Dec. 14, 1871J 



NATURE 



135 



Mr. Wm. Boyd Dawkins, F. R.S., gave a short account of the 

 discoveries in the Victoria Cave, made since the last account was 

 published in the Transactions of the Society. The clay forming 

 the bottom of the cave, and which hiiherto had been barren, was 

 now yielding broken fragments of bone, some of which had been 

 gnawed liy the cave-hy.xna. A lower jaw of this animal was 

 found, which indicated the presence of the characteristic Pleisto- 

 cene mammalia in a part of Yorkshire in which they had not 

 been known to have existed up to the present time. There 

 were, therefore, three distinct groups of remains in the cave, 

 the Romano-Celtic on the surface, the Neolithic beneath, and 

 lastly that which has been furnished by the clay which is glacial 

 in cbar.ioter. And since two feet of talus had been accumulated 

 above the Romano-Celtic layer during the last 1,200 years, it is 

 very probable that the accumulation of debris of precisely the 

 same character between tlie Romano-Celtic and Neolithic layers, 

 si.N feet in thickness, was formed in about thrice the time, or 

 3,600 years. If this rough estimate be accepted, and it is pro- 

 bably true appro.ximately, the Neolithic occupation of the cave 

 must date back to between 4,000 and 5,000 years ago. There is 

 no clue to the relative antiquity of the group of remains found in 

 the clay ; but it may safely be stated to be far greater than that 

 of the Neolithic stratum. Throughout Europe the break between 

 the Pleistocene age represented in the cave by the bones in the 

 clay and the Prehistoric age- the Neolithic of the cave — is so 

 great and so full of difficulty that it cannot be gauged by any 

 method which has hitherto been invented. Mr. Boyd Dawkins 

 also exhibited a remarkably perfect javelin head of bronze which 

 had been dug up in a field near Settle. — "Species viewed 

 Mathematically," by Mr. T. S. Aldis. We have learnt that 

 all energy is really one, whether seen in heat, constrained posi- 

 tion, or motion. Many also believe that life is really one, whether 

 seen in man or a toadstool. But for our part we have often felt 

 a difficulty. Why, if all life be one, do we not see it passing 

 through every variety of form instead of being restricted to certain 

 well-defined types ? The present paper is an attempt to explain 

 this. Let us consider what Plato might have called the aurofujoc 

 or complete type of animal. It consists of a certain definite 

 number of organs, composed of a certain definite number of 

 parts. It will also have certain aliments, location, enemies, &c. , 

 which we may call its province, necessary for its life. Thus our 

 type animal is capable of a flux passing through all possible forms 

 and provinces in all possible combinations. I include amongst 

 these, of course, many arrangements necessarily absurd. To 

 each arrangement of organs and provinces thus imagined would 

 correspond a certain vitality or power of living in the type. I 

 mean not merely power of individual existence, but existence as 

 a race. The vitality is therefore a function of a large number of 

 variables, some independent, others connected by equations of 

 condition. It is to us quite an unknown function, but not there- 

 fore indefinite. Therelore, as in any other function of variables, 

 certain relations amongst the variables will give maxima values of 

 the vitality. These maxima of vitality constitute species. 

 Vitality is not mere ph)sical might or agility or fecundity, but 

 compounded of all. Now for a maximum, we know that any 

 change in the variables lessens the function. We thus see how 

 species are stable. In the constant variation, for no being seems 

 capable of reproducing itself exactly, all individuals have less 

 vitality as they depart from the special type which gives the 

 maximum of vitality, and will be choked out by those which, 

 being nearer to the type, possess more vitality. So hybrids, in- 

 termediate between two maxima, will possess less vitality than 

 either, and wiil be choked out, though the main cause of failuie 

 is that the process is like that devised by Swift's Lapiitan 

 philosopher, who sawed the Whigs' and Tories' heads in half, 

 and changing them, left each brain to settle its politics in iiself. 

 So the poor mule, with a bundle of habits, half horse and half 

 ass, in this intestine conflict, has little power to take caie of 

 itself. Of course all maxima may not have plants or animals 

 representing them. If there be several maxima suited for nearly 

 the same province, the maximum of greatest intensity will choke 

 out the others. So, too, there are probably many maxima now 

 unoccupied, as, for instance, the thistle represented a maximum 

 of vegetable life in South America, but till man imported the 

 thistle to fill it up, other maxima of less intensity held the gi'ound. 

 In some cases possibly several maxima are closely related, and 

 differ little in their intensity, so that slightly differing species exist 

 together, and may in their variation pass one into the other, as 

 perhaps in brambles and some species of St. John's wort, &c. 

 If then the province of a species, i.e., the physical geography of 



a country, alter, and its enemies and food with them, clearly the 

 maximum will shift and the species change. But this is not the 

 evolution of new species, though to a person who only notes geo- 

 logical evidence it appears so. For, just as in a storm the light- 

 ning shows the trees still, though really waving to and fro, so the 

 different species in geology are probably but steps in a constant 

 change. Such a change of course must be slow for life to follow 

 it, for a species consists quite as much in a bundle of acquired 

 and transmitted habits as in a certain formation of organs, and 

 the change in habit will probably be far slower than the change in 

 form. How then do new species arise ? For we see that, if the 

 species be a maximum of vitality, in a multitudinous progeny 

 those nearest the type will choke out the others, and the species 

 will be stable. Varieties will be connected with maxima of 

 vitality in two ways. Firstly, slight differences in the province 

 will slightly shift the maximum. Thus moimtain sheep would 

 be more agile than lowland sheep. Secondly, in such a way as 

 this. Suppose this table a low mound, narrow though long. 

 Then the height at any point will be a function of the distances 

 from the north and east walls of the room. There will be one 

 point of maximum height, but whilst a change north or south 

 produces a great change in the altitude, one east or west will pro- 

 duce but little. So there will be variations in some characteristics 

 which will produce little alteration in the whole vitality. Thus, 

 amongst wild oxen probably no varieties without horns would 

 exist, for they affect the vitality. Amongst protected races they 

 do not, and so hornless varieties arise. Still these varieties are 

 but varieties, and are not steps towards a new maximum which a 

 gulf of lesser vitality still separates them from. Or let us con- 

 sider the varieties that we try to make by select breeding. These 

 are least of all likely to produce new species. We simply by 

 main force depress vitality in removing individuals as far as we 

 can (rom the normal type, and when the vitality is sufficiently 

 depressed we can go no further. As for altering the province, 

 the independent variables, so to speak, we know so little how to 

 do it, and certainly could not do it gradually enough, that we 

 have no chance in this way of eflecting anything. How then can 

 new species arise ? Apparently in some such way as this, by what 

 we may call the bifurcation of a maximum. If we drew a horizontal 

 line along which the variation of the organs of an animal were 

 expressed and the corresponding vitality were drawn by ordinates, 

 we should get a curve we might call the vitality curve, whose 

 maxima values would be species. As time elapses and the con- 

 ditions of the earth, &c., alter, the constants, so to speak, of the 

 curve alter, and we get our curve to vary and the maxima shift ; 

 and as the curve alters, one maximum may separate into 

 two or more others, and thus in the lapse of time, one 

 species may separate into two or more others. Roughly 

 to illustrate it, suppose some species developed free from 

 the influence of camivora, and that, owing to various causes, 

 size little affects its vitality, it may vary all through, from 

 little and swift to big and heavy. Now, introducing car- 

 nivora, we can see how a bifurcation of our maximum would 

 take place. The very light and swift would preserve them- 

 selves by their agility, the strong and heavy by their strength, 

 whilst the intermediate would be killed out, and thus two distinct 

 species would arise, which might in course of time by further 

 variation separate still further apart. Doubtless, however, this 

 bifurcation goes back to very remote times. Carnivores and 

 herbivores probably separated not as mammals but as reptiles, 

 or even long before, whilst ruminants and non-ruminants may 

 have separated since they became mammals. Thus Australia 

 seems to have possessed at one time only one marsupial, which 

 has bifurcated into various marsupials, but not into any of another 

 kind. The older the species grow, the deeper is the gulf between 

 them, and, like a river, we have to ascend nearly to the source 

 before we can make a passage from one bank to the other. To 

 recapitulate — Maxima of vitality are species. Any alteration 

 from the normal type produces less vitality, hence the normal type 

 is stable. A slow change of physical geography, &c., slowly 

 changes these maxima, and the species change with them, extinct 

 species being generally glimpses of steps in this change. New 

 species will generally arise from the bifurcation of maxima under 

 circumstances over which man can exercise little control, and 

 which, if he could, he would very likely alter so as either hardly 

 to affect the maximum at all, or too rapidly for the species to 

 shift with it. Selected breeding produces types of less vitality, 

 and therefore will hardly prod'ice new species. Thus the present 

 stability of species is no argument against the doctrine of evolu- 

 tion. 



