314 
NATURE 
[August 5, 1886 
May 13 to 16 there fell 106 mm. rain, about ove-ninth of our 
total yearly quantity ; on the 13th, 26 mm. ; 14th, 27°63; 15th, 
22°4; 16th, 30. These heavy rains were undoubtedly due to 
the northern storm, although they came two days later. 
Caracas, June 29 A. ERNST 
The Indivisibility of Certain Whole Numbers 
ANOTHER exception has been found to Fermat’s assertion 
regarding the indivisibility of whole numbers of the form 
m 
2 + 1 (see several notices in NATURE, vols. xviii. and xix. ). 
The matter now stands as follows :— 
5 
2 +1 divisible by 5:27 + 1 (Euler) 
2 +1 1 1071°28 + 1 (Landry) 
ape I a 7°2!44 1 (Pervouchine) 
ae I ri 5°2°°+ 1 (Pervouchine) 
2 i I An 5299+ 1 (Seelhoff). 
= M. 
A Quadruped Duck 
Ir may interest some readers of NATURE to hear that there is 
at present living in Bardsea a duck which has four feet. The 
two abnormal feet, which are webbed like the others, and of the 
same shape and size, spring from one leg, which is about the 
same length as the normal legs, but rather thicker. This leg 
grows from a point just beneath the tail. Its bone does not 
seem to be directly connected with the other bones of the bird, 
as it can be freely moved in any direction. This duck is more 
than a month old, and is healthy. EDWARD GEOGHEGAN 
Bardsea, August 3 
PHVSIOLOGICAL SELECTION: AN ADDI- 
TIONAL SUGGESTION ON THE ORIGIN OF 
SPECIES 
I. 
HERE are three cardinal difficulties in the way of 
natural selection, considered as a theory of the 
origin of species. 
(1) The difference between species and varieties in 
respect of mutual fertility. Many of our domesticated 
varieties differ from one another to an extent greater than 
that which distinguishes many natural species: yet they 
continue perfectly fertile z7er se, while the natural species 
are nearly always more or less sterile. The difficulty is 
not met by pointing to the fact that sterility between 
natural species is neither absolutely constant nor constantly 
absolute ; for the question still remains, Why are the modi- 
fications of organic types supposed to have been produced 
by natural selection, so generally attended with some more 
or less pronounced degree of mutual sterility, when even 
greater modifications of such types produced by artificial 
selection so generally continue mutually fertile? That 
this question does not admit of any answer by the theory 
of natural selection Mr. Darwin himself acknowledges, 
and therefore suggests a wholly independent hypothesis 
by which to explain the fact. This hypothesis is, that 
varieties occurring under nature “ will have been exposed 
during long periods of time to more uniform conditions 
than have domesticated varieties, and this may well make 
a wide difference in the result.” Now, whatever we may 
think of this hypothesis, it is certainly quite distinct from 
the theory of natural selection ; and, therefore, any one 
who adopts the supplementary hypothesis is, so far, con- 
fessing the inadequacy of that theory, considered as a 
theory of the origin of species. For my own part, I deem 
the hypothesis wholly insufficient to meet the facts. 
When we remember the incalculable number of species, 
living and extinct, we immediately feel the necessity for 
1 Abstract of a Paper read before the Linnean Society on May 6, by 
George J. Romanes, M.A., LL.D., F.R.S. &e. 
some much more general explanation of their existence 
than is furnished by supposing that their mutual sterility, 
which constitutes their most general or constant distinction 
as species, was in every case due to some incidental effect 
produced on the generative system by uniform conditions 
of life. To say nothing of the antecedent improbability 
that in all these millions and millions of cases the repro- 
ductive system should happen to have been affected in 
this peculiar way by the merely negative condition of uni- 
formity, there remains what seems to me the overwhelm- 
ing consideration that, at the time when a variety is first 
forming, the condition of prolonged exposure must neces- 
sarily be absent as regards that variety: yet this is just 
the time when we must suppose that the infertility with 
its parent form arose. Because, if not, the incipient 
variety would have been reabsorbed into its parent form 
by intercrossing. 
(2) For the swamping effects of free intercrossing upon 
an individual variation constitutes the next, and perhaps. 
the most formidable, difficulty with which the theory of 
natural selection is beset. The only answer which Mr. 
Darwin has to make in this case is that a number of in- 
dividuals inhabiting the same area may vary in the same 
way at the same time. Of course, if this assumption were 
granted, there would be an end of the present difficulty ; 
for if a sufficient number of individuals were thus simi- 
larly and simultaneously modified, there need no longer 
be azy danger of the variety being swamped by inter- 
crossing. But the force of the difficulty consists in the 
very fact of this assumption being required to meet it. 
The theory of natural selection trusts to the chapter ot 
accidents in the matter of variation ; and in this chapter 
we read of no reasons why the same beneficial variation 
should arise in a number of individuals simultaneously. 
Moreover, if it does so, the fact of its doing so cannot be 
attributed to natural selection, which thus again fails as a 
theory of the origin of species. Lastly, as will imme- 
diately be shown, a very large proportion, if not the 
majority, of features which serve to distinguish species 
from species, are features presenting no utilitarian signifi- 
cance ; and, therefore, even if it be conceded that they 
each arose in a number of individuals simultaneously, 
their reabsorption by intercrossing could not have been 
in any degree hindered by natural selection. 
(3) The difficulty just alluded to of the inutility to 
species of so large a proportion of specific distinctions, is 
one which Mr. Darwin frankly acknowledges in the later 
editions of his works. In other words, he allows that a 
large proportion of these distinctions resemble the more 
general distinction of sterility in not admitting of any 
explanation by the theory of natural selection. They 
consist of small and trivial differences of form and colour, 
or of meaningless details of structure, which, being of no 
service to the plants or animals presenting them, cannot 
have arisen through the agency of natural selection. If 
it be suggested that all such distinctions are of disguised 
utility, the answer is that to offer this suggestion is to. 
reason in a circle. For the only evidence we have of 
natural selection as an operating cause in any case is 
derived from the utility of the observed results: therefore, 
in cases where utility is apparently absent, we may not 
assume that it must be present only because, if it were 
not present, the results must be due to some cause other 
than natural selection. Observe, the case would be 
different if the great majority of specific distinctions— 
like the great majority of higher distinctions—were of 
obvious utilitarian significance ; for in this case we might 
reasonably set down the exceptions as proof of the rule, 
or hold that they appear to be exceptions only on ac- 
count of our ignorance. But it is certainly too large a 
demand on our faith in natural selection to appeal to the 
argument from ignorance when the facts require that the 
appeal should be made over so very large a proportion of 
instances. But it is needless further to insist upon this 
lO ——— 
