144 
NATURE 
[ Fune 17, 1886 
has no cause for complaint. 
a function of two variables. 
(3) Inreply to Mr. Lock’s request for other slight inaccuracies 
I might ask, without leaving the subject of interest, what 
under the sun ‘‘inverse interest” is: but though inaccuracies 
of language are not desirable in a school-book, I prefer 
to draw his attention to more important matters. Every arith- 
metician knows that the practical questions which come 
under such headings as Simple and Compound Interest, 
Exchange, Discount, Stocks, &c., are not questions of a different 
kind arithmetically, being all so-called ‘‘ proportion ” questions, 
and that no more important fact can be taught to the student of 
arithmetic regarding them. Now here is Mr. Lock’s treatment. 
Simple and compound proportion questions are put under the 
headings ‘‘ Problems” and ‘‘Complex Problems”—names, by 
the way, quite illogically chosen and not consistently adhered 
to. Exchange is tacked on to Complex Problems by the 
words, ‘‘examples in Exchange can be worked by the above 
method ”—indeed, these words and a worked example consti- 
tute the sum total of information given in the book on this sub- 
ject. No one could object to the union here indicated, but 
surely the same is equally true of several of the other subjects. 
After Exchange comes a section headed ‘On Problems concern- 
ing Time: I., Time and Distance.” These are not problems 
in the sense previously specified, but belong to the genus of 
examination questions which concern bodies moving in the 
same path with different speeds. A like remark applies to the 
section which follows, headed ‘‘II., Time and Work.” Late 
in the day, after Interest, Discount, &c., there appears a chap- 
ter “On the Use of the Term Per Cent.” So far as it is on 
anything (for it consists of seven or eight lines of introduction, 
three worked and forty-five unworked examples), it is on the cal- 
culation of rates of gain and loss. Now all this, one is bound 
to affirm, is strangely illogical, and tends to give a most 
erroneous conception of arithmetic as applied to practical affairs. 
I used the expression ‘‘slight inaccuracies of thought” in 
referring to such a mode of treatment, because it was impossible 
to be more severe without going into detail, and because it 
seemed imperative to say something against a practice, which 
our examination system fosters, of forming text-books by col- 
lecting all the kinds of exercises met with in examination papers 
and separating them into carelessly ticketed groups prefaced by 
a definition or two. The purely arithmetical, and larger, part of 
Mr. Lock’s book is not of this character, and is, especially as 
regards the definitions, very carefully prepared ; he would con- 
siderably enhance the value of the whole by wisely modifying 
the rest in the second edition. THE REVIEWER 
He ought to know that interest is 
I THANK you for your courtesy in permitting me to see the 
reply of your reviewer to my letter which appeared in NATURE 
of June 3 (p. 100). That my letter was written under very ex- 
ceptional circumstances will be clear to any one who will take 
the trouble of comparing your reviewer’s defence of his criticism 
with the book itself. I will, however, with your permission, 
make one or two comments on his reply. 
(1) That a wrong inference was suggested by the words of the 
reviewer is, no doubt, of little consequence, except that it 
afforded me a ground for an appeal to you for further informa- 
tion. 
(2) Your reviewer did not quote in his review, as he now does, 
my definition of rate of interest; he asked whether rate of 
interest is totally independent of the time, implying that I 
stated that it was so, and ignoring the fact that the manner in 
which time is involved in Interest (not in rade of interest, 
on which point your reviewer seems a little confused) is 
gradually explained in the next few pages. Might I ask your 
eviewer whether in Compound Interest the Interest varies simply 
as the Time? 
(3) In his third paragraph your reviewer gives his answer to 
my request that he should quote verbatim the other instances on 
which he based his unfavourable criticism. There is little or 
nothing here for me to answer, except that I am compelled, 
in justice to myself, to point out the reviewer’s own mistakes. 
(i.) He suggests that Exchange ought logically to be placed 
between Compound Interest and Discount. “It would seem 
necessary to remind him that in questions on Exchange there is 
no reference to ¢7me, and that it is the peculiar manner in which 
time is involved, which distinguishes Interest and Discount from 
other Problems involving money. (ii.) He states that questions 
which I have called “Problems concerning Time” areimproperly 
so-called. It will be clear to any one who reads the chapter on 
“Problems” that a Problem is a question on Variation ; so that 
problems concerning time are exactly what their name indicates. 
But (even supposing your reviewer were right on these two 
points) in charging me with being strangely illogical as regards 
the order of my chapters, he must have overlooked the fact that 
in the preface I expressly state that ‘‘ novelty in arrangement 
has been avoided as much as possible,” but that ‘the order in 
which his chapters are taken may be varied at the discretion of 
the teacher.” For my part I think that the established order of 
subjects is not to be lightly upset, certainly not without more 
sound and weighty reasons than those adduced by your re- 
viewer. 
But besides this your reviewer draws an unfair inference, due. 
I suppose, to mere carelessness. The words ‘‘ Inverse Interest ”” 
appear only as the heading of pp. 187, 188, and are obviously 
an abbreviation for convenience of printing of the words on 
p. 186, ‘‘ Inverse questions ‘on Interest.” As far, however, as 
I can understand the general effect of your reviewer’s explana- 
tion, his objection to my book seems to be this—that it fails to 
bring into sufficient prominence the fact that the Practical 
Applications of Arithmetic (which, in accordance with esta- 
blished custom, I have collected under the heads of Exchange, 
Problems concerning Time, Interest, Proportional Part, &c.), 
really present the same idea under different circumstances, ex- 
pressed in different language. I entirely agree with him as to 
the importance of this fact, and endeavoured, as far as the 
scope and object of my book would allow, to give it due pro- 
minence. For example, for this reason, it seemed unnecessary 
in Exchange and in the chapter on Profit and Loss to give more 
than a few words of explanation in addition to the examples 
worked out. Joun B. Lock 
Gonville and Caius College, June 14 
PASTEURS RESEARCHES 
ie the current number of the Royal Agricultural 
Society’s Journal (vol. xxi. part 1) is a full and able 
account of the work of the great French experimenter from 
an agricultural and veterinary point of view, by Dr. 
George Fleming. The development of Pasteur’s genius 
is traced from his early chemical researches on dextro- 
andlvo-tartrates tofermentationsin milk andinmalt. The 
combination of microscopic with chemical modes of investi- 
gation led him to the definite determination of the part 
played by living organisms in acetic, butyric, and alcoholic 
fermentations. In these inquiries his own labours were 
almost entirely original, but it must not be forgotten that 
a few microscopists in England and many in Germany 
were working on the same lines, and contributed to the 
establishment of the modern doctrine that fermentation 
and putrefaction are both processes dependent on the 
presence and growth of minute parasitic plants. Pasteur’s 
experimental investigations led him in two directions— 
in one to the establishment of the now accepted theory of 
biogenesis: that every living thing is the product of a 
living parent ; in the other to the practical application of 
the facts ascertained to the manufacture of vinegar and 
the process of brewing. 
Ingenuity in devising experiments and patience in 
carrying them to a successful issue belong more or less 
to every successful investigator, but the union in 
addition of clear theoretical conceptions with skill in the 
useful application of results is characteristic of Pasteur as 
it was of Faraday and a few other of the highest intellects. 
His investigation into the cause of pébr7ve, or silkworm 
disease, was undertaken against his will, in deference to 
the urgency of the eminent chemist Dumas. Pasteur 
wished to return to his original department of chemistry, 
and it is remarkable that having once left it he has been 
drawn further and further into biological researches, 
while Dumas, who began with valuable work on the 
development of the ovum, was diverted to chemistry and 
there made his enduring reputation. Perhaps no instance 
more remarkable than Pasteur’s work on the fébrz7e can 
