Oct 11895 
subscript to the decimals ; that Gunter and Wingate followed 
Napier, while Oughtred adopted Briggs’s method and made an 
improvement in the mode of drinting it. Napier has left so 
many instances of the decimal point as to render it pretty certain 
that he thoroughly appreciated its use ; and there is every reason 
to believe that Briggs had, in 1619, an equal command over his 
separator, although there are not enough printed instances of 
that date to prove it so conclusively as in Napier’s case (there is 
no instance in the “ Lucubrationes” in which a quantity begins 
with a decimal point, and there could not well be one). Napier 
did not use the decimal point in the ‘‘ Descriptio ” (1614), nor 
_ in his book of arithmetic first printed under the editorship of 
Mr. Mark Napier in 1839, and there is only the single 
_ doubtful case in the ‘*Rabdologia,” 1617, so that there is reason to 
believe that he did not regard it as generally applicable in or- 
dinary arithmetic. The only previous publication of Briggs’s 
_ that I have seen was his ‘‘ Chilias,” 1617, which contains no 
_ letterpress at all. The fact that Napier and Briggs use different 
_ separating notations is an argument against either having been 
_ indebted to the other, as whoever adopted the other’s views 
__ would probably have accepted his separator too. It is doubtful 
__ whether, if Napier had written an ordinary arithmetic at the close 
_ of his life he would have used his decimal point. Wingate em- 
__ ployed the decimal point with much more boldness, and regarded 
_ it much more in the light of a permanent symbol of arithmetic 
_ than did (or could) Napier. The Napierian point and the Briggian 
separator differ but little in writing, and as far as MS. work is 
y concerned it is quite easy to see why many should have consi- 
_ dered the !atter preferable, for it was clear and interfered with 
no existing mark. A point is the simplest separator possible, but 
it had,already another use in language. In all the editions of 
_ Onughtred’s ‘‘ Clavis”” (which work held its ground till the be- 
ginning of the last century) the rectangular separator was used, 
__and it is not unlikely that it was ultimately given up for the same 
reason as that which I believe will lead to the abandonment of 
the similar sign now used in certain English books to denote fac- 
torials, viz., because it was troublesome to Zrin¢, But be this as 
it may, it is not a little remarkable that the first separator used 
(or more strictly, one of the first two) should have been that 
which was finally adopted after a long period of disuse. All 
through the seventeenth century exponential works [seem to have 
been common, on which see the accounts in Sir Jonas Moore’s 
**Moor’s Arithmetick,” London, 1660, p. 10; and Samuel 
Jeake’s “Compleat Body of Arithmetick,” London, 1701 
(written in 1674), p. 208, which are unfortunately too long to 
quote in this abstract. In his account Peacock is inaccurate in 
saying that the ‘* Logarithmicall Arithmetike” was published by 
Gellibrand and others, the mistake having arisen, no doubt, from 
a confusion with the ‘‘ Trigonometria Britannica,” 1633; and in 
any case the reference is not a good one, as the ‘‘ Arithmetike” of 
1631 shows (for reasons which must be passed over here) a less 
knowledge of decimal arithmetic than do any of the chief lo- 
garithmic works of this period, Also Briggs died in 1631, not 
1630. 
There is no doubt, whatever, that decimal tractions were first 
introduced by Stevinus in his tract, ‘‘ La Disme.” De Morgan 
(‘* Arithmetical Books,’ p. 27) is quite right in his in- 
ference that it appeared in French in 1585, attached to the 
* Pratique d’Arithmétique.” A copy of this work (1585) with 
“La Disme” appended, is now in the British Museum. On 
the title-page of the ‘‘ Disme” are the words ‘‘ Premierement 
descripte en Flameng, et maintenant conuertie en Frangois, par 
Simon Stevin de Bruges.” These words appearing also in Albert 
Girard’s coilected edition of Stevinus’s works (1634) no doubt 
gave rise to De Morgan’s inference that ‘‘the method of decimal 
fractions was announced before 1585 in Dutch.” The Cambridge 
University Library possesses 21585 copy, entitled ‘‘ De Thiende... 
Beschreven door Simon Stevin van Brugghe....Tot Leyden. By 
Christoffel Plantijn, M.D. LXXXV.” (privilege, dated December 
20, 1584), and there seems every reason to believe, inthe absenc 
of any evidence to the contrary, that this was the first edition of 
this celebrated tract. Peacock’s statement that ‘‘it was first 
published in Flemish about the year 1590, and afterwards trans- 
lated into barbarous French by Simon of Brages”’ is also, I sus- 
pect, founded on no other evidence than the sentence on the title- 
page of the ‘‘Disme,” which appears also in Girard. De 
Morgan rightly remarks that Simon of Bruges is Stevinus him- 
_ self, but he cannot tell whence Peacock derived the date 1590. 
It is probable that it was merely a rough estimate obtained by 
considering the dates of the other works of Stevinus, 
naa 
NATURE 
Stevinus’s method involved the use of his cumbrous exponents, 
Thus he wrote 27°847 as 27(0)8(t)4(2)7(3)* and read it 27 com« 
mencements, § primes, 4 seconds, 7 thirds ; and the question 
chiefly noticed in this abstract is the consideration of who first 
saw that by a simple notation the exponents might be omitted, 
and introduced this abbreviation into arithmetic. 
Napier’s ‘‘ Rabdologia ” was translated into several languages 
soon after its appearance, and I have taken some pains to exa- 
mine the different ways in which the translators treated the 
example which Peacock regarded as the first use of the decimal 
point, as we can thereby infer something with regard to the state 
of decimal arithmetic in the different countries. Napier (1617) 
wrote 1993,273 in the work, and 1993,2’7"3” in the text. In 
Locatello’s translation (Verona, 1623) this is just reversed, viz. 
there is 1993.2'7”3” in the work, and 1993,273 in the text. 
“The Lyons edition (1626) has 1993,273 in the work, and 
1993,2(1)7(2)3(3)+ in the text, while De Decker’s edition 
(Gouda, 1626) has 1993,273 in the work, and in the text 
1993(0)2(1)7(2)3(3), the last being exactly as Stevinus would 
have written it. Ursinus’s ‘‘Rhabdologia,” Berlin, 1623, is 
not an exact translation, and the example in question does not 
occur there. 
SANITARY PROGRESS t 
ANITARY science is a thing of yesterday, comparatively 
«speaking ; but sanitary art, the art of preserving the health, 
whether of individuals or of communities, has been studied and 
practised for ages, Sanitary science is the latest and highest 
development of medicine. I say it is the highest branch ot 
medical science because of the extreme importance of its objects, 
and I may also add ofits results. It is the study of the causes 
of diseases, and it points out the means of preventing them ; and 
Iam sure you are all agreed that ‘ prevention is better than 
cure ;” as Rollet of Lyons well said, ‘‘ Medicine cures indi: 
viduals, hygiene saves the masses.” But while we contrast hygi- 
ene (another name for sanitary science) with curative medicine, 
we must not forget that it is altogether a medical science, and 
that its great lights have been all medical men (mind, I am not 
speaking of the art now, but of the science), and this is neces- 
sarily so, and always must be so. I have said that sanitary 
science is the study of the causes of diseases, of the modes in 
which they originate, and in which they spread from one person 
or place to another. It is therefore only those who are acquainted 
with disease, that are competent to deal with it all, and these are 
those who have made medical science generally their special 
subject. You sometimes hear it said that medical men don’t 
know much about diseases. Just think what this means; disease 
has been studied by earnest men inall its various forms for thou- 
sands of years; experiences have been recorded, comparisons 
made ; the effects of remedies noted from generation to gene- 
ration, and yet we are asked to believe that medical men don’t 
ae anything about diseases ; the thing is absurd on the face 
of it. 
Sanitary science is, then, a medical science, and the most inti- 
mate acquaintance with diseases is necessary for its prosecution 
—I mean for its advancement as a science. Sanitary inves- 
tigations can only be scientifically conducted by medical men, just 
as pianos can only be played by musicians. This science is also 
the latest development of medical science. We must understand 
simple things before we canstudy complex ones. It is little use fora 
boy to study higher algebra until he has mastered the rule of 
three ; and so pathology, or the study of diseased actions, be- 
comes more and more advanced as physiology—the study of 
normal healthy actions—is more scientifically pursued ; while the 
study of sanitary matters in a scientific way has only become 
possible of later years from the great advances made in the study 
of pathology, physiology, and chemistry ; but being possible, it 
has made such rapid strides, and evolved such startling facts 
with regard to the causes of diseases, that it has become the 
popular subject of the day. Everyone thinks that he is com- 
petent to speak about it, and everyone who wants to make an 
effective discourse must needs take upon himself to expound 
* Stevinus enclosed the exponent-numbers in complete circles, which 
have been replaced above, for convenience of printing, by parentheses. 
+ These parentheses are printed instead of the circles which appear in 
these works as in Stevinus. 
t Abstract of the Inaugural Lecture delivered at the Town Hall, Birming 
ham, Thursday evening, Oct. 9, 1873, by Prof. Corfield, M.D. Oxon. 
517 
