enlist the reader as a companion in a sort of gossiping ramble amongst some of the most familiar and noteworthy members of the pine family, gathering, as we go, such bits and scraps of pine lore as good fortune may cast in our way.

It would be difficult to find, even amongst the most beautiful of Nature's forest handiwork, a more graceful, widely-distributed, or generally useful tree than the larch (Pinus lariz), the cone and foliage of which is represented at Fig. 1. By the Romans this tree was held in high esteem, and the larch forests, from time to time discovered by them, were made extensive use of. During their German wars vast quantities of larch timber were obtained. The trees, after being felled and trimmed in the Alpine fir forests, were sent, via the river Po, to Rome, where a great demand existed for larch for building purposes. Pliny, in writing of the larch, says: "This tree is the best of the kind that bears resin. It rots not, but endures a long time;" and there can be little doubt that the praise thus bestowed by the historian was just. There appears little reason to doubt the truth of the statement which has been made, that the Emperor Trajan's vast floating palace, which was constructed for him on a lake, as a place of resort during the heats of summer, was almost entirely composed of larch and cypress combined. We read that this extraordinary structure was built of cypress and larch, sheathed with lead, fastened with copper nails, doubly planked, and the seams caulked with linen rags, laid over with Greek pitch. After 1,400 years had passed away, some portions of the submerged palace were removed from the depths of the lake, when the fir timber of the building was found to be in an extraordinarily sound condition. We also find that Tiberius, knowing the remarkably durable qualities of larch timber, caused vast numbers of trees, brought from Rhætia, to be cut into planks, for the purpose of rebuilding the Naumachiarian bridge, which was originally built by Augustus, but met with destruction by fire. This socalled Rhætia larch appears to have been of remarkably good quality and luxuriance of growth; for we find it related that one pole reached 120 feet in length, and was of such perfect growth that all Rome flocked to examine it. For art purposes larch wood appears to have been held in high esteem from the very earliest periods. Some of the most admirable paintings executed by the masters who flourished between the periods when Pliny wrote and Raphael painted were executed on boards hewn from the substance of the larch; in fact, the term immortale lignum was applied to larch wood, on account of its extra ordinary powers of resistance to deteriorating influences. Much of the picturesque beauty possessed by that land of fine landscapes, Switzerland, is more or less dependent on the larch. The wild crag, deep ravine, and brink of the foam-flaked torrent each and all have their larch-plumes to break the monotony of rock scenery. Then, again, the peasants' châlets, perched on some wild ledge, or the frail-looking yet reliable mountainbridge or chasm-guard rail, which, as though secured by industrious spiders of a larger growth, stretch across cliff-tracks and giddy passes, which would be well-nigh impassable, were it not for the light, straight larch-poles which, felled hard by, are made to minister to man's requirements; and it is most fortunate that in the very situation where there is exposure to alternate wet and dry, heat and cold, and the rough buffetings of the tempest, this timber, so admirably calculated to resist decay, should be so abundantly found. Lambert, when speaking of the strength of larch wood, expresses himself as follows: -"By observations made on the strength of timber, it appears that a beam of larch, clear and free from knots and every other

imperfection, especially at or near the middle, eleven inches square and six feet and a half long, can bear, if placed horizontally on its two extremes, a weight of 200,000 lbs. suspended to the middle of it, and that it can bear a still greater weight in an oblique position." It was from the adoption of a system of analogical reasoning, that the constructors of the Royal Navy first turned their attention to the use of larch as a wood for ship-building purposes. The first larch-built ship we learn much about was constructed entirely from larch timber, furnished for the purpose by the Duke of Athol. This ship was called the Serapis. Then, for experimental purposes, the Sibylle frigate, the bottom of a lighter, and a number of piles for tidal use, were constructed at Woolwich dockyard. Quoting from the history of the experiments, we read that "the Athol, of twenty-eight guns, was built entirely of larch, of the same growth, whilst the Niemen, a ship constructed at the same time, was built of timber from Riga. At the expiration of their first course of service, both vessels were officially examined, when the Niemen was found so much decayed as to be condemned forthwith. The Athol was re-commissioned, completed her second term of service, provisioned, and made a store-ship of, when for a period of more than thirty years she was subjected to the wear and tear of almost every climate." It is somewhat curious, and not generally well known, that the larch, although so commonly met with throughout the length and breadth of Great Britain, is not one of our indigenous trees. We find that in the year 1629 Parkinson, in speaking of trees of this kind, refers to them as rarities, or out of the common order of trees. Evelyn, too, although perhaps possessed of more information regarding trees than any person who wrote in his time (1664), describes a larch tree of goodly stature, which grew at Chelmsford in Essex, and speaks of it as though he considered it a rare tree. Ben Jonson speaks of the juice of the larch as possessing some mystic virtues, but gives no information as to whether the tree yielding this sap was rare or not. Thus he writes

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"Yes, I have brought to help your vows
Horned poppy, cypress boughs,

The fig-tree wild, that grows on tombs,
And juice that from the larch-tree comes."

It would be difficult to over-estimate the importance to be attached to the cultivation of this valuable tree in situations where little else could be grown. The Athol family have been celebrated for their zeal in the cause of larch growth. The extent to which their fir-tree cultivation has been carried on in Scotland will be best shown by a reference to the following statistics :-14,096,719 young larch trees were planted in the neighbourhood of Blair Athol and Dunkeld. The plantation covered a track of land 10,324 imperial acres in extent. The trees flourished and grew rapidly, and on felling one, at the ninety-fifth year of its growth, it was found to be 100 feet long, 10 feet 6 inches in girth, at five feet from the point at which it was cut through. It contained 368 cubic feet of timber. It has been truly said that the man who plants good trees abundantly stores up wealth for those who follow. An approximate calculation has been made as to the money value of the vast fir forests thus raise by one man's strong will and industry, and the sum arrived at is £6,500,000. In addition to this princely sum we must estimate the thinnings and trimmings as being worth about £7 per acre of forest. At the death of this noble pine-tree planter, a coffin was constructed from the wood of one of his forest favourites, which, on being felled, measured 106 feet in length.

Most of our readers will be familiar with a substance known as Venice turpentine, and sold by all druggists for a variety of medicinal and art purposes. This substance, although bearing the name of Venice turpentine, is not brought from Venice, but is simply the hardened sap of the larch. Considerable quantities are obtained in France, the Briançonnais being celebrated for the production of turpentine, which is obtained by tapping or perforating the trees with large augers. The first hole bored is commonly at about three feet above the ground-surface. Other holes, or outlets, are then made in the tree-trunk to a height of twelve or thirteen feet. A number of small wooden tubes, or spouts, are so cut as to fit these holes, just as a tap fits a barrel, and as the liquid resinous juice of the tree flows outwards through the spouts, it drips into a corresponding

number of little pots, or other vessels, placed for its reception. The turpentine-gatherers say that the side of the tree facing the south yields a notable quantity of juice more than either the north, east, or west surfaces of the tree.

The manner in which fir-tree sap is collected appears to have undergone but little change since periods of remote antiquity. Ovid thus writes of turpentine-gathering as practised in his day

"The new-made trees in tears of amber run, Which harden into value by the sun." Next to the larch in point of abundance in this country, and the freedom with which it yields its resinous juices, we may men. tion the Scotch fir (P. sylvestris). Fig. 2 represents the cone, foliage, and seed. This conifer

uninterrupted stream of tar composition from the heating chamber in which it was prepared.

A great deal of tar is manufactured in the north of Europe, and a great portion of this is commonly known as Stockholm tar. Such supplies, however, as are furnished from the firs of this country are mainly obtained from the Scotch pine. The roots and other cuttings of old trees furnish the largest return on treatment. P. sylvestris is not, however, the only pine from which the tar of commerce is obtained. The tar of the North American botanists is obtained from a conifer known

as P. rigida. P. Treda and P. Australis also yield it. Between four and five millions of barrels of wood tar are annually imported into this country.

The substance known as lampblack is, as most of our readers

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is rich in a product, the loss of which would entail enormous inconvenience and difficulty.

There is perhaps no product yielded by the pine which, for importance and general usefulness, can be compared with tar.

The rope-maker, the shipwright, the timber merchant, and the sailor are all debtors to it. Those wondrous cables which furnish a medium for the conveyance of messages and intelligence from pole to pole and sea to sea, owe much of their power to resist decay and deterioration to the tar used in saturating the yarns or hempen cords which, layer after layer, envelop both the electric and protecting wires used in fashioning these submarine ropes. We were much pleased a short time since, on visiting the submarine cable manufactory at Silvertown, with the ingenious manner in which an endless band of heavy chainlinks were made to deposit, agitate, stir, and carry upwards to the rope, in the course of manufacture, a perfectly regular and

will be aware, extensively used in the arts. This is made in very large quantities from the waste products resulting from the manufacture of common tar, and it may not prove unin. teresting to the reader to follow out the manner in which this soft, jet-black, and generally useful substance is prepared. The Germans manufacture lampblack extensively, and find it a valuable addition to the return from the tar-works, about which we shall have more to say as we proceed. When about to prepare lampblack, the manufacturer prepares for himself a sort of coffer or box. This is accurately closed at every joint, but at the top a sort of ventilated stopper-arrangement is placed. This is provided with number of holes, over which a sort of cone or case of linen cloth is fastened. At a convenient distance from the box and cone a narrow-mouthed furnace is constructed in such a way that as the waste tar products are subjected to heat, the vapours given off

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