SCIENCE. 
SCIENCE: 
A Weekly Record of Scientific 
Progress. 
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SATURDAY. DECEMBER 25, 1880. 
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less $4, the subscription price of “ Science.” 
Professor Tait, in a recent number of Nature 
(Nov. 25, 1880), directs attention to the necessity of 
perfect definiteness of language in all scientific work. 
“ Want of definiteness,” he says, “ may arise from 
habitual laziness, but oftener indicates a desire to 
appear to know, where knowledge is not.” 
It is also claimed that scientific writers, even of the 
present day, have not that clear comprehension, 
which is essential, of what is subjective and that 
which is objective, and thus much confusion arises. 
To use Professor Tait’s own language, our only 
source of information in physical science is the evi- 
dence of our senses. To interpret truly this evidence, 
which is always imperfect and often wholly mislead- 
ing, is one of the tasks set before reason. It is only 
by the aid of reason that we can distinguish between 
what is physically objective and what is merely sub- 
jective. Outside us there is no such thing as noise 
or brightness ; these no more exist in the aerial and 
ethereal motions, which are their objective cause, 
than does pain in the projectile which experience has 
taught us to avoid. To arrive at the objective point 
of Professor Tait’s article, we may state that it in- 
volves a disagreement between himself and Mr. Her- 
bert Spencer, as to the real meaning of certain words, 
and the propriety of making use of them on occa- 
sions which are mentioned. 
In one of his works, Mr. Spencer states that, 
“ Evolution is a change from an indefinite, incoherent 
homogeneity, to a definite heterogeneity, through con- 
tinuous differentiations and integrations.” 
309 
Mr. Kirkman translates the foregoing into “plain En- 
lish,” or as Professor Tait rather profanely asserts, 
“ strips it of the tinsel of high flown and unintelligible 
language,” thus : 
“ Evolution is a change from a nohowish, untalka- 
boutable, all-alikeness, to a somehowish and in- 
general talkaboutable not-all-alikeness, by continuous 
somethingelsifications and sticktogetherations.” 
Mr. Spencer claims that the explanation of the 
meaning of the word “ Evolution ” is a formula. 
Professor Tait calls this “ a definition ;” hence the 
difference of opinion, the latter asserting it to be not a 
mere quibble of words, but that an important scien- 
tific distinction is involved, to which the attention of 
the scientific world is directed. 
The perusal of a communication from Professor 
Asaph Hall, of Washington, which will be found in 
this column, will greatly assist those who desire to 
solve the question. Professor Hall does not enter 
into any details of the controversy, but offers “ an 
illustratio?i ” which appears to strike at the root of the 
matter in dispute. 
We think that Mr. Spencer may rest satisfied with 
applying the term “ definition ” to his form of words, 
for by the rule presented by Professor Hall, it is evi- 
dently straining a point to assert that in them we find “a 
formula ,” using that word in the same sense as when 
we speak of the law of gravitation. 
By the law of gravitation astronomers are able to 
predict the positions of known celestial bodies four 
years before the event, and Professor Tait asks if Mr. 
Spencer, with his “ formula,” can predict, four years 
before hand, the political and social changes which 
will happen in the history of Europe. 
AN ILLUSTRATION. 
In regard to the controversy between Professor 
Tait and Mr. Herbert Spencer, I beg to offer the fol- 
lowing illustration. If we take by chance the three 
numbers 11, 12, 13, and form their squares, we have 
(up = 121 
(12) 4 = 144 
(13) 2 = 169 
Now take the numbers with the figures in an in- 
verted order, and we have, 
(up = 121 > 
(2 ip = 441 
(31P = 961 
We see that the figures of the squares are also invert- 
ed ; and this holds in the case of three consecutive 
numbers. We infer therefore that this is a general 
law in the formation of square numbers. Arguments 
of this kind might have an extended application in 
various branches of science ; but if we make further 
examination we soon find numerous exceptions to our 
