362 



THE POPULAR EDUCATOE. 



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 

 animal as the rough and spined outside is to its defence. In- 

 deed, the smooth secretion in somo 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 con- 

 tracted, 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 pas- 

 sively 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. 



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 intes- 

 tine passes directly through the heart a little in front of the 

 anus. 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 sup- 

 port 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 razor- 

 like 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 develop- 

 ment than in the Mollusca hitherto treated of, inasmuch as 

 there are always two compartments, one less muscular, to re- 

 ceive the blood, and the other more so, to drive it through a 

 system of vessels, where its course is impeded by their elastic 

 wails. In some species there are two auricles or receivers, and 



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 re- 

 ferred 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. XLY. 



VARIOUS ARITHMETICAL PROBLEMS. 



1. WHEN will the hour and minute hand of a clock be first 

 together after 4 o'clock? 



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 tV of a minute 

 division ; and when the minute hand has gained 20 minute divisions 

 (which is the case of the question), the hour hand has moved over ?? 

 of a minute division, and the minute hand over 12 x f J of a minute 

 division. Hence the answer is 21i 9 f 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 hands, and (2) when they are 45 minute spaces apart, measuring iii 

 the same direction. The hands started 5 minute spaces apart ; there- 

 fore in case (1) the minute hand has gained 10 minute spaces upon the 

 hour hand ; iu 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 } and JJ minute 

 spaces; or, by the minute hand, |J x 10 and i? x 49 minute spaces. 

 Hence the required times will be 101? and 43/ T past 11 o'clock. 



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 t*j of a whole revolution in 1 hour, 

 The second tV ,, ,, ,, in 1 hour; 

 Therefore the first gains -fe rV, or a l j of a revolution in 1 hour ; hence 

 it will gain |J- 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 60 x 21+1, that is, 1441 of its minutes, are equivalent 

 to 1440 true minutes. Therefore, when it points to 12 o'clock, the 

 true time will be -J-J-J 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 13 x 125 dollars in notes. A deduction 

 of 5 per cent, on 135 dollars leaves i 9 u s o x 135 dollars. Hence he receives 

 in change notes to the amount of 150 128'25 dollars, or 21J 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 94 yards ; B runs 100 yards while D runs 96 yards. 



Hence A would run W x 100 yards while D runs 96 yards ; and C 

 would run V x 96 yards while D runs 96 yards. 



Hence A would run \a 9 x 100 yards while C runs *g? x 96 ; hence A 

 would run J x vs x 100 yards while C runs 100 ; or A would run 

 JlfJ x 100 yards while C runs 100 ; hence A loses by Iffo 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 he 

 receive if the income tax be raised to a shilling ? 



9d. in the pound reduces 1 to 191 shillings. Hence, to find what 

 actual per-centage he receives before the deduction of the income tax, 

 we have 



As 19} : 20 : : 3. This gives 3j\. 



Q 



The price he gives therefore is x 100, or 96 J. 

 SjV 



When the income tax is raised to a shilling, he receives clear on 100 

 invested 5 x 3 T B f) which is 2'96 per cent, very nearly. 



8. A man bought a house, which cost him 4 per cent, upon 



