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the door; pres. ich schließe
zu; impf. ich schloß zu; p.
past zugeschlossen.

(16) Anstecken, set fire to.
(17) Sammt, together with.
(1) Wimmerten, were whining.
(19) Vermochte, impf. of vermigen,
to be able.

(20) Sich zu fristen, to have a
respite.

VOCABULARY AND NOTES.

can prey, and can shut their folding doors when they are them-
selves likely to be victimised. These shells are usually thick
and heavy, especially in those species which are marine, for the
wear and tear of the sea is greater, and the predatory creatures
more powerful than those in fresh water. Moreover, the box or
house must be tolerably capacious, otherwise the creatures
could not breathe while they were in a state of siege, and must
surrender at discretion to the expectant lobster or other free-
booter of the deep. It follows that this arrangement is not
well suited to locomotion; and not being locomotive to any
great degree, they are not endowed with those perfect organs of
sense that must be possessed by those animals which chase
their prey.
When organs of sense are possossed, they are

17. Joseph II., Kaiser von Oestreich. Joseph II., Kaiser von Destreich, wollte einem alten Offizier zur Unters usually collected on a protruded part of the body, and placed baltung und Pflege von dessen kranker Frau seine lebten 24 Goldstücke above the mouth, which opens at the front part. Such a progeben. „Das ist zu viel," unterbrach ein Höfling,,,24 Gulden sind genug."jection, which supports the eyes, feelers, ears, and smelling Haben Sie diese ?"-Der Dienstfertiges zicht solche emsig aus der Börse; capsules, and contains a nervous centre conveniently and closely Joseph nimmt sie, fügt seine 24 Golzstücke hinzu, und giebt sie tem Offizier situated to these gateways of knowledge, is usually called a zusammen mit den Worten: Beranken Sie sich bei dem Herrn, der sehr head. Now these bivalve molluscs are distinguished from the vergnügt darüber ist, auch Etwas zur Linderung Ihrer Noth beigetragen? higher orders in having no heads, and are called acephalous. They have mouths, and a nerve-knot above this; but the mouth is not prominent, and lies far within the shelly box, and often between soit projections of the body, which extend some distance beyond it. Their organs of sense are also very poor and imperfect; and when they are possessed at all, they are placed in other parts of the body. The two classes which together compose the group of headless, two-shelled Mollusca are extremely different in structure throughout. There is, however, an external difference by which they may be distinguished secreted on extensions of the membrane of the body on the by a superficial observation. In the Brachiopods the shells are back and front of the animals; while in the Conchifera the shells are placed upon membranes which are developed from the sides of the animal. Thus, if both animals were split down the

(1) Unterhaltung, f. sustenance.
(*) Pflege, f. nursing, care.
(3) Unterbrach, the imperfect of
the verb unterbrechen, to in-
terrupt.

(4) Höfling, m. courtier.
(5) Dienstfertige, officious, (liter-
ally) ready to serve.
(6) Linderung, f. lessening, relief.
(7) Beitragen, to contribute.

18. Friedrich der Große und sein Arzt. Zimmermann, ein ausgezeichneter Arzt1 kam von Hannover, um Friedrichy den Großen in seiner leßten Krankheit zu behandeln.2 Eines Tages sagte der König zu ihm; Sie haben, wie ich vermuthe,3 Manchem in tie antere Welt geholfen."4 Dies war eine grobe Redeweise und eine unangenehme Pille für den Doctor; aber die Dosis, welche er dem Könige wieder gab, war ein scharfsinniges Gemisch von Wahrheit und Schmeichelei:7 Nicht so vielen, als Ew. Majestät, und auch nicht mit so viel Chre."

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VOCABULARY AND NOTES.

() Distinguished physician.
Behandeln, to treat.
(3) Wie ich vermuthe, as I guess.
(*) Geholfen, p. p. of helfen, to help.

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(5) Grobe Reteweise, rude
speech.

(6) Scharfsinnig, clever.
(7) Schmeichelei, f. flattery.

19. Carl der Zweite und sein Bischof. Garl der Zweite fragte den Bischof Stillingfleet, wie es zuginge, daß er gewöhnlich ohne Buch pretigte, aber bei Hofe seine Predigten immer abläse. Der Bischof antwortete: „Die Ehrfurcht vor einem so großen und weisen Fürsten macht, daß ich mich nicht traue. Aber wollen Ew. Majestät mir tagegen auch eine Frage erlauben? Warum lesen sie Ihre Reten im Parlamente?" Warum?" erwiederte der König, „das will ich dir aufrichtig fagen. Ich habe sie so oft um Geld gebeten, daß ich mich schäme, ihnen ins Gesicht zu sehen.“ 48

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COMPARATIVE ANATOMY.-XV. BIVALVE MOLLUSCS: BRACHIOPODA (= PALLIOBRANCHIATA) AND CONCHIFERA (= LAMELLIBRANCHIATA). THERE are two classes of soft-bodied animals which secrete a hard, chalky substance in the form of two hollow saucer shaped pieces, that fit more or less closely together along their edges, and which, therefore, when drawn together, can completely protect the animal, that lies wholly between them, from all injury. These are called Bivalve Molluscs. The shells are usually so united at one point in their circumferences as to play upon that point as a hinge, while the remainder of the two shells can be separated so as to gape more or less widely on the side opposite the hinge. In this manner the creatures can keep open hase when their guests are likely to be those upon which they

middle by a cutting instrument, which should leave the divided halves more or less alike, that instrument would pass through both shells of the Brachiopods, dividing them both into two equal parts, while it would not cut the shells of the Conchifer at all, but only sever them the one from the other. This arrangement of the animal to the shell is contrasted in the illustration, in which it will be seen that the separate shells of the Brachiopod are bisected into two absolutely similar halves by a line running down the middle. On the other hand, a line dividing the Brachiopod so as to sever the shells leaves two portions, which are unlike, both in size and form. A similar line, separating the conchiferous shell, leaves two equal and similar parts. It should, however, be remarked that the ordinary position occupied by both classes of bivalves, resting as they

do on the bottom of the sea, sometimes interferes with the

bilateral symmetry of the Conchifers, while it leaves that of the flattened as if the back and front of the animal had been Brachiopods untouched. In the Brachiopods the double shell is squeezed together, and this kind of flattening is technically called depression. In Conchifera the double shell is usually flattened as though the creatures had been squeezed by pressure applied to its sides, and this flattening is called, in the language of Comparative Anatomy, compression. Now, as these passive creatures, whether fixed or free, usually rest on the floor of the sea, it follows that they must lie, not on the edges, but on the flats of their shells; and when thus lying, they rest habitually on one shell, and this shell is often so modified in relation to the other as to suit the lying posture. The Brachiopods rest on their ventral shell, with the back or dorsal shell uppermost, and therefore this modification does not interfere with the symmetry or equality of their two halves; but it does interfere with the symmetry of the Conchifera, because they rest on their sides.

A similar instance of this effect of habit on the two-sided arrangement of the body is seen in the soles, turbot, etc., which constitute the family of fishes called Pleuronectida, as contrasted with the equally flat rays. The depressed rays, lying with their backs uppermost, are quite symmetrical; while the soles, resting on their sides, are quite distorted in shape, and the two sides differ in colour. Notwithstanding this tendency to one-sidedness in the Conchifera due to habit, most of them have nearly equal valves; and in none is the internal arrangement of organs much interfered with.

Having thus drawn attention to the superficial contrast between the classes, we proceed to describe the Brachiopoda,

which are far inferior to the Conchifera, and bear a stronger
relation to the Tunicata and Polyzoa than they do to the other
class, which will come under our notice in the after-part of the
lesson.
Brachiopoda.-These creatures are, for the most part, fixed to
the rocky bottom of the sea, either by a fleshy stalk, which
passes out from the body through a hole, a slit, or a passage in
the ventral valve, or else by having this under-valve fixed to its
support directly. In the first case the connection is organic,
and the creature can move
itself upon its stalk by the
aid of muscles, which are
placed inside the shelly
box; and in the latter case
the connection is inor-
ganic, and the creature is
entirely immovable. Tak-
ing the Waldheimia as a
type, because it is the
genus which has been best
studied, not only by Con-
tinental anatomists, but
also by Hancock, Huxley,
and Owen, we proceed to
describe its structure. The
reader should, however, be
warned that though this is
a good typical Brachiopod,
all that will be said about
it does not apply to every
species of the class, and
that the structure has
been very differently in-
terpreted and explained by
the great naturalists above
named.

The shells are best understood from the illustration. It will be observed that the ventral shell is very concave and globose, lodging the animal as in a cup, while the dorsal shell is nearly flat, and acts as a lid to the cup. The ventral shell has a round hole in one end through which the stalk passes. Between this hole and the great opening of the shell is a triangular space, and at the angles at the base of the triangle are two little teeth. These teeth

and long extensions of the body stretching beyond this confined space. Thus, two large vascular membranous sheets line the valves right up to the very edge of the shell, where they are fringed with strong and numerous bristles. There are also two long arms, which stretch away from the mouth on each side. These are so long that, if unfolded, they would stretch beyond the limits of the shell; but they are supported by the calcareous loop, and follow its bendings. These arms have a delicate fringe of little fingers, which arise all along their outer sides; and these little fingers are

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clothed with cilia, which create currents of water towards the mouth, and thus the animal is fed. The mouth has no hard parts or jaws, but only two lips, of which the arms may be considered the sidelong extensions. It opens towards the gaping part of the shells, and also downward. The stomach is rounded, and receives the passages from the liver which surrounds it, and the intestine bends downward and ends blindly below. At the back and above the stomach is the simple saccular heart, which sends off from each of its sides two vessels, one of which goes to the stomach and viscera, and the other to the mantle lobes. These lobes of the mantle are so well supplied with blood, and the vessels are so large which traverse them, that it is supposed that the blood is there aërated, and hence these creatures have been called Palliobranchiata, or breathers by means of the mantle. Round the edge of each lobe of the mantle which lines the valves is a circular channel, and this first receives the blood from the heart, and from there it passes back through the more central parts of the lobes, being first conveyed through fine vessels, and then collected into larger and larger vessels until it is returned by large sinuses to the central parts. When the blood has arrived at these central parts, some of it goes to supply them directly, whilst the residue runs along the vessels of the arms and the membranes connecting the arms, and so returns from them after having passed through the fine fringes. Thus it is probable that these ciliated fringes of the arms are efficient, and perhaps the most efficient, instruments of aëration of the blood. After the return from the arms and viscera, the blood on both sides of the body is collected into a vessel which runs along above the stomach, and then enters the heart again.

fit into sockets in the flat BRACHIOPODA.-I. WALDHEIMIA. II. DITTO, SIDE VIEW.

VALVE.

III. DITTO, VENTRAL
IV. DITTO, DORSAL VALVE. V DITTO, SHOWING THE MUSCULAR SYS-
TEM. VI. DITTO, TO SHOW ARRANGEMENT OF VISCERA.

shell, which has also de-
veloped from it a large
calcareous loop. This loop
consists of two arms,
which run forward on
either side, and then, leav-
ing the shell, are turned
back to unite almost above
(or below, in the natural
position of the animal) the
point from which they spring. When the two shells are placed to-
gether as when the animal occupies them, they look not unlike the
Eastern oil-lamps which are always represented as being carried
by the ten virgins in pictures of the parable; the hole in the ventral
shell, of course, corresponding to that through which the wick
passes in the lamp. Hence, these shells have been called lamp-
shells. When the valves are united on the hinge as in life, this
hinge does not allow them to be parted from one another, except
for a short distance. The soft parts of the animal occupy a
very small part of its hard box, being confined almost exclusively
to the part between the arms of the loop, and to about the one-
third of this space nearest the hinge. This restriction applies
to the visceral and muscular masses. There are, however, large

Refs. to Nos. in Figs.-III. 1, aperture through which pedicel is passed; 2, impres
sion of capsular muscle; 3, teeth of the hinge; 4, impression of the adductor
muscles; 5, impression of pedicel muscles; 6, impression of cardinal (adductor)
muscles. IV. 3, posterior adductor and (3) anterior adductor impressions; 7,
carbonate of lime loop to support the arms. V. 3, 3, adductors; 4, pedicel
muscles; 5, pedicel; 6, cardinal and (8) ventral pedicel muscles; 7, loop. VI.
1, mouth; 2, stomach; 3, intestine; 4, anus; 5, heart; 6, entrance to pul-
satile vessel; 7, adductor muscle; 8, loop; 9, arm-fringes.

|

Two organs, each with two compartments, and situated one on each side of the body, have sometimes been considered as hearts; but they seem more probably to belong to the watervascular system, as they open externally to the animal, and convey away the generative products.

The nervous system of the animal is very simple; the central

ganglion being situated above and in front of the stomach. The system of muscles to which it sends nerves is very complicated. This is the only system in which the Brachiopods seem to have a more complicated structure than the Conchifera. A pair of muscles called adductors run from the ventral to the dorsal shell. They are attached to depressions, which are close together in the ventral shell; and at their other ends to other depressions, which are wider apart in the dorsal shell. These in contraction, of course, close the valves. Arising from the outside and front of these are two paired muscles, which are inserted in the dorsal valve behind the hinge-joint, and which thus open the shell when contracted. Other muscles go from the ventral and dorsal valves to the stalk, and these, as well as the pair last named, have smaller muscles to assist their action. The position of these muscles, and of the pits in the shell to which they are attached, vary in the different species of the class, and form good distinctive characters. The calcareous loop also is very different in different species, and sometimes wholly absent. In one whole family, now extinct, it is twisted into a regular spire of many whorls, which grow smaller and smaller as they proceed from the place of attachment outward. They are called, from these organs, Spirifers. The arms in these were closely bound to the spires, and little spurs of chalky matter also supported the elements of the fringe. The Brachiopoda are now rare, especially in the British seas; but at an earlier age 67 of the world they swarmed in immense multitudes, then taking the place of the cockles and mussels which we now find.

The Conchifera are mainly characterised by their breathing organs. They have no fringed arms stretching away from the sides of their mouth; and their mantle not being sufficiently effective as an organ of respiration, they have, developed from the body, and lying between the mantle-lined shells and the body mass, two sheets of membrane on each side. The relation of these breathing plates is best

is drawn out into two long tubes, one of which communicates with the chamber in which the gills lie, and the other with the smaller lined chamber into which the anus opens, and into which, also, the gill-tubes discharge the water. This last arrangement is carried to an extreme in those species which burrow and live in holes of the rock or mud of the sea-bottom. The only communication which these have with the outer world is by means of their extended tubes or siphons, as they are called. In their case the two tubes are united into one sheath, although a partition passing down the double tube always keeps them functionally distinct. In these creatures the action of the cilia drives the water in one continuous stream from the gill chamber to the atrial chamber through the tubes; and this motion necessitates a flow down one tube and up another. By this means floating food is passed along the gills to the mouth, which is situated at the lower end of the buried molluscs, and thus we have a similar mode of life to that of the tunicates, though the breathing apparatus is of a different structure.

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CONCHIFERA.-I. CARDIUM. II. DITTO, SIDE VIEW.

IV. DIA

III. CYTHEREA. GRAMMATIC TRANSVERSE SECTION OF A CONCHIFER (LAMELLI BRANCH). ISOLATED ALIMENTARY CANAL OF A SOLEN.

V.

Refs. to Nos. in Figs.-III. 1, umbo or elbow; 2, external ligament; 3, cardinal teeth of the hinge; 4, lateral ditto; 5, anterior adductor; 6, posterior ditto; 7, mantle lining; 8, the sinus. IV. 1, shell; 2, mantle; 3, gills; 4, heart traversed by the intestine; 5, foot inclosing folds of the intestine and vessels. V. 1, mouth; 2, stomach; 3, blind sac containing the endostyle; 4, intestine; 5, heart; 6, anus; 7, 7', membranous lips.

seen in the illustration, where there is a section given of the animal as it would appear if it were cut across so as to divide both shells. These gill-plates secure that the blood shall be well aërated, not only by exposing as large an amount of surface as possible, but also by having gilltubes, which run through the plates from one edge to the other, through which the water passes. As is usually the case with breathing surfaces in marine animals, the plates are covered with cilia, whose motion secures a constant change in the water. The gill-plates are very variously modified in the different families of Lamellibranchiata; but they are constant throughout the class.

In some, as the oyster, the mantle simply lines the shells and ends at their edges, so that the water has free entrance from all sides. In other families the mantle of one side passes across the aperture of the shell to be united at certain points, or along almost its whole length, to the mantle of the opposite shell. In others the animal is not only almost entirely walled in by the union of the two lobes of the mantle, but part of this mantle

The mantle being thus relieved from the duty of exposing the blood to the oxygen dissolved in the water, is wholly employed in its proper function of secreting the shell. It performs this office in a very efficient manner, so as always to allow for the growth of the animal and for the strengthening of the shell as the contained animal becomes more weighty, and therefore liable to experience more violent collisions. The method of secretion is the following:- Round the edge of the mantle lobes, or at that part where they leave the shells, are situated a great number of glands, whence secretions of different substances are poured out and mingled together. These glands secrete horny matter, a large quantity of carbonate of lime, and some pigment. Thus a fresh rim of hard matter is added at intervals to the shell. size, shape, markings, and colours of the shell are all determined by the edges of this mantle; and the whole of these characters

The

differ so greatly in the different species, and the result is so beautiful in many, that a collection of shells is very interesting. The nucleus, or starting-point from which the formation of the shell proceeds, is called the umbo; and the manner in which the additions are made is very various. Sometimes the mantle edge secretes a great deal of matter at one time of the year, and is nearly inactive, or only pours out a thin secretion, at another; and this will produce a shell with ridges and furrows parallel to the edges of the shell, which are called sulca. If the mantle secretes at certain points, in larger quantity, and but little between these points, or if it be folded or puckered, and the folds remain so during the whole of the growth, then ridges and channels are formed, stretching continuously from umbo to margin. If the margin of the mantle is much folded and thrust out during secretion, it sometimes results in long points or projections, which reach far beyond the rest of the outside of the shell. In the same way it will be seen that the lining and colouring of the shell into patterns may be effected by the partial and intermittent secretion of colouring matter. The shell, while it is being

in some very wide Conchifers there are two distinct hearts, each with its receiving and distributing chambers, or auricle and ventricle as they are respectively called.

For a classification of the bivalve Mollusca the reader is referred to Woodward's excellent manual, for the families are so numerous that their characters cannot all be given in this limited article, and a list of names would be little instructive.

LESSONS IN ARITHMETIC.- XLV.

extended, is also thickened by a thin secretion poured out all over the external surface of the mantle, and therefore all over the internal surface of the shell. This latter secretion is always smooth and colourless, or with only a faint unvariegated pink or purple tint. It is, however, sometimes of a pearly lustre; but the rainbow-like tints of pearl are not caused by the absorption of the other kinds of light, as is the case with coloured surfaces, but from the way in which it is reflected from a very fine ridge and furrow surface, the undulations of which are too small and too close to be seen by the naked eye. The nacre or lining of the shell feels perfectly smooth, and contrasts with the rough outside of the shell. The polished internal surface is no doubt constructed as much with reference to the comfort of the 1. WHEN will the hour and minute hand of a clock be first animal as the rough and spined outside is to its defence. In- together after 4 o'clock ? deed, the smooth secretion in some species will soon encrust any foreign body introduced between the mantle and the shell, and hence the origin of pearls, which usually have as their nucleus a grain of sand. Thus the pearl oyster has supplied to the poetical moralist another instance to corroborate the dictum of our greatest poet-"Sweet are the uses of adversity."

The two valves of the shell are united by the mantle, and at or near the umbo of each valve there is a hinge surface upon which the valves open. This hinge has often a complex system of teeth, which, while they allow the valves to gape, will not permit them to be shifted or wrenched aside on one another. Very powerful muscles run directly from shell to shell, and can, when contracted, hold them together with such force that it is impossible to open them without the assistance of an oyster-knife; and as none of the natural enemies of the molluscs, except man, possess oyster-knives, they are tolerably safe from this kind of forcible entry upon their fortresses. In most Lamellibranchs there are two muscles to close the valves, one in front and the other behind; but in the oyster family there is but one, and this is near the centre of the shell, and represents the hind muscle of the others. Opposed to these muscles is the ligament which runs from shell to shell on the outside of some species, and lies in a pit in the hinge surface in others. These ligaments have no power of active contraction as the muscles have, but are passively elastic. In the case of the external ligament, it is in a state of strain when the valves are closed, and opens them when the muscles relax; while in the case of the internal ligament, it is compressed when the muscles are contracted, and presses the valves apart when they relent.

anus.

The mouth is without hard teeth or jaws; but it often has large flattened lips. The throat is short, and leads into a roundish stomach, which receives the biliary ducts. The great peculiarity of the stomach is the long blind sac which is attached to it, in which is enclosed a cartilaginous rod, the function of which is not known. The intestine twists about in several folds, entering the foot in those bivalves which have feet, and always ending at the opposite side to the mouth and in the atrial chamber. Singularly enough, in many species the intestine passes directly through the heart a little in front of the The foot is an organ of very various development and very various functions in the different species. In some its main office seems to be the secretion of threads by which the creatures moor themselves to rocks. These threads are formed in a groove in the foot, and one end of the thread, while yet viscid, sticky, and unconsolidated, is applied by the foot to the rock. To this it adheres; and when the foot is pulled back, the thread is pulled out of its groove and a fresh one made, so that, at length, a bundle of very strong threads passes from the support to the base of the foot. In other cases, as in the solen, the foot is large and broad, and passes out in front of the long razorlike shell by a slit in the mantle, and with this foot the creature burrows in the sand. In the cockle the foot is long, and can be thrust out and applied to the earth so as to jerk the animal along. In other species it is little else than a muscular investment of the

viscera.

The heart is always systemic, that is, it drives the blood, not to the respiratory organs, but to the system, leaving it to return unaided by mechanical force to the gills, and from thence to the heart again. In all species the heart shows a higher development than in the Mollusca hitherto treated of, inasmuch as there are always two compartments, one less muscular, to receive the blood, and the other more so, to drive it through a system of vessels, where its course is impeded by their elastic walls. In some species there are two auricles or receivers, and

VARIOUS ARITHMETICAL PROBLEMS.

The minute hand moves over 12 minute divisions while the hour hand moves over 1; therefore the minute hand gains 11 minute divisions in this time. Hence, when the minute hand has gained 1 minute division, the hour hand will have moved over of a minute division; and when the minute hand has gained 20 minuto divisions (which is the case of the question), the hour hand has moved over ?? of a minute division, and the minute hand over 12 × of a minute division. Hence the answer is 21 minutes past 4 o'clock.

2. When will the hands of a clock be 15 minutes apart between 11 and 12 o'clock?

There will evidently be two positions: (1) when the hands are 15 minute spaces apart, measuring in the direction of the revolution of the same direction. The hands started 5 minute spaces apart; there the hands, and (2) when they are 45 minute spaces apart, measuring in fore in case (1) the minute hand has gained 10 minute spaces upon the hour hand; in case (2) the minute hand has gained 40 minute spaces upon the hour hand. These correspond respectively [see last example) to distances travelled by the hour hand equal to 1 and 1 minute spaces; or, by the minute hand, 12 × 10 and 1x 40 minute spaces. Hence the required times will be 101 and 43 past 11 o'clock.

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3. Two clock hands turn upon the same centre. One revolves in 12 hours, and the other in 18 hours. In how long will one have gained a complete revolution upon the other ? The first performs of a whole revolution in 1 hour, The second in 1 hour; Therefore the first gains As, or of a revolution in 1 hour; hence it will gain 33 of a revolution, that is, a complete revolution, in 36 hours. 4. A clock gains a minute a day. If it is set right at 12 o'clock to-day, what will be the correct time when it points to 12 o'clock to morrow?

When it points to 1 minute past 12 to-morrow, the true time will be 12 o'clock. Hence 63 x 21+ 1, that is, 1441 of its minutes, are equivalent to 1440 truc minutes. Therefore, when it points to 12 o'clock, the

true time will be 1 of a minute to 12.

5. When gold is at 20 per cent. premium, a person buys goods marked 135 dollars, and offers gold to the amount of 125 dollars. What change ought he to get in notes, 5 per cent. being abated for ready payment ?

125 dollars in gold are worth 138 x 125 dollars in notes. A deduction of 5 per cent. on 135 dollars leaves 135 dollars. Hence he receives in change notes to the amount of 150 - 128-25 dollars, or 212 dollars.

6. A and B run 100 yards race, and A wins by 2 yards; C and D run over the same course, and C wins by 6 yards; B and D also run over it, and B wins by 4 yards. If A and C run, which will win, and by how much?

A runs 100 yards while B runs 98 yards; C runs 100 yards while D runs 9 yards; B runs 100 yards while D runs 96 yards. Hence A would run × 100 yards while D runs 96 yards; and C would run 109 x 96 yards while D runs 96 yards.

Hence A would run 10? × 100 yards while C runs 100 × 96; hence A would run x 100 x 100 yards while C runs 100; or A would rau

113 x 100 yards while C runs 100; hence A loses by % of a yard.

7. A person invests in the Three per Cents. so as to receive 3 per cent. clear after paying an income tax of 9d. in the pound. What price does he buy at, and what clear per-centage will ne receive if the income tax be raised to a shilling ?

9d. in the pound reduces £1 to 19 shillings. Hence, to find what actual per-centage he receives before the deduction of the income tax, we haveAs 191 203. This gives 3.

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the purchase-money to put into repair. It then stood empty for a year, during which time he reckoned he was losing 5 per cent. upon his total outlay. He then sold it for £1192, by which means he gained 10 per cent. upon the original purchasemoney. What did he give for the house?

The expense of repair was of the cost price; therefore the total outlay was of the cost price.

By the house standing empty he lost of the cost price. Therefore, before he sold the house, his expenses had been × 2 of the cost price, and by selling it for £1192 he gained of the cost price. Hence, of the cost price + of the cost price is £1192; or of the cost price is £1192; or rar of the cost price is £8. Therefore the cost price was £1000.

9. A person buys an article, and sells it so as to gain 5 per cent. If he had bought it at 5 per cent. less, and sold it for ls. less, he would have gained 10 per cent. Find the cost price. 125 of the cost price is the selling price. If he had bought it for of the cost price, and sold it for 10% of the cost price 1s., he would have gained 10 per cent.

100

Therefore 1 of 1 of the cost price is 183 of the cost price or 183-(11 × 48) of the cost price is 1s.; or as of the cost price is 1s. The cost price was therefore £10.

|the first gun, he would have heard the second 6 minutes afterwards. But since he hears it 351 seconds afterwards, he has in this time travelled over a space which sound would traverse in 9 seconds. Therefore the velocities of the train and of sound are in the ratio of 9: 351. Hence the speed of the train is T x 1125 feet per second, that is, feet per second.

The noise which the train makes at a distance of 2 miles will take 1760 × 6 seconds to reach the station. During this time the train will 1125 1760 × 6 375 13

travel

1125

X

2

feet, or X 1760 feet. 13

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1s. ;

3. 117261.

4. 335553.

5, 7335344.

cent. on his gross income

6. 227950.

in.

10. A man allows his agent 5 per for collecting his rents. He spends of his net income in in- 7. 28 sq. ft. 82 sq. suring his own life, and this part of his income is in consequence exempt from income tax. The income tax being 10d. in the pound, and his income tax amounting to £38 19s.; find his gross income.

After paying 5 per cent. to his agent, 1 of his gross income is left, which is his net income; but since of this is exempt from income tax, he pays tax on x 8 of his gross income.

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11. Suppose the cost of working a train to be directly proportional to the speed, and the number of passengers. Then, if the cost be £37 for conveying 185 passengers 531 miles in 1 hours, how far can 1070 be conveyed in 2 hours for £161 ? Suppose the speed be reckoned by the number of miles travelled in 531 214 one hour. This, in the first case, is or miles per hour; and, 19' in the second case, if a represent the required distance, the speed will be represented by

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2, from which z is found to be 51 miles. 185 × 24

12. A cistern has two pipes, A and B, which singly could fill it in 9 and 10 hours respectively. It has also two taps, C and D, which could empty it in 12 and 8 hours respectively. When the cistern is half full, A and D are turned on for 3 hours; then B is also turned on for 2 hours; next A and D are turned off, and C is turned on for 8 hours. Then, all being shut, it is found that the cistern contains 95 gallons more than the half content. Find the capacity of the cistern, and how much the cistern could lose or gain in an hour if all four pipes were set open

together.

A can fill of the cistern in 1 hour; B can fill in 1 hour; C can empty in 1 hour; D can empty in 1 hour.

A is open altogether 5 hours; B is open altogether 10 hours; C is

open altogether 8 hours; D is open altogether 5 hours.

Hence the effect will be to add ; + 18 − − 1, or 2 of the whole cistern, and this by the question is 95 gallons.

Hence the cistern holds 3 x 95, or 360 gallons.

If all the pipes were set open at once, in one hour the cistern would gain +1-75-1, or so of its contents, that is, 1 gallon.

13. The time between the firing of two guns at a railway station is 6 minutes, and a passenger in a train which is approaching the station at a uniform rate hears the second 5m. 51secs. after the first. Now, supposing that the sound of the train when it is two miles off will reach the station, how long after it is heard approaching will it pass the station, the velocity of sound being 1125 feet per second?

If the passenger had remained stationary at the place where he heard

8. 268 cub. ft. 996 cub.

in.

IN LESSONS IN ARITHMETIC.-XLIV. EXERCISE 63.

9. 105 sq. ft. 5' 4" 5" 5, 4.

15. 48 feet.

16. £8 6s. 4d.

10. 85 sq. ft. 1' 11" 0" 17. 1023 feet.

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Erratum.-Lesson XLII., Example 6.-Auswer should be £100 165.

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75. All systems of shorthand adopt the principle of abbreviation explained in the Sixth Lesson, namely, the writing of every frequent word by some one letter that is heard in its pronunciation. Such words are called in the old, or a, b, c systems of shorthand, "arbitrary words; in Phonography they are called "grammalogues." It has been found by a calculation of the occurrence of words in numerous specimens of English, on various subjects, scientific and literary, that in 30,000 words, the occurs 1,727 times, or once in 17 words; and occurs 1,221 times, of 1,163 times, to 864, in 581, a 478, that 416, is 366, etc. Now as the letters of the alphabet serve no purpose as letters, and are used only as component parts of words (except in the three words a, I, 0), there can be no objection to their being employed as the representatives of these frequent words, as far as the letters and words can be adjusted to each other, so that no letter shall represent two words, and every letter shall represent a word that contains it. This principle might have been adopted in ordinary longhand writing, and doubtless would have been, had there not been in existence systems of shorthand which saved time upon the forms of the letters as well as in the use of arbitrary words or grammalogues.

76. In the next lesson the pupil will be introduced to a more extended list of grammalogues than the one given in the Sixth Lesson, whereby he will greatly abbreviate his writing. The subject is mentioned here for the purpose of comparing and supplementing this principle of abbreviation, which is common to all shorthands, with another principle which is peculiar to Phonography, as to the extent principle of abbreviating the letters of the alphabet, by giving shorter to which it is carried, and its harmonious application. It is the

forms for them.

77. The comparison may be made thus:-As letters, when put together, make a word, and if the word is frequent, its expression is abbreviated by the employment of a logogram, or one of its letters; so letters themselves, if frequent, are shortened by various devices of circles and hooks, attached to other letters, and by shortening and lengthening the letters themselves.

78. The frequency of the occurrence of letters in English has been made the subject of calculation, and the results are, that passing by about 70 of the most frequent words in the language, which are provided with grammalogue signs, the letters or sounds occur in point of frequency in the following order: n, s, t, r, l, d, k, z, m, f, b, p, v, ng, ing (affix), j, coz, w, g, tion, h, sh, ith (breath), the (breathe), ch, y, zh, in one subject, and s, r, t, n, 1, d, p, m, k, z, f, ing (affix), v, b, tion, sh, ith, the, ch, g, coTM, w, h, ng, zh, y. slight difference in the calculations is due to a difference in the subjects. The two calculations are sufficiently near to show the order

The

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