IS© 



SCIENTIFIC NEWS. 



[Aug. 17, 1? 



will give the points for the hours VII., VIII., IX., X., 

 and I. 



We have now to find the centre of the dial, or the 

 point from which the hour lines radiate, this being also 

 the point where the style, or the edge of the gnomon 

 meets the plane of the dial. On the circle FKGL, Fig. 8, 

 considering AB as the axis, and CD as the equator of the 

 globe, mark off the point R, corresponding to the latitude 

 of the place, the angle RED being the angle of latitude. 

 This angle may be easily drawn by the aid of the table 

 of tangents of co-latitude. EF being 10 divisions of any 

 scale, and FS 17*95 divisions if the dial is for use in 

 London. Draw RT at right angles to RE, cutting AB at 

 T. T will be the centre of the dial. The triangle FSE 

 represents the gnomon folded down flat. The hour lines 

 may then be drawn through the points already found, as 

 in Fig. 9. The hour lines for IV. and V. in the morning 

 are merely extensions of the IV, and V. lines in the 

 afternoon, and similarly for the VII. and VIII. lines of 

 the afternoon. 



A complete horizontal dial is shown in plan and in 

 perspective in Fig. 10. 



(To be continued.) 

 ■ — i^»ti5«S5<f-» — 



THE MATHEMATICAL ARGUMENT 

 AGAINST ORGANIC EVOLUTION. 



\A/"E are about to examine, and we may venture to 

 say, to refute an argument which was first 

 brought forward by Prof. Fleeming Jenkin in the North 

 British Review for June, 1867, and which at one time 

 not only created some sensation but seems to have stag- 

 gered even Charles Darwin. 



The argument, strictly speaking, does not tell against 

 evolution in general, but against evolution as effected 

 mainly by Natural selection, or, as it is commonly called, 

 "Darwinism." However, as the two terms are very 

 commonly regarded as synonymous — it is by no means 

 certain that Prof. Fleeming Jenkin understood their 

 difference — it deserves brief notice. 



Its author contended that if some advantageous pecu- 

 liarity made its appearance on any given species it would 

 probably be in the outset confined to one individual. If 

 that favoured individual mated with one of the unmodi- 

 fied original type, its offspring would possess the distin- 

 guishing feature of the improved parent only to the 

 extent of one half, and thus in the course of a few 

 generations the improvement will be " bred out," and we 

 have a reversion to the old type. 



This argument is, of course, entirely founded upon the 

 assumption that the offspring of any pair of animals 

 will be intermediate, exactly or at least approximately, 

 between their parents. Such an assumption is contrary 

 to general experience. Were it well founded, a " family 

 likeness " could never exist, since any peculiarities of, 

 an ancestor in face or figure would not be traced beyond 

 at furthest the third generation. In reality we know 

 that such likenesses are handed down for centuries. 

 The "Bourbon nose" and the " Hapsburg lips" are 

 matters of history. In not a few instances, where a 

 family has been for a long time in a position to accumu- 

 late and preserve a series of ancestral portraits, its living 

 members strongly and distinctly embody the features 

 and expression of forefathers who flourished in the days 

 of Queen Anne, or even earlier. Were such collections 

 of portraits more general we should unquestionably find 

 such hereditary likeness as common among the families 



of peasants as of kings and nobles. 



If a momentary digression may be allowed, we should 

 strongly urge the preservation of photographic portraits 

 which are now within the scope of the great mass of the 

 public, and which in course of time will become, from 

 this point of view, valuable scientific documents. 



But we may go a step, and a long step further. Any 

 peculiarity, whether it be a new development or a re- 

 version to some long-forgotten ancestral type, so far 

 from necessarily disappearing in its offspring may even 

 be intensified. As an instance, we quote from the 

 Journal of Science (October, 1882, p. 623) the following 

 passage, taken originally from Land and Water : — 



" About twelve months ago, Mr. Peter Low, flesher, 

 High-street, Montrose, bought a ram with four horns 

 from a lady in town, which she had gained at a raffle 

 at a church bazaar in Brechin. Mr. Low put the ram 

 into a park with a black- faced Highland ewe, and the 

 result was that the ewe gave birth to twins, male and 

 female, on July 9th last, the male lamb having five and 

 the female four horns, all well-developed." 



We remember a similar case for which unfortunately 

 we can give no details of place and date, but of the 

 main fact of which we are absolutely certain. Every 

 one knows that the domestic fowl has three toes in 

 front, and the so-called spur behind the leg. A farm- 

 yard cock was found to have four toes in front, the spurs 

 being developed as usual. This redundancy was trans- 

 mitted to almost all his descendants, and four-toed fowls 

 became — and are possibly yet — very numerous in the 

 district. 



Nor are cases in point wanting in the human species. 

 We know an instance where a man having very dark 

 hair and eyes married a blue-eyed fair-haired girl. 

 One of the sons had eyes and hair darker than those 

 of the father — the hair, in fact, being of the kind which 

 novelists and poets call " purple black " — whilst another 

 had the fair hair and blue eyes of the mother not in the 

 least darkened. 



Now, in all the cases which we have mentioned, the 

 peculiarity thus transmitted to descendants has been of 

 a kind not likely to confer any advantage in the struggle 

 for existence. But if such useless abnormalities are 

 transmitted, it is almost certain that advantageous varia- 

 tions are still more likely to be perpetuated. 



The advantages gained by even a slight variation 

 from the original type may be almost unlimited. Let 

 us suppose a species of bird hard pressed by some 

 enemy its superior in powers of flight. But if one bird 

 of this species is produced swifter than the enemy, the 

 chances of survival of this exceptional individual will be 

 greater than that of any of the original stock, not by ten 

 or fifty per cent., but, practically speaking, infinitely. If 

 this bird, as we have seen it is possible, transmits its 

 exceptional powers of flight to its descendants unim- 

 paired or still more intensified, the original strain of 

 bird will disappear, and will be replaced by what we 

 may call the improved type. 



Prof. Fleeming Jenkin thinks that as variations may 

 take place in all directions, they will be likely to neutra- 

 lise each other. But, in the instance we have just been 

 taking, any variation in the direction of slower flight 

 would quickly prove fatal to its possessor. 



Hence, we see that even allowing — which we do 

 not — natural selection to be the sole or main cause of the 

 variation of organic forms, the contention of the North 

 British Revieiv is not of capital moment. 



