attributed to the little winged creature from which it is reflected. In the Mollusca instincts are not wanting, and locomotive and perceptive powers are also evidenced; but they are wholly inferior in these faculties to the Articulates, and in turning to them we feel to be turning from the higher modes of life to the lower. The body of the insect is so fitted for rapid and dexterous action that it seems to have become almost ethereal; while in the slug the very senses seem to be dulled to suit the requirements of the coarser material parts. For a further contrast of the Articulata and Mollusca we must refer the reader to a former lesson. It suffices here to mention one or two points of general structure which are intimately connected with the habits of these creatures. First, since the Mollusca are less adapted for locomotion than other animals, the requirements which swift locomotion dictates are not insisted on with such strictness. Rapid locomotion necessitates what is called bi-lateral symmetry-that is, that the body shall be precisely alike on both sides. This, accompanied with an elongated form, whose axis is in the line of locomotion, is the form best suited for advance. A ship is better than a tub for locomotion, and the keel must not only be straight, but the hold must not be lopsided. Thus we found that in the insect every part, down to the shape of the nerves in its netted wings, is accurately represented by its counterpart on the other side. In the Mollusca, however, this symmetry is not essential, and it is liable to be dominated by other requirements. A pecten (scallop) lies on its side, and hence has one side flat and the other rounded. A snail has its body rolled into a spiral for compactness' sake, and for the convenience of having a large orifice for its respiratory chamber; that spiral is not equilateral, but twisted to one side. Secondly, since rapid locomotion is not the first object, the walls of the body represent a rounded bag to contain the viscera, rather than a fulcrum, upon which lever-like limbs H. IV. is directly from the Hydroid Coelenterata. These creatures are compound animals-that is, the product of a single egg or reproduced animal may grow into a multitude of similar heads or parts, each one of which has all the essential organs of life, and can live when detached; hence their name Polyzoa, or multiple animals. The plant-like growth of these compound animals is a process of budding, but it is carried on in very various directions. According to these directions and methods, very various aggregate forms are produced. In many instances it results in an incrustation composed of closely-set cells. These crusts spread from a point, and often closely invest sea-weeds and rocks. They seem to have a special partiality for the shells of other Mollusca, exercising, however, a discrimination by affixing themselves rather to the shells of the less locomotive bivalve Mollusca than to those of the univalves. Thus they have the benefit of a slight change of place without being subject to abrasion by constant locomotion. These incrustations so much resemble the clothing of moss which spreads over stones and walls, that some naturalists have applied the name of Bryozoa to these animals, a term which signifies moss-like animals. The crusts are to be found by any one who examines objects which are generally covered by the sea, and, when examined by the naked eye, they look like fine lace of different patterns. So great is the diversity and beauty of these forms that they repay even this superficial investigation. The Polyzoa have existed from a very early period in the history of the earth, and they then had the same habits, as a class, as they now have. This is evident from the fact that no one can make a collection of fossil shells without also collecting many of the Polyzoa attached to them. In these cases they are usually attached to the outside of the shells. When they are found covering the inside of the shell, of course this is a proof that the shells remained for some time at the bottom of the ancient sea after the death of their owners, before they were co are plied; and hence it is al- POLYZOA.-I. FLUSTRA. II. PLUMATELLA REPENS (ONE POLYP) CUT OPEN vered with the mud or sand TO SHOW INTERNAL ORGANS. III. SCRUPOCELLARIA, SHOWING VIBRA- ways soft and flexible, and the limbs are not jointed organs, but lobes or protrusions of the bag wherewith to crawl or grasp, not to raise or propel. Thirdly, since protection is not sought in flight, it is afforded in a structure which would impede flight, and the creatures, when on the defensive, retract and nullify all their feeble locomotive apparatus, casting themselves wholly on the defensive efficiency of their shells. The lowest class of the Mollusca is widely different from the more typical classes, and the structure of its representatives seems to indicate that the starting-point of the molluscous classes of the deposit in which they are found embedded. One comparatively recent formation is so full of the remains of these creatures as to be called the Coralline Crag of Suffolk. This name was given when the creatures were supposed to resemble coral polypes (Actinizoa), and now that they have been discovered to be of higher standing in the animal scale, and, in fact, to belong to an altogether different sub-kingdom, of course the name is inappropriate. Sometimes the crusts do not cling closely to the substance from which they spring, but rise up from it. In such cases the free frond may be flattened, being, in reality, two crusts placed back to back, and mutually supporting each other. This is the case with the ordinary sea-mat (Flustra maxima), which is one of the largest of these compound animals, and may have been often mistaken for a sea-weed by the casual observer. In other cases the stems, instead of being wide and flat, may be much narrower, presenting single or double chains of cells, which branch and spread freely in the water. In some rarer instances the whole compound animal is locomotive, the crust, with its many cells, and their contained simple zooids, travelling, by common consent, in one direction. It will be seen by the above description that the outward form of these creatures is closely paralleled by those of the Coelenterata, and when to this outward resemblance is added the fact that each of the simple animals which occupy the cells has a head almost precisely similar to the Hydro zoa, it is not surprising that they should have long been confounded with them. A mouth, surrounded by a circle of tentacles capable of motion, is characteristic of both the compound Hydrozoa and the compound Polyzoa; but it was early observed that the tentacles of the latter were always clothed with cilia, while those of the former were unfurnished with them. The reader of these lessons will remember the na tare of the organs called cilia, and the nature of their action as described when the Rotatoria were treated of. By the aid of these organs currents are set in motion and directed towards the funnelshaped mouth, and thus small parti III. rightly considered to be of high physiological importance, and TUNICATA.-I. PEROPHORA LISTERI. II. SALPA MAXIMA (ONE OF A CHAIN TO SHOW CIRCULATION). cles of food are Refs. to Nos. in Figs.-I. 1, nervous ganglion; 2, atrial chamber and outlet; 3, respiratory pharynx so-called head may be protruded or retracted from the cell at pleasure, it is, of course, necessary that some considerable part of the outer wall which joins it to the hard part of the same should be soft and flexible. A reference to the illustration of Plumatella will show the relation of the flexible to the hard part of the wall, and the muscles by which the head is pulled back. This illustration will also show the character of the alimentary canal, and how it is bent upon itself, so that the after part passes up close to the first descending portion. This arrangement of the food canal is very constant in the Polyzoa, and is dictated by the fact that, since the animal can only protrude one end of its body from the cell, both the entrance and the exit must be at that end. Muscles originating from the bottom of the hard part are attached to the stomach and throat, so as to pull these parts back when the head is withdrawn. In the re-entering angle between the mouth and arms a single ganglion is found, and this sends a few nerves round the throat and to the body walls, in some, at least, of these creatures. The reader will have gathered from the illustration and description that while some of these creatures have all the bodycavities of their simple zooids in communication with one another, others have these completely separate. In both cases, however, the simple animals seem, in many respects, dependent in some measure on the general structure. Thus many of them have external organs not possessed by each cell, but only by some of them, which organs, nevertheless, minister to the wants of all. These external organs are very singular, and are of two kinds. One kind is like a vibrating whip, and the other resembles the head and beak of a bird. Both are endowed with a power of motion which is apparently automatic. It is supposed that the whips constantly stir the water, so as to bring fresh food within the action of the cilia, while the singular beaks snap up, kill, and hold any small creature till it decays, and so, by disintegration, furnishes food. We have indicated the reasons for considering the Polyzoa superior to the Polypi, and before quitting them we ought to state in what respects they are inferior to the other Mollusca, so as to justify us in placing them lowest in the list. Their inferiority mainly consists in the want of a heart, and any true blood-vascular system, and also in not possessing a well-developed liver, which organs are constantly possessed by the other molluscs in great perfection. The liver in these creatures is only represented by some scattered brown-coloured glands placed on the outside of the stomach. The Tunicata seem to be more nearly allied to the Polyzoa than the Brachiopoda, and therefore we treat of them next; although it seems to be also true that they are more closely related to the Conchifera than the Brachiopoda are. Perhaps the distinctness of the Brachiopoda as a class may be accounted for by the fact that they are a very ancient class of animals, having inhabited the earth from the earliest primary period. Many of the Tunicata, like the Polyzoa, are compound animals. They are, however, not exclusively so, and they are usually of a much larger size. They do not deposit any chalk or shell in their outer mantle. They have a heart with a single chamber, and a singular respiratory apparatus. sac, and so drives the water and the substance out again. This action has procured for the simple tunicate the name of the Sea Squirt. Compound Tunicates do not differ much in structure from the simple ones, but they are connected together in some instances by a stalk, through which the blood is driven from zooid to zooid. This is the case in the family of the Clavellinida. In the family called Botryllida the separate zooids are only the products of a budding process, and though they are at first connected organically and always cohere, yet when mature the vascular connection is obliterated, and each feeds and respires for itself. In another family a multitude of zooids are united in a tube, one end of which is closed and the other open. All the mouths, or in-current orifices, of these are outside the tube, and all the ex-current orifices inside, so that the current of water which passes into the tube, being compelled to pass out at one end, drives the whole animal along; these creatures differing from the foregoing families in being free and locomotive. Another free and locomotive family is characterised by what is called an alternation of generations. In these a solitary individual gives birth by budding to a whole chain of zooids unlike itself, and united to one another end to end, not, indeed, organically, but by simple attachment. These have their in-current orifices at one end, with a valve attached to them, so as to prevent the water escaping outward. When, therefore, the body is contracted the water is driven out at the other end, and so contributes to the onward motion of the chain. Across the respiratory sac there is a band or ribbon stretched, and this is the main instrument of respiration. One of these creatures (i.e., one link of the chain) is represented in the engraving. Each zooid, or link, gives birth to one solitary form, unlike itself but like its mother, and so the so-called alternation of generations is completed. The production of the solitary Salpa is a true reproductive process corresponding to the rearing of a plant from seed, but the production of the chain is analogous to the growth of a branch from a leaf-bud. We will commence by the description of a simple animal, such as may be found adhering to the under side of a rock near low-water mark. The outer form is that of an Eastern leathern bottle, with a prominent mouth at one end; but it is unlike this bottle in that it has another opening on the side a little below the mouth. The mouth leads into a wide, dilated throat, which occupies a large part of the centre of the bag-like animal, and is of a very peculiar structure. It has in its walls a series of slits which lead into a cavity directly communicating with the lower orifice. The slits are very numerous and small, and their edges are fringed with cilia which continually drive the water from the central throat to the atrial chamber, as the cavity is called. At the top of the throat is a circlet of tentacles which protrude into it, while at the bottom is an opening LESSONS IN GEOGRAPHY.-XXXII. leading by a short esophagus into a stomach, from which an CONSTRUCTION OF PROJECTION OF MAP OF ASIA. intestine, twisted a few times, leads into the atrial chamber near its orifice. The remainder of the viscera, consisting of THE method to be adopted by the learner in preparing a proliver, heart, etc., are closely united with the stomach at the jection for a map of Asia is precisely the same in every respect bottom part of the sac. From one end of the heart a vessel as that laid down in Lessons in Geography, XXV. (Vol. IL, runs off, and is continued as a capacious channel along one side page 355), with the exception of the position of the point from of the sac-like throat, while another channel along the opposite which the arcs representing the parallels of latitude are deside runs to the viscera, and through them to the other end of scribed; which, however, is determined in a similar manner to 1 the heart. The two channels above-mentioned communicate that adopted for finding the centre from which to describe the with one another by many transverse vessels, which branch in arcs representing the parallels of latitude of a map of Europe. the membranous walls of the sac. Let us now consider the A base line must first be drawn, as C D in Fig. 17 (Vol. II., relation of these organs to the functions of respiration and page 356). This line must be bisected in E, and through E a alimentation. First, with regard to respiration. The cilia straight line A B must be drawn, which will represent the central which fringe the slits are the prime movers of the water by meridian line of the map. It will be convenient to number this driving it from the inner sac into the chamber which surrounds line as the 85th meridian east from Greenwich. Now take any it. This motion necessitates that a current should set in at space to represent ten degrees, but be careful that the space the mouth, or end opening, and another out at the anal or side thus assumed is not taken too long in proportion to the base opening, and thus fresh water is constantly brought to the line of the map, and set off from E, the point of intersection inner, or what may now be called the respiratory sac. In the of the base line c D, and the perpendicular A B, fifteen of these substance of this sac the blood is constantly changed by the spaces, and number the points, beginning with E, 5, 10, 15 20, motive power of the heart, which, though a simple tubular 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, and through the organ, contracts at one end first, and by the successive contrac- point numbered 80 draw the straight line G H parallel to D. tion of its circular fibres drives the blood to one of the channels, The figure of a projection of a map of Asia, it should be said, and from thence through the tissue of the sac into the other, is not given here, as the method of constructing it will be made and so, by way of the viscera, into its other end. It is peculiar sufficiently clear to the learner by directing his attention to to these animals that the current is occasionally reversed. After the lettering of Fig. 17, to which reference has been already working in one direction for some time the heart remains at made above. Now, as in the projection of the map of Europe, rest, and then begins to propel the blood in the other direction. the straight line G H will be the limit of the map towards the Next, in relation to food, it will be seen that the current will top, and the points numbered upwards in succession from E will bring with it many of those little creatures which are so nume- be the points through which will pass the parallels of latitude rous in the waters of the sea. By some mysterious action the corresponding with the numbers. To find the centre from which cilia do not allow these particles of food to pass out by the to draw the arcs representing the parallels of latitude, set off slits, but propel them down towards the entrance to the stomach, five spaces more, of five degrees each, and bisect the last space and so onward. The excrement is, of course, passed out at the thus set off. The point of bisection of the last space thus anal opening by the current. When any obnoxious substance obtained will be distant 12° 30' from the point representing the is introduced by the current of water, it is felt by the tentacles pole, and which would be numbered 90, continuing the numberwhich hang down inside the throat, and when this is the case ing from 80 upwards. This will determine the point from which the animal contracts the outer muscular coat so forcibly as to the arcs representing the parallel of latitude may be described compress not only the atrial chamber, but also the respiratory through the points numbered 5, 10, 15, 20, etc., sufficiently near for all practical purposes; although it should be stated that the distance of the common centre of these arcs from the pole is 12° 8', instead of 12° 30′, to speak with greater accuracy, since the first named of these points-namely, that which is distant 12° 8' from the pole, or the point numbered 90-is that at which a straight line, drawn through the points 25 and 60 in Fig. 14 (Vol. II., page 356), would cut the straight line c E, if it were produced far enough towards E. As the method of forming a conical projection, or a projection in which the surface of a right cone is supposed to enter and come out from the spherical surface of a sphere in two circles, the planes of which are at right angles to the common axis of the cone and the sphere, has been described at length in Lessons in Geography, XXV. (Vol. II., page 355), it will be unnecessary It will be sufficient, therefore, to remind the to repeat it here. learner that, as we suppose the cone on which the map of Asia is to be projected to enter the sphere at the 25th and 60th parallels, these parallels being equidistant, supposing the globe to be a perfect sphere, from the points numbered 5 and 80, through which the lines limiting the map at top and bottom are drawn, the conical and spherical surfaces correspond at these parallels, and at these parallels the degrees of longitude, or rather the distances between the meridians, will possess their correct proportions; that is to say, that along the 25th parallel the distance between two meridians measuring a degree apart will be 54-38 geographical miles, while along the 60th parallel it will be 30 geographical miles, as may be seen by referring to the table at the end of Lessons in Geography, XXV. (Vol. II., page 357). To determine the length of either of these spaces in the necessary proportions to the line that may have been assumed to represent five degrees, a diagonal scale of proportional parts, similar to those shown in Figs. 15, 16 (Vol. II., page 356), must be constructed. Spaces equivalent to 54:38 geographical miles may then be set off along the 25th parallel, on either side of the central meridian that was drawn perpendicular to the base line, and straight lines drawn through the points thus obtained from the common centre of the arcs that represent the parallels of latitude. The straight lines thus drawn will represent the meridians 80, 75, 60, etc., and 90, 95, 100, etc., all east from Greenwich, numbering to the right and left from the centre The border lines of the map, meridian, which is numbered 85. the scale of miles, and the subdivision of the spaces between the meridians and parallels of longitude and latitude, may then be completed according to the directions given for constructing the projection of a map of Europe in the lesson that has been already named. The following table will afford sufficient names for the construction of a map of Asia on a.small scale. If a large scale Lanchang be adopted, the latitudes and longitudes of additional places may be obtained from the index of places appended to any Macao ordinary atlas. Macassar Martaban Lucknow . Latitudes. Longitudes. 85 0 LESSONS IN ARITHMETIC.-XLIII. SCALES OF NOTATION-DUODECIMALS-SQUARE AND CUBIC MEASURE. 1. IN the common or decimal notation, as we have seen, the value of the figures representing any number increases from right to left, by powers of ten. Thus, 5638 means 5 x 103 +6 x 102 + 3 x 10 + 8. Now although this employment of 10 as the radix, as it is called, of our Scale of Notation, is convenient, it is quite arbitrary; and we might express any number by means of powers of any other number than 10. For instance, if 4 were taken as the radix of the scale of notation, 231 would denote 2 x 42+ 3 x 4 + 1. Similarly, if 8 were the radix of the scale, 5732 would mean 5 x 83+ 7 x 82 + 3 x 8 +2. The numbers here represented by 231 and 5732 are said to be expressed in the scale of 4 and the scale of 8 respectively. 56789 = 2 x 12 +8 x 123 + 10 x 12 +4 x 12 + 5. So that, in the duodecimal scale, 56789 would be written The above process, which manifestly would apply to any scale, will sufficiently explain the following Rule for Reducing a Number given in the Decimal Scale to any other Scale. Divide the given number by the radix of the scale, putting down the remainder; divide the quotient again by the radix, and so on, until the quotient is less than the radix, so that the division is no longer possible. The last quotient and the suc cessive remainders, written down in order from left to right, will be the correct notation for the number in the required scale. 4. Given any number expressed in the Duodecimal Scale, to reduce it to its equivalent expression in the Decimal Scale. This can evidently be done by dividing successively by 10, taking care to recollect what the value of each figure in the dividend really is. EXAMPLE.-Express 28t45 in the decimal scale. Ten in 28 (duodecimal scale) is really 10 in 2 x 12 + 8, or 32, which Ten in 2t is really 10 in 2 x 12 + 10, or 34, which gives 3 and 4 over. 2. It is evident that each of the figures or digits which occur Suppose we take 12 for the radix of the scale, we must then have symbols to represent the numbers 10 and 11. If we use t and e respectively for them, then such a number as the following, 57t4e9, would mean 5 x 12 +7 x 12 + 10 x 123 + 4 x 122 + 11 x 12 + 9. The scale of which the radix is 12 is called the duodecimal or duodenary scale. We do not mean here to go at length into the various propositions connected with scales of notation, for they belong properly to algebra, and cannot be satisfactorily explained without its aid. We subjoin, however, one or two propositions, which will be useful in giving the student a clearer insight into the principles of arithmetical notation. 3. A number being given in the Decimal Scale, to express it in the Duodecimal Scale. 2 x 128 x 123 + 10 x 12 + 4 x 12 + 5 = 5 x 10+6 x 103 +7 x 10+ 8 x 10 + 9. 5. Similarly, a number expressed in any scale whatever can be transformed to any other scale, by successively dividing by the radix of the scale into which it is to be transformed. We content ourselves with giving an example, with its explanation. EXAMPLE.-Given 56435, expressed in the scale of 8, to reduce it to the scale of 6. 6) 56435 6) 7604 5 6) 1226 6) 156 2 6) 22 2 ... 6) 3 0 302205,-Answer. The division is performed as follows: |