3io 
SCIENCE 
law, and we conclude finally that, although in the com- 
mon phrase there may be something in it, yet our 
assumed law is in fact no law at all. 
Again I examine my table of squares, and I find a 
rule of this kind : The second differences of the squares 
are constant, and equal to 2. I make many trials of 
this rule and never find an exception. Others do the 
same and always the same result is found. We con- 
clude therefore that we have at length discovered a 
real law that exists in the formation of squares ; but 
at the same time we invite every one to make the ex- 
amination for himself, and if possible to find an ex- 
ception. A. Hall. 
Washington, D. C., December 17, 1880. 
PROFESSOR TAIT AND MR. HERBERT 
SPENCER. 
In another column we have referred to the controversy 
between Professor Tait and Mr. Spencer. Since this 
was put in form we have received a copy of Mr. Spen- 
cer’s reply and, with pleasure, give his own explanation, 
which appears in Nature of the 2d instant : 
“ I pass now to his implied judgment on the formula, 
or definition, of Evolution. And here I have first to ask 
him some questions. He says that because he has used 
the word ‘ definition ’ instead of ‘ formula,’ he has in- 
curred my ‘ sore displeasure and grave censure.’ In 
what place have I expressed or implied displeasure or 
censure in relation to this substitution of terms ? Al- 
leging that I have an obvious motive for calling it a 
‘ formula,’ he says I am ‘ indignant at its being called a 
definition.' I wish to see the words in which I have ex- 
pressed my indignation ; and shall be glad if Prof. Tait 
will quote them. He says — ‘ It seems I should have 
called him the discoverer of the formula !’ instead of 
‘ the inventor of the definition. Will he oblige me by 
pointing out where I have used either the one phrase or 
the other ? These assertions of Prof. Tait are to me 
utterly incomprehensible. I have nowhere either said or 
implied any of the things which he here specifies. So 
far am I from consciously preferring one of these words 
to the other, that, until I read this passage in Prof. Tait’s 
lecture, I did not even know that 1 was in the habit of 
saying ‘ formula ’ rather than ‘ definition.’ The whole of 
these statements are fictions, pure and absolute. 
“ My intentional use of the one word rather than the 
other, is alleged by him apropos of an incidental compar- 
ison I have made. To a critic who had said that the 
formula or definition of Evolution ‘ seems at best rather 
the blank form for a universe than anything correspond- 
ing to the actual world about us,’ I had replied that it 
might similarly be ‘ remarked that the formula — “ bodies 
attract one another directly as their masses and inversely 
as the squares of their distances,” was at best but a 
blank form for solar systems and sidereal clusters. 
Whereupon Prof. Tait assumes that I put the ‘Formula 
of Evolution alongside of the Law of Gravitation,’ in 
respect to the definiteness of the provisions they sever- 
ally enable us to make ; and he proceeds to twit me with 
inability to predict what will be the condition of Europe 
lour years hence, as astronomers ‘ predict the positions 
of known celestial bodies four years beforehand.’ Here 
we have another example of Prof. Tait’s peculiarity of 
thought. Because two abstract generalizations are com- 
pared as both being utterly unlike the groups of concrete 
facts interpreted by them, therefore they are compared 
in respect to their other chaiacters. 
“ But now I am not unwilling to deal with the contrast 
Prof. Tait draws ; and am prepared to show that when 
the conditions are analogous, the contrast disappears. 
It seems strange that I should have to point out to a sci- 
entific man in his position, that an alleged law may be 
perfectly true, and that yet, where the elements of a 
problem to be dealt with under it are numerous, no spe- 
cific deduction can be drawn. Does not Prof. Tait from 
time to time teach his students that in proportion as the 
number of factors concerned in the production of any 
phenomenon becomes great, and also in proportion as 
those factors admit of less exact measurement, any pre- 
diction made concerning the phenomenon becomes less 
definite ; and that where the factors are multitudinous 
and not measurable, nothing but some general result can 
be foreseen, and often not even that ? Prof. Tait ignores 
the fact that the positions of planets and satellites admit 
of definite prevision, only because the forces which ap- 
preciably affect them are few ; and he ignores the fact 
that where further such lorces, not easily measured, 
come into play, the previsions are imperfect and often 
wholly wrong, as in the case of comets ; and he ignores 
the fact that where the number of bodies, affecting one 
another by mutual gravitation, is great, no definite previ- 
sion ot their positions is possible. If Prof. Tait were 
living in one of the globular star-clusters, does he think 
that after observations duly taken, calculations based on 
the law of gravitation would enable him to predict the 
positions of the component stars four years hence ? By 
an intelligence immeasurably transcending the human, 
with a mathematics to match, such prevision would 
doubtless be possible ; but considered from the human 
standpoint, the law of gravitation, even when uncompli- 
cated by other laws, can yield under such conditions only 
general and not special results. And if Prof. Tait will 
deign to look into ‘ First Principles,’ which he apparently 
prides himself on not having done, he will there find a 
sufficient number of illustrations showing that not only 
other orders of changes, but even social changes, are 
predictable in respect to their general, if not in respect 
to their special characters.” 
REVERSION IN FLORAL PARTS. 
By William A. Buckhout. 
One of the best plants for showing the reversion of 
floral parts to the form of leaves is the common red field- 
clover ( Trifolium pratense.) 
It is always easily obtained, and during the fall of the 
year these heads of reverted flowers are quite common. 
The pedicels of the flowers are much elongated, and 
somewhat reduced in number; hence the heads have 
a loose appearance, which, with their very leafy look 
and absence of color, makes them conspicuous among 
Fig. 1. Fig. 2. 
hose having well developed flowers. Fig. 1 gives at 
fair idea of one of these heads. A dissection of a 
