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1S82.J 



KNOWLEDGE 



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&nv Corresipontienre Columns. 



POPULATION OF THE EAETH : A CCEIOtJS PROBLEM. 



[891] — A correspondent, James Connal, asks how much space 

 would be required on the earth, on the assumption that, beginning 

 with a single pair, the human race had multiplied during 5,000 

 years at the rate of 30 children to each pair, sons and daughters 

 being bom altornatelj, and each husband and wife being at the 

 time of marriage respectively 21 and 20 years old — there being also 

 no deaths. The problem is too difficult " for any use," as Americans 

 Bay ; but it may be roughly dealt with thus : — Children being born 

 from the twenty-first to the fifty-first year of husband's life, and 

 from the twentieth to the fiftieth of the wife's, we shall obtain a 

 fair mean estimate, rather under than over, if we take 30 children 

 for each pair at the age of 40 (nineteen or twenty being really bom 

 before and the rest after 40). On this assumption the population 

 of the world in 5,000 years (or 125 times 40) would be 

 2 -f 30 -e 450 -(- Ac. to 126 terms 



= 2 [ =-(15'^) approximately. 



L 15 — 1 I 7 

 Now log. 15 = 1-1760913, and multiplying by 126 



log. (15'*) = 1481875038 

 log. '/ = 0-8450980 



log. (number representing population) = 147-3424058 

 =log. 2190015, followed by 141 digits, which digits we may repre- 

 sent without appreciable inexactness by cyphers. Now, assuming 

 that ten persons could stand on a surface one yard square, 30 

 millions could stand on a square mile, and on the entire earth, whose 

 surface is about 200,000,000 square miles, some 6,000 millions of 

 millions. Dividing the number just obtained by this, we get 3666526, 

 followed by 125 cyphers. It would require this inconceivable number 

 of worlds like our own for the population on the assumptions made. 



Let us see how large a single globe would suffice to give standing 

 room to this population, ten to the square yard. 



Such a globe must have a diameter exceeding the earth's as the 

 cube root of the above quantity exceeds unity, or, roughly, as 7 

 followed by 43 cyphers exceeds unity. (In reality it will bo larger 

 considerably, but this is near enough in such a problem as the pre- 

 sent.) Now the diameter of the orbit of Neptune, roughly, exceeds 

 the earth's diameter nearly 700,000 times. Hence the diameter of 

 the required globe exceeds the diameter of Neptune's orbit more 

 than a hundred billions of billions of billions of times. 



Supposing the farthest star visible in the great Rosso telescope 

 to lie some thirteen or fourteen millions of times ^farther from us 

 than the nearest, which lies about 7O,0C0 times farther than 

 Neptune, the distance of that star, 1,000,000,000,000 times farther 

 than Noptune (or a light-journey of some 40 millions of years), 

 would be but the 



100,000,000,000,000,000,000,000,000th 

 part of the radius of such a globe as would be required to hold the 

 population we are considering. A sphere having a radius equal to 

 100 millions of years' light-jouraey would not suffice even to contain 

 so many human beings. 



COD SOUNDS AND SCIENTIFIC PRIVILEGE. 

 [392] — Though I am glad to see Mr. Mattiou Williams' exposi- 

 tiou of his views upon the subject of Cod Sounds, as it enables one 

 to understand the way in which his (as I take it) misconception of 

 the nature of that structure has been brought about, yet I am very 

 sorry that any clumsiness of expression upon my part should have 

 led him to think that 1 am an upholder of that paltry spirit of scien- 

 tific exclusiveuess which he with such vigour and justice condemns. 

 Versatility in my eyes ranks next only to accui-acy in a scientific 

 man, and' I agree entirely with Professor de Morgan that the ideal 

 scientist should " know something of everything, and everything of 

 something," indeed my own studies in biology have been undertaken 

 mainly with a view to enlarging my grasp of another science from 

 which I have borrowed the nam de plume under which 1 write. 



This notwithstanding, I trust Mr. Williams will pardon my point- 

 ing out that, for instance, Pasteur's splendid acheivements " in the 

 domain of the biologist " were not published as the recollections 

 of work done in his student days twenty or thirty years previously. 

 Since the days when Mr. Williams was a student of natural history, 

 A-c, at Edinburgh, biology has made vast strides, partly by the 

 mere increase of the number of observers, but mainly by the aid of 

 absolutely new methods of research with refinements in appliances 

 undreamed of forty years ago. The grand generalisations of 

 Darwin have, besides, directed inquiry along linos entirely new. Did 

 Mr. Williams acquaint himself with the writings of modem Com- 

 parative Anatomists, and then perform one careful dissection of 

 a •■ Cod-fish," I feel sure he would come to a very different conclu- 

 sion as to the nature of the " Sound." As, however, it would be 

 unreasonable to ask him to recommence the study of so large a. 

 subject after such a lapse of time, I will just give an account of the 

 appearances presented in my recent dissections of the fish under 

 discussion. 



I would point out that, as a preliminary, the blood-vessels were 

 injected with a brightly coloured fluid which made them so distinct 

 as to leave no room for doubt as to their nature. 



Just under the throat the heart is situated, and from it proceeds 

 forwards a large vessel, the ventral aorta ; this subdivides into a 

 number of branches which distribute blood to the gills. After 

 traversing the minute capillary vessels of those organs, the blood is 

 carried into a corresponding set of large vessels, which, after giving 

 off one or two unimportant branches, unite to form a medium trunk, 

 the dorsal aorta, which almost immediately sends branches to the 

 stomach, intestine, and various glands. From the point whence 

 these arteries are given off, the aorta bends up and runs in direct 

 contact with the underside of the backbone down to the tail. Lying 

 beside the aorta are two large veins. 



Beneath these blood-vessels is a large bag (the sound) with 

 fibrous saccular walls, the dorsal (upper) wall of which is very thin 

 and delicate, and the ventral (lower) and lateral walls exceedingly 

 thick and strong. This bag extends through almost the entire body- 

 cavity, and is quite shut. It terminates in front in two blind 

 prolongations which He loosely among the nerves and blood-vessels 

 just behind the head. Within it (besides air, which I have always 

 found) is a body known as rete mirabile, a closely-packed arterial 

 network, which receives its blood from a very small branch of the 

 aorta. Between the sound and the backbone are the kidneys, 

 elongated bodies of a deep-red colour, which in the dead fish, at any 

 rate, contain a gi-eat deal of blood. They are divisible into tlireo 

 regions^a thick head Sidney, not in contact with the sound, extend- 

 ing from the hinder part of the skull backward to the mid-kidney, 

 a much thinner portion, occupying the middle region of the body- 

 cavity ; and a very thick portion, the coalesced right and left hind 

 A-idiiei/«, passing back beyond the hinder end of the body-cavity. 

 The kidneys are supplied with blood by a number of small branches 

 of the aorta, and their ducts (the %ireters) pass right through the 

 sounil, perforating both its upper and under walls, and carrying 

 side by side with them a small artery. 



When the coloured fluid was injected into one of the large 

 arteries, it passed freely into the aorta (the dorsal one I style 

 simply the aorta) and all' its branches, even to the most delicate ,• 

 yet not one drop found its way iiito the cavity of the sound. 



