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weighs 2 pounds, these amounts are 1 pound, pound, pound, and pound, together 17. Take this from 12, and we have an effective power of 10 remaining; and as the gain is 16, the weight raised is 16×101, or 162 pounds.

3. Friction requires a strain of 9x 20, or 180 pounds, to overcome it, and of the weight has to be borne. The strain, therefore, is 180+ 448, or 628 pounds.

4. Friction is here is of 27 cwt., which equals cwt. The amount of the weight sustained by the horse is of 27 cwt., or 1 cwt. total strain is thus 1 cwt., or 144 pounds.

5. The weight of the carriage is 25 × 80, or 2,000 pounds,

6. The co-efficient of friction is, or nearly.

The

LESSONS IN ARITHMETIC.-XXVIII. FRACTIONS IN CONNECTION WITH COMPOUND QUANTITIES.

1. To find the Value of any Fraction of a Compound Quantity. It is evident that we have only to divide the given compound quantity by the denominator, and then multiply by the nume rator. The first part of the process determines the magnitude of the equal parts into which the denominator indicates that the quantity is to be divided, and the latter takes as many of those parts as are indicated by the numerator. Thus, Again, of £2

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of £1 = 3 × 308. = 15s. of 408. = 4 × 188.

1.

of £1;

Ys. =103s.

4 x 8 3

= -8.

s.;

2.

of £1;

of ls.; H of 3s, 2d.

3.

Again, of a shilling is of 12 pence, or 2 x d. 8d. Therefore, of £2 = 10s. 8d.

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2. Find of 3 days 4 hours 25 minutes.

days. hrs. min.

of 1 yard; of 1 rod.

of 1 gallon; of 1 peck.

of 1 hour; of 1 minute; of 1 degree.

7. 3% of of a mile; off of a week.

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= 2 × 917 1834 minutes.

4560+25= 4585 minutes.

Therefore, of 3 days 4 hours 25 min.

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Therefore, of 3 days 4 hrs. 25 min. is 1 day 6 hrs. 34 min.

3. To reduce one Compound Quantity to a Fraction of any other.

Finding what fractional part of one compound quantity another given compound quantity is, is called reducing the latter quantity to the fraction of the first.

Thus, finding what fraction of one pound 6s. is, is reducing 6s. to the fraction of a pound.

This is, in fact, only another name for performing the operation of dividing one compound quantity by another, or of finding the ratio of two compound quantities (see Art. 11, Lesson XXVII., page 101).

4. EXAMPLE.-What fraction of £1 7s. 6d. is 3s. 6d. ?

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11. Find the sum of of 2s. 6d. + of £3 2s. 6d. + }

of £5 7s. 31d. 12. And of of 168. 61d. 13. Find the value of 14. Find the value of

15. Find the value of

+ of 12s. 10d. + of £2 46. 8d. of £7 148. 1d. — of £4 08. 1d. of £4 0s. 1d. —3% of £3 10s. 1d. of # of 1 of £1. of + of

Reduce to the fraction of a pound

16. 438.; 4s. 7d.; 9s. 2 d.

17. 13s. Od.; 3‡d.; £3 15s. 91d.

18. What part of £1 is of a penny? 19. What part of 1 lb Troy is 7 oz.? 20. Reduce

21. Reduce

of a quart to the fraction of a gallon. of 1 secon to the fraction of a week. 22. Reduce £3 17s. 11 d. to the fraction of £7 3s. 23. Reduce 3 pecks 2 gallons to the fraction of 2 bushels. 24. Reduce 15 cwt. 65 lbs. to the fraction of 2 tons 3 cwt. 25. Reduce 1° 15′ 10′′ to the fraction of a right angle. 26. Reduce 1 acre to the fraction of 5 acres 2 r. 40 p. 27. Reduce of £1 to the fraction of a penny.

28. Reduce

29. Reduce of

of a week to the fraction of a minute. of £2 8s. 9d. to the fraction of £1 1s. 8d. 30. Express as a fraction of £10 the difference betwen £8! and of £8. 31. Find the value of

32. Find the value of

136 gals. 2 qts. 178 gals. 3 qts.

33. Find the value of

1 lb. 7 oz. 4 dwts. 2 lb. 7 oz. 10 dwts. 77 dys. 4 hrs. 30 min. 6 dys. 12 hrs. of 517 square feet 72 inches. £3 18s. 8d. £6 12s. 9d.

of 15 guineas.

of

1° 17 17′ 15′′

of

of 104 yards 9 inches.

KEY TO EXERCISES 44, 45, 46, LESSONS XXVI., XXVII.

1. £9 2s. 8 d. 2. £3 5s. 10d.

3. 8 cwt. 1 qr. 6 lbs. 10 oz.

4. 24tons1cwt. 83 lbs. 5. 19 miles 289 rods 2 feet.

6. 1 league 1 m. 7 fur.

10 rods 12 feet.

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13. 24645 cub.ft.930 in.
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14. 176 rt.ang.51°13′30′′
21°45′ 0′′
39955° 4' 48"
15. £174673 18s. 7 d.
£195788 78. 3d.
16. 40 tn.6cwt.8lb.5oz.
3667 12 84 7
4393 2 10 1
17. £14540116 18s. 3d.
£16871008 98. 3d.

yrs. d. hr. m. sec. 9. 10 35 1 13 11

1 123

1. £4 17s. 3d.

5. 46 bush. 81 qts.

41

121

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13. 1718.

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15. 137900.
16. 30.
17. 219.

7. 9 yds. 1 qr. 0}} nls.

1° 17' 38'
1° 0′ 22′′
11. 10s. 11 Pgd.
12. 15.

truly represent the actual rectangular axes which are employed on the surface of the globe. The aspect they would then assume will be understood by reference to Fig. 6, where the circle P MET PNQ 8 may represent the first meridian, and the circle E O Q R the equator, their point of intersection E being their origin as rectangular axes. We still call these rectangular axes, because the planes of the circles cut each other at right angles, and the spherical angles PEO, PER on each side of the meridian are right angles, whether taken from the upper or north pole P, or from the lower or south pole P; so that we still have four right angles round the origin E; but these are now spherical right angles, that is, angles formed by the quadrants or fourth parts of the circumferences of these great circles of the sphere. In order to have a proper view of the rectangular axes on the sphere, we should require to be looking at the edge or circumference of the circle PEPQ, and not at its plane or surface as in the figure; then we should see the edge or circum5 308 10 48 41ference of the circle R E O Q cutting the former at right angles, 97 31 and both exhibiting at a distance the same appearance as the 1 40 8 32 3 lines X X and Y y'in Fig. 10. In this view, the point E being 10. 1° 48′ 41′′ the origin of the axes, all points on the surface of the sphere included between the semicircle EM P SQ and the semicircle EOQ, are said to be in north latitude and east longitude; the longitude being measured from E along the eastern half of the equator EOQ, and the latitude from the same part of the equator on a meridian passing through any of the points in question and the two poles PP. All points on the surface of the sphere included between the semicircle EMP SQ and the semicircle E R Q, are said to be in north latitude and west longitude; the longitude being measured from E along the western half of the equator ER Q, and the latitude from the same part of the equator on a meridian passing through any of the points in question and the two poles P P. All points on the surface of the sphere included between the semicircle E T P N Q and the semicircle E R Q, are said to be in south latitude and west longitude; the longitude being measured from E along the western half of the equator E R Q, and the latitude from the same part of the equator on a meridian passing through any of the points in question and the two poles PP. Lastly, all points on the surface of the sphere included between the semicircle ETP NQ and the semicircle E O Q, are said to be in south latitude and east longitude; the longitude being measured from E along the eastern half of the equator E O Q, and the latitude from the same part of the equator on a meridian passing through any of the points in question and the two poles PP.

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LESSONS IN GEOGRAPHY.-XVIII. LATITUDE AND LONGITUDE-FIRST MERIDIAN, ETC. IN the preceding view of the determination of the position of a given point, we have not considered all the possible positions of a point P round the point A, the origin of the co-ordinate axes. If these axes were produced in the preceding figures so as to assume the appearance represented in Fig. 10, then, with the same given distances or rectangular co-ordinates, there might be four different positions of the point P with reference to the rectangular axes xx' and Y Y', or the north and south straight line y y', and the east and west straight line x X'. prevent confusion, therefore, and to fix the exact position of the point in question, it might be agreed upon that every distance measured from the origin A, along the portion of the axis AX, should be called east, and every distance measured from the origin a along the portion of the axis A X' should be called west; in like manner, that every distance measured upwards from the axis x X' should be called north, and every distance measured downwards from the axis x x' should be called south. Moreover, it might be agreed upon that every distance measured upwards from the axis xx should be called north latitude, and every distance measured downwards from the axis XX' should be called south latitude; and in like manner, that every distance measured from the point A to the right or eastward, should be called east longitude, and every distance measured from the point A to the left or westward, should be called west longitude. Now this supposition is that which has actually been agreed upon; so that in a map of the world upon Mercator's projection, as it is called, the straight line Y Y' would represent the first meridian or that of Greenwich; and the straight line x x' would represent the equator; also, the point A would represent the point of intersection of this meridian with the equator, which are, in fact, the two rectangular axes to which all points on the earth's surface are referred, in order that their true positions (geographical positions) may be determined. Accordingly, the point P (Fig. 10) would be described as the position of a place in north latitude and east longitude; the point r', that of a place in north latitude and west longitude; the point p", that of a place in south latitude and west longitude; and the point p", that of a place in south latitude and east longitude.

If the straight lines X X', and Y Y', which we have supposed to represent the first meridian and the equator, were to become circumferences of circles of the same size, they would then more

The student who reads the above explanation of latitude and longitude on the rounded surface of the earth for the first time, may have a difficulty in realising the appearance of the sphere from the diagram made on a flat surface, but he must endeavour by his natural ideas of perspective to obtain as clear a notion as he can. Of course the difficulty would be entirely removed by the actual inspection of a globe; but, as it may not be possible for him to have a globe by his side while he is reading this lesson, we must try what we can do by means of the small Map of the World in the next page, although it must be remembered that the surface of no solid body as a whole can be truly represented on a plane surface such as the page referred to. With that map before you, then, you will see the two sides of the globe represented in what are called the eastern and western hemispheres. In order to see the whole of only one side, or half of the globe, the eye must be supposed to be at an infinite distance, and still possessing the power of sight; accordingly, two such sights directly opposite to each other will enable you to see the whole of the globe. This is the reason that two circles are necessary to represent the globe, because only one-half can be seen at a time. If these two circles could be pasted along their edges or circumferences, back to back, so that their north and south poles coincided, and then inflated till they assumed the form of a globe, they would then form a pretty correct representation of the earth's surface. The equator, which you know is a circle equally distant from the two poles, is represented on the Map of the World by a straight line drawn across the middle of both hemispheres, marked by the word equator, and with degrees from 0° to 180° east, and from 0° to 180° west, reckoned from the first meridian.

In the map referred to, these degrees are marked only at the distance of every 20 degrees, on account of its smallness; in

larger maps they are marked at the distance of every 10 degrees; and in larger still, at less distances; the best being those where they are marked at the distance of every single degree; but these, of course,; must be of enormous size. The first meridian, that of Greenwich, is known by its being marked with 0 on the map or the equator. On looking at the eastern hemisphere, you will see this 0 marked on the equator, in the Gulf of Guinea, south of the coast of Guinea in Africa; this is the origin of the rectangular co-ordinates, the first meridian, and the equator, and it is to this point that all measurements of longitude are to be referred. On running up the meridian, passing through this zero point, towards the north pole, you will find that it passes through London in the British Isles; this, you know, is not strictly the case, the meridian of St. Paul's Cathedral, London, being about 6' or geographical miles west of the meridian of Greenwich; but this is so small in ordinary maps, that it is scarcely perceptible, and certainly not mark able; whence the meridians of London and Greenwich are, for common purposes, considered the same. The meridian of Greenwich has been chosen as the first meridian, in preference to that of London, because Greenwich is the site of the Royal

its intersection with the equator are marked 0, to show that latitude begins to be reckoned from these points. Each of the four quadrants (or fourth parts) of these circles is marked with degrees from 0° to 90° reckoned from the equator to the poles. In the map referred to, these degrees are marked only at the distance of every 10 degrees, on account of its smallness; in larger maps, they are marked at less distances; and the best are those in which they are marked at the distance of every single degree; but these, of course, must be of very great size. In the same map, circles are made to pass through the corre sponding points on the upper or northern quadrants of the outer or surrounding circle of each hemisphere, and of the upper or northern half of the middle straight line extending from pole to pole, at the distance of every 10 degrees; these upper quadrants, and this upper half, actually denoting the northern por tions of meridians passing respectively through the points of the equator marked longitude 20° W., longitude 160° E., and longitude 709 E. These circles, which on the globe are parallel to the equator, are, from the nature of the projection employed in this map, not actually parallel to that line or to each other, being drawn from different centres; but they are still called parallels

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Observatory. Accordingly, all meridians which cross the equator to the right of that of Greenwich, are said to be meridians of places in east longitude; and all meridians which cross the equator to the left of that of Greenwich, are said to be meridians of places in west longitude. For example: if you look at Peking, in China, on this map, you will find that it lies to the right of the first meridian in the northern half of the eastern hemisphere, between two meridians which cross the equator, the one being that which is, or should be, marked at the point of intersection 110°; and the other that which is, or should be, marked at the point of intersection 120°: this enables you to guess, by the vicinity of Peking to the latter meridian, that its longitude is about 116° east; now the actual longitude is 116° 26' E. Again, if you look at Buenos Ayres, in South America, on the same map, you will find that it lies to the left of the first meridian in the southern half of the western hemisphere, between two meridians which cross the equator, the one being that which is, or should be, marked at the point of intersection 50°, and the other that which is, or should be, marked at the point of intersection 60°: this enables you to guess, by the vicinity of Buenos Ayres to the latter meridian, that its longitude is about 58° west; now the actual longitude is 58° 25′ W.

On the first meridian, the degrees of latitude are not marked; but they are marked, in the Map of the World, on the circle which surrounds each hemisphere. On this circle, the points of

of latitude, and are used to enable us to determine the latitude of any place on the map. Similar parallels of latitude are drawn through the corresponding points on the lower or southern quadrants of the outer or surrounding circle of each hemisphere, in the same manner, and for the same purpose. For example: if you look at Peking, in China, on this map, you will see that it lies between the equator and the north pole in the eastern hemi sphere, and just upon the parallel of latitude marked 40° at each side of the map: this enables you to guess that the latitude of Pekin is nearly 40° north; now the actual latitude is 39° 54' N. Again, if you look at Buenos Ayres, in South America, on the same map, you will find that it lies between the equator and the south pole in the western hemisphere, and nearly in the middle between the parallels of latitude marked 30° and 40° at each side of the map: this enables you to guess that the latitude of Buenos Ayres is nearly 35° south; now the actual latitude is 34° 36′ S. Having thus shown how to find separately the lati tude and longitude of any place on the surface of the globe by means of the circles and lines drawn in the Map of the World it is easy for the student to combine these, and thus to deter mine the actual position of any place on the surface of the globe. Thus, we have found that the city of Peking, in Chin is situated in lat. 39° 54' N., and long. 116° 26' E.; and that the city of Buenos Ayres is situated in lat. 34° 36' S., and long. 58° 25' W.

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I., II. EUDENDRIUN RAMOSUM (HYDROZOON). III. HYDROZOON ENCRUSTING A SHELL (NATURAL SIZE). IV. RHOPALONEMA VELATUM, THE VEILED CLUB-TENTACLED MEDUSA-A FREE SWIMMING MEDUSA. V. PERPENDICULAR SECTION OF A SEA ANEMONE. VI. TRANSVERSE SECTION OF A SEA ANEMONE. VII. PLEUROBRACHIA, A CTENOPHORE BELONGING TO THE ACTINOZOA. VIII. TRANSVERSE SECTION OF PLEUROBRACHIA (CTENOPHORE). Refs. to Nos. in Figs. (I.) 1, feeding organs, with fringe of tentacles, mouth, and stomach (shaded); 2, flower-like organs of reproduction which become detached and swim away, as in Fig. II.; 3, creeping stem. (IV.) 1, polyp suspended within (2) the swimming-cup; 3, its veil. (V.) 1, organs of reproduction on the edge of a septum; 2, the face of a septum. (VI.) 1, the stomach wall; 2, the body wall; 3, septa joining the walls. (VII., VIII.) 1, mouth; 2, centre of the stomach; 3, comb-like locomotive organs; 4, sack into which the tentacles can be withdrawn; 5, tentacles cut short; 6, nerve-knot and organ of sense.

tozoa, but also from the fact, that in this class we find the first indications of many of the structures which are necessary to, and acquire such a great development in, the animals higher than themselves. Definite membranes, muscular fibre, nervous and hepatic (liver) tissues are found in some of these animals.

A glance at any of the more common forms, such as are represented in Figs. I., II., III., will at once suggest that these animals have a mode of growth and a general form very similar to the higher forms of vegetables, such as grow in

VOL. II.

but in another respect the resemblance is better maintained, for in the centre of the bell there rises a thick club-shaped body, which may well represent the clapper. The resemblance to a plant is maintained throughout the whole of the external form of this animal. With a creeping network of roots (if we may so call them), it encrusts some submarine rock, or stone, or shell. From this it sends up branching stems, each branch of which is terminated either with a flower-like cup, which protects a tubular body with a mouth at its far end, surrounded with a circlet of

36

they contain. They then close around the prey, and press it in through the mouth into the interior, where its soft parts are dissolved, and its insoluble part is passed out again by the way it entered.

This short description leads us to remark upon the character which cuts off the Colenterata from the higher animals. In the case mentioned, it will be noticed that the animal is, so to speak, all stomach. The bounding wall of the stomach is also the wall of the body. In the higher animals the food cavity is distinct from the body cavity. These higher animals consist of a tube within a tube. The nutriment derived from food by them is strained through the walls of the inner tube, or other

feelers, or else with a fruit-like rounded organ, which, like a fruit, eventually drops off when fully developed. It is true that if we were to attempt to guess at the functions of these organs from this analogy, we should find these appearances very deceptive. These creatures never derive any nutriment through their roots or stems as plants do, but only through the little mouths at the ends of the branches. Again, the flower-like heads are in function rather like leaves than flowers. Nevertheless, whatever the function, the general plan of structure and growth is identical, and the likeness was so marked that naturalists were long before they would admit that these creatures were not plants. The animals whose branching stems are so exactly like to plants and shrubs, are microscopic; but this same resem-wise abstracted from it before it can be applied to the mainblance to vegetables is exhibited, though in a less striking form, in the higher and larger members of the sub-kingdom. If the reader, while peering into the clear waters of a pool left by the ebb of a spring tide, should see a rock covered by a multitude of flower-like heads, each with many circles of purple-tipped tentacles radiating from a common centre like the anthers of the wild rose or the buttercup, all of which seem to float and sway passively with each little eddy he excited, he would certainly take them for sea flowers. Even the common actinia, which is left dry on the rock, collapsed into a dome of jelly, might readily be taken for a flower when, at the first approach of the sea, it expands from this bud-like condition into a spreading disc, fringed not only with tentacles, but with a circular row of bright blue knobs.

Otherwise well-educated men, who know nothing of the natural sciences (and the number of these is large), often declare that the lowest animal is but little removed from the highest plant. This, however, is a popular error, and the reverse of this is the case. The true statement is that both kingdoms start from the same point. The simplest and lowest forms of both, especially in their immature condition, are almost identical. At this simplest and earliest stage of development, the plant makes quite as decided an approach towards the typical life of an animal as does the animal make a counter-approach towards the typical life of a vegetable. The young spore of a conferva (vegetable) is locomotive, and moves by the same mechanism as a protozoon. Thus the animal and vegetable kingdoms not only meet at their lowest point, but the vegetable, so to speak, travels more than half way to effect the meeting. From this common point of contact the two kingdoms slowly diverge from one another; but the divergence is so gradual, the angle of divergence is so small, that for some distance they move in an almost parallel course. Now, as the vegetable stops far short of the development of the animal kingdom, we must look for the parallel to its higher forms, not in the lowest animals of all, but in those at some little distance up the scale; not in the last and lowest division, Protozoa, but in the penultimate sub-kingdom, Colenterata. It must, however, be remembered that the analogy to plants is only a parallel. There are no intermediate forms connecting the most plant-like hydrozoon with the most coral-like plant. To find the links of the chain of life which connects them, we must run downward through all the grades of animal life, to mount up again by the different grades of vegetable development. We shall find that though there are fundamental differences, yet the analogy is very strict between Colenterata and plants in very many respects.

Though unlimited growth and repetition of parts be the main characteristic of both Coelenterata and the higher plants, some of the former are simple enough. Just as the little paschflower (Anemone pulsatilla) sends up its one blossom in the grass, so does the little fresh-water hydra extend its few tentacles around the mouth end of its tubular body, while it attaches itself, by the other end of the tube, to a water-weed. This animal is simply a tube or bag, while its tentacles are narrower tubes, whose hollows communicate with the main one. These are arranged in a circle round the mouth, which is a perforation in the free end of the tube. The bag is flexible, and composed of two layers of tissue closely adhering to one another. The stuff of which the bag is made is double, and the lining is so like the outer stuff, that the bag can be turned inside out, as Baron Munchausen served the wolf, without deranging its economy. The long arms sway about in search of food. Any little animal unfortunate enough to come in contact with them, becomes benumbed by some stinging organs

tenance of the tissues of their bodies. In all the Cœlenterata, the food tube is not shut off from the cavity of the body. In the hydra, the stomach is identical with the body cavity; in others, the stomach is continuous with the body cavity, being only partially cut off from it by a circular valve, so that the stomach acts as a kind of porch or vestibule to detain the food a short time, and it is then passed on into the lower part of a tube of equal dimensions. In others, the central stomach divides into radiating hollows, and these divide and subdivide, and often produce a network of fine canals. In these the stomach presents the structure, and has also the office of both stomach and blood system of higher animals. All the animals which have stomachs such as we have described, belong to the subdivision of the Colenterata called Hydrozoa. The other subdivision, called Actinozoa, presents a different arrangement. With them, although the stomach freely communicates with the body cavity, it is not identical with it, and cannot be said to be continuous with it. Indeed, these animals show an approach to a higher grade by having a stomach within the body wall; but this tube within a tube is not a perfect one, but opens below into the general cavity of the body. Also a number of partitions run from the body wall to the stomach, so as to maintain the latter in its position, and to divide the body cavity into compartments. This arrangement is well seen in Figs. V. and VI.

This

To return to the Hydrozoa. The simple hydra is a locomotive tube, but it fixes itself by one end in a temporary manner. animal produces young not only from eggs in the ordinary way, but also by putting forth buds from its sides, which, while attached to the parent, develop mouths and arms, and then become separated, being able to live for themselves.

The hydra, therefore, exhibits functions and tendencies which, when carried to a greater extent in other species, produce very many modifications, and these may be grouped under two types, which, though apparently very different, are, as we shall see, closely connected with one another.

1st, the fixed and branched hydrozoa, with long branching stem, each of whose heads is very like the hydra; and 2nd, the free swimming hydrozoa, which float at large in the ocean, and have locomotive organs to raise them to the surface and propel them along.

The animals which range themselves round the first of these types are the most perfect examples of the vegetative habit. The home of the Cœlenterata is the water, and almost all except the hydra live exclusively in the salt waters of the ocean. These fixed hydrozoa, of course, need not only an atmosphere of water, but a bottom whereon to grow. They are to be found around our coasts, some of them in the pools left by the retreating tide between high and low-water mark. The dredge has brought up some of these animals from great depths, and it is probable that they flourish at still lower levels; but it is unlikely that they could live under the enormous pressure exerted by the overlying waters in the profundity of mid-ocean. Most of these plantlike compound animals are invested with a horny sheath which covers the stem and branches, so that the beautiful patterns in which they grow may be preserved after the soft parts of the animal have been dried up. A collection of such dried specimens gives a far better idea of the animals than a dry herbarium gives of the different species of plants; for the hard parts being of a stiffer nature, and external instead of internal, the outer form is far better preserved. Some of these hard sheaths or skeletons have at the end of each branchlet a little cup which, in the living state of the animal, defends the little hydra-like poly• pite (as it is called). In another order the sheath ends abruptly, allowing the polypite to be protruded nakedly beyond it.

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