U\nrn 1, 19(X1.] 



KNOWLEDGE 



Hi) 



Siiuaif luf uauiial square is latent in exactly tlic same 

 way. 



lu Figs. 13, 14, each Square is seen to be latent in 

 the othor with its rows and columns in Knight's paths. 



In Figs. 15, 16, each square is seen to bo latent in 

 the other with its rows (or columns) in Knight's paths, 

 and its columns ^or rows) in Bishop's paths. 



Polarity of direction with regard to paths is thus es- 

 tablished. 



VI. XoT.KTlo.N. — If each number of the Natural 

 Square is denoted by a combination of two letters 

 A, B, or C, and a, b, or c, one denoting the row, and 

 the other the column of the Natural Square in which 

 the number occurs, the notation of the Natural and 

 Magic Squares, Fig. 2 and Fig. 1, will resiJcctively 

 be: — 



A;v Ab Ac Be Aa Cb 



Ba Bb Be and Ca Bb Ac 

 Ca Cb Cc Ab Cc Ba 



Now let the Magic Square Fig. 1 bo written in similar 

 notation : — 



Aa Ab Ac 

 Ba Bb Be 

 Ca Cb Cc 

 the notation of the Natural Square will then be; — 

 Ab Ca Be 

 Cc Bb Aa 

 Ba Ac Cb 

 which is seen to be precisely the same as the notation 

 of the Magic Square in terms of the Natural Square, 

 except that the rows of one arc the columns of the 

 other. 



If the rows and columns of either of these squares 

 formed from the other are examined it will be found 

 that in any row or column of either, every row and 

 column of the other is represented. Or to put it in 

 another way, evei-y capital letter and every small letter 

 is found in every row and column of either square. 



The existence of a law under various aspects, and the 

 essential unity of the law, has now been as fully illustra- 

 ted as our space permits. It is needless to say that if a 

 square of higher dimensions is subjected to the same 

 sort of analysis many more illustrations of the same 

 law are discovered, but their very multiplicity is rather 

 a disadvantage than otherwise. It is the simplicity 

 of the 3 squares which makes it such a good " subject.' 

 Under whatever form the law may appear in greater 

 squares we may be siu-e that the same principles under- 

 lie it in all cases. 'WTiatever rules have been heretofore 

 devised, or may be devised hereafter, for the construc- 

 tion of magic squares — must be based upon the same 

 principles. 



♦ 



PLANTS AND THEIR FOOD.-II. 



By H. H. W. Pearson, m.a. 



We have seen that more than half of the substance of 

 a plant is composed of Carbon.* Carbon, therefore, is 

 the most important constituent of plant food, and we 

 will now consider whence and in what form it is ob- 

 tained. The forms in which this element is found in 

 Nature are not numerous, although there is an immense 

 quantity of it. It exists in the pure form, as is well 

 known, in Diamond and Graphite (of which " lead " 

 pencils are made) ; combined with other elements it is 

 found in great abundance in the air as Carbon dioxide 



• Kkowledok. January, 1900. 



gas,t and in the earth in the form of Carbonates (e.g., 

 Dolomite, Limestone, Chalk, &c.); it also occurs nearly 

 all over the eai'th's surface as organic mattei", which is 

 the result of the alteration and decay of the dead 

 bodies of animals and plants. Plants obtain their 

 Cavlon mainly from the Carbon dioxide in the air. 



" Organic " subst;'«nces were so called because it 

 was thought that they could only bo produced in the 

 couree of the pi'occsses of life in a living animal or 

 plant. They were thereforo considered to be of an 

 essentially different chai'acter from simpler substances 

 — such as Carbon dioxide, Nitric Acid, &c. — which the 

 chemist could prepare in his laboratory. In 1828, 

 however, a German chemist succeeded in preparing arti- 

 ticially a solid compound called " Urea," whick, before 

 that time, was supposed to bo produced only in the 

 body of a living animal. Since then many more of tho 

 so-called organic substances have been fabricated oy 

 chemists. We now believe that in the course of time 

 the chemist will be able to prepare ai-tificially all tho 

 substances which are found in animals and plants, or 

 at least, compounds which are chemically identical 

 with them. The term " organic " can therefore no longer 

 be used in tho sense in which it was at lirst applied 

 to these substances, but as a matter of convenience it 

 is still customary to use the term to include the very 

 large number of compounds which Carbon makes with 

 other chemical elements, although many of them are 

 now quite as easily made as a simple inorganic sub- 

 stance. For our present purposes we may say that an 

 organic substance is a compound of Carbon and Hy- 

 drogen (or Nitrogen), which usually contains Oxygen 

 as well, and frequently other elements (e.g., Pho.sphorus 

 and Sulphur) in addition. 



Certain plants, such as the Fungi, obtain the whole 

 of their Carbon from organic matter which they ilud in 

 the soil or other substances upon which they grow. 

 Others, however, which contain the green colouring 

 matter, chlorophyll, in their leaves, derive at least part 

 of their Cai-bon — it may be all — from the Caibon 

 dioxide in the air. It is with these green-leaved plants 

 that we are most generally familiar. The green colour, 

 although present, is in some cases masked by other tints, 

 as in the leaves of the common red cabbage and the 

 " copper " beech. For the present we shall consider 

 the Carbon food-supply of green plants only. 



Air contains a very small proportion of Carbon 

 dioxide. It was found dui-ing 1898 that in the air 

 of the Royal Gardens, Kew, at a height of 4 feet 

 6 inches from the ground, there were from 2.7 to 3 

 parts of Carbon dioxide in 10,000 pai-ts of air.t Thus, 

 although the stock of Carbon in the atmosphere taken 

 in the aggregate is immeasurably large, it is in an 

 extremely diluted condition, and we cannot easily form 

 any idea of the va.st amount of air which must be 

 drained of its Carbon in order to supply the needs of 

 the world's green vegetation. It has been calculated 

 that in attaining its full size, a single tree havini? a 

 di7 weight of 11,000 lbs. has abstracted a.11 the Carbon 

 from over 15 million cubic yai-ds of air.§ 



The Carbon thus taken from the atmosphere is not. 



t Carbon dioxide is that constituent of the air whieh eauscs lime 

 water, exposed in an open dish, to become " milky." A few other 

 gases which contain Carbon arc also found m the atmosphere in 

 certain localities, e.r/., Marsli gas. 



I Presidential Address to the Chemical Section of the Briti:<h 

 Association, Dover, 189'J. 



§ " A Text-book of Botany," by Strasburger, Noll, Scheuck, and 

 Schimper (English translation;, p. 19(i. 



