186 



♦ KNOWLEDGE ♦ 



[July 1, 1889. 



Fig. 3. 

 From a dissection. 



muscular pharynx, which is pushed forwards as the animal 

 eats. Below thus the canal narrows into the gullet— the 

 (esophagus, into which open three several pairs of glands, 

 secreting a surprisingly large 

 * quantity of cirbonate of lime. 



Nothing like them is known to 

 exist in any other animal. They 

 ai-e very richly supplied with 

 blood, so that at first sight even 

 one feels sure the}' must serve 

 some important purpose in the 

 animal's economy. That purpose 

 is probably twofold in character ; 

 they serve as organs of excretion, 

 that is, to cast out of the body 

 something which is useless or 

 actually harmful ; and secondly, 

 they directly aid digestion. You 

 will almost always find an accu- 

 mulation of carbonate of lime, 

 sometimes in crystals, sometimes 

 in little almost shapeless lumps, 

 and you don't find those worms 

 which live in chalky soils and 

 whos3 intestines are full of chalk, 

 with smaller or less well-filled 

 glands, so we may fairly argue 

 that the lime is an excretion, 

 •a, mouth ; /8, pharynx ; 7, Again, worms live largelv on 

 cEsophagus ; 5, calciferous f^Qg^ leaves, as we shall see 

 glands; ..crop; C gizzard, ggg^t] ^^j these contain a 

 7), intestine i 1, supra-oeso- f •" 



phageal ganglia ; /c, double 'arge amount of lime, of _ no use 

 nerve-cord. to the tree, which gets rid of it 



in this way. Secondly, the half 

 ■decayed leaves generate in themselves various kinds of 

 acids ; the secretion of the earth-worm's alimentary canal is 

 alkaline, and it is believed that these masses of lime 

 neutralise the acid food so as to allow the alkaline secretion 

 to have fair play. On jiasshig on from these glands one 

 finds that the canal swells out into the crop, and a little 

 lower down into the gizzard, which the worm uses as a 

 fowl uses its gizzard to crush and reduce to a pulp hard 

 food. To assist this, the bird swallows gi-avel and small 

 stones. Our earth-worm has no t«eth, and not even a beak ; 

 its gizzard is formed of very strong circular muscles, and 

 generally encloses a store of sand and tiny stones. From 

 the gizzard, the intestine, which has a number of dilatations 

 on each side, runs in a straight line to the vent at the 

 posterior end of the body. From its upper surfiice all along 

 proceeds downwards into it a dip or involution — the 

 typhlosole — serving to extend the absorbent surface very 

 greatly. The nervous system of the earth-worm is very 

 simple. In the third segment, overlying the pharynx, are 

 two ganglia united together ; from these nerves run to the 

 mouth and skin of the firet segment. These ganglia are 

 supposed to represent the brain of a higher animal. From 

 these, two nerve-cords run round the pharynx to the ventral 

 surface of the intestine ; they join there, and run the whole 

 length of the body, swelling at every segment into a gangli- 

 form enlargement, whence two pairs of nerves are given 

 off on each side, while from the intermediate nerve cords one 

 pau- supplies the deep muscles. We may consider this 

 ventral nerve chain as comparable to the spinal cord of 

 higher animals, while a tiny nerve-filament — the .so-called 

 stomato-gastric — coming from the supra-o.>sophageal ganglia 

 dorsally over and to the intestine, is the equivalent of the 

 .sympathetic system. With regard to the vascular system, 

 there are two kinds of blood in the earth-worm. ^Iv. Busk 

 put forward the ingenious idea that in the blood of 



mammals there may be a division made into two functional 

 parts, i.e., that of the red corpuscles, which are carriers of 

 oxygen, and the white corpuscles and plasma, conveying 

 nourishment to the tissues. This idea has also been sup- 

 ported with his accustomed vigour by Ray Lankester. In 

 the vessels of the earth-worm red blood is very extensively 

 supplied to the skin (a breathing organ), while a colourless 

 plasma with white cells in the segmental chambers bathes 

 all the visceral organs. The division of function which has 

 been suggested is rendered probable by the analogy of the 

 worm, though not certainly proved. As regards the l^lood- 

 vessels, a dorsal one — rhythmically contractile — runs the 

 whole length of the animal's body ; there is also a sub- 

 intestinal and a sub-neural one, all of which communicate 

 with each other, and in the eighth to the sixteenth segments 

 these communications are called hearts. 

 (To be continued.) 



SOME PROPERTIES OF NUMBERS. 



By RoBT. W. D. Christie. 



AKE any multiple of 7 having two digits 

 only, then we may place any other figure on 

 each side, and the number with four digits 

 thus obtained will also be a multiple of 7 : 

 e.g., suppose we take 21 or 28 or 35, then 

 1211,2212,3213, 4214, 521.5, 6216,7217, 

 8218, 9219, kc, are all multiples of 7 ; so 

 also 1281, 3283, 5285, 3353, 4354, 6356, Ac, are divisible 

 by 7 without remainder. 



The same principle applies to multiples of 1 1 or of 13 : e.g., 

 let us take 33, 55, 77 ; 26, 52, 78. Then the numbers 1331, 

 4554, 6776; 4264, 7527, 9789 are multiples of 11 and 13 

 respectively. 



"The same principle applies to numbers having eight digits 

 (or 6m — 4 digits): e.g., 12345676 is divisible by 7; con- 

 sequently 1123456761, 2123456762, 3123456763, <fec., are 

 also divisible by 7. 



We need not confine the principle to numbers of two or 

 eight digits : e.g., we know that 567 is divisible by 7 ; so 

 also is 14679. Here I place 9 on the right side, according 

 to the rule, but instead of placing 9 on the left side I add 

 9-1-5 to get 14. Again, 234 is a multiple of 13 ; so also is 

 9347 for the same reason. Again, 2678:=13M; .so also is 

 31785. Here 26-|-5=:31, and so on for any number of 

 digits. The figure placed on each side need not necessarily 

 be the same. Any figure of the S'une form will do equally 

 as well. Thus 8211, 2219, 17213, 144214, etc. Here 8 is 

 of Form 7M-I-1, 144 of Form 7^1 -f 4, kc. In applying 

 this principle, though we may have any number of figures 

 on the left, we are restricted to one figure on the right hand. 

 The proof is easy. Let ^^7, 11, or 13. 



We have 10?(-|-c=N(Mi) by hypothesis. 



Therefore 10-A-l- 10c=N(M„) .... (1) 

 AlsolO'V(-f-rt=1001a=N(M3) .... (2) 

 Thus lO^c-t + 1026-l-lOc-f a=N(M). Q.E.D. 



(2) If we take any number with 6 digits (or 6u digits), 

 having remainders 1, 2, 3, 4, 5 or 6 when divided by 7, we 

 may by prefixing 6, 5, 4, 3, 2, 1 respectively obtain an exact 

 multiple of 7 : e.g., the number 123456-r 7 has a remainder 4. 

 Therefore 3 123456 = 7M. Here we have 7 — 4 = 3. Again, 

 123456, when divided by 13, has 8 for remainder. There- 

 fore, since 13— 8=5, we have 5123456 = 13M. Similarly, 

 123456789012=13M-|-11. Therefore 2123456789012= 

 13X. 



(3) Take any number of two digits and double it. The 

 four figures placed side by side are divisible by 17. 



