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_ attended the classes during the last winter session, Of these, 
_ 35 came up for examination in May, and 23 passed. Several of 
these obtained very advanced success in more than one subject, 
so that the total number of successful candidates in the seven 
subjects taught amounts this year to 49, including four outside 
candidates, leaving an increase of 13 from last year. Mr. 
‘Ethelbert Dowlen, one of the pupils, has been awarded 
the ‘‘ Queen’s Silver Medal” in botany, and besides nu- 
merous other prizes and certificates, he also obtained the 
*Queen’s Gold Medal” for geology at St. John’s College, 
¥ Woking. Altogether these classes seem to have been highly 
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successful, and we hope they will continue to be increasingly so. 
The classes will be re-opened for instruction on Tuesday, 27th inst., 
and will be continued every!Monday and Wednesday evening for 
Physical Geography, and on Tuesdays and Fridays, from 6 to 9 
P.M., in the other subjects. A class will be held on Saturdays for 
- ladies, in Botany, at a convenient time, commencing from the 11th 
inst. at 11 A.M. Proposed Subjects :—1, Mathematics (Ist, 2nd, 
and 3rd stage), or theoretic mechanics ; 2, sound, light, and heat ; 
3, magnetism and electricity ; 4, chemistry, inorganic ; 5, animal 
physiology ; 6, elementary botany; 7, biology; 8, physical 
geography. ‘The fees are very moderate. 
- THE volume of Artizans’ Reports upon the Vienna Exhibition, 
published by the Society for the Promotion of Scientific Industry, 
_ Manchester, will be published about the 2oth of this month. 
There are thirty-six reports, which are said’to be of a very high. 
class character. 
WE are glad to see, from the Report of the Chester Society of 
Natural Science, that that Society, which has concluded its 
second year, continues to increase in prosperity ’so far as num- 
bers are concerned—the number of members being now 454. 
Among these are not a few working members ; and the’secre- 
tary gives excellent advice in counselling each member 
to devote himself to a special subject, as thus fonly can the in- 
terest of the Society and the advance of science be best pro- 
moted. During the past year two societies of natural science 
have been founded in the neighbourhood of Chester—one at 
Wrexham, the other at Whitechurch. The Chester Society does 
its work by means of field excursions, general lectures, and sec- 
tional meetings. 7 
Tux forthcoming number ot Petermann’s AMiittheilungen will 
contain a detailed account of Captain Hall’s Po/arzs Arctic ex- 
pedition, with its scientific results. 1t will be accompanied by 
a carefully constructed map showing the course of the Polaris 
from the 80th degree northwards, her course southward from 
Aug. 15 to Oct. 15, 1872, the course along which the floe con- 
taining the nineteen persons drifted after they were separated 
from the ship on the night of Oct. 15, 1872, until they were 
picked up off the coast of Labrador six months afterwards, the 
distance drifted each day, along with the state of the weather, 
and the places where seals, &c. were obtained, being indicated ; 
and lastly, the course taken by the men who were picked up 
in Melville Bay last June. 
SHORTLY before his death the late Colonel J. W. Foster 
completed the manuscript of a work upon the prehistoric races 
of the United States, which has just made its appearance from 
the press of S. C. Griggs and Co., of Chicago, This contains 
an excellent summary of the present state of our knowledge of 
the aborigines of North America, as illustrated by the remains 
found in mounds, shell heaps, and ancient mines, as well as 
by their crania. 
Tue City of London College, Leadenhall Street, to judge 
from the programme we have received, offers excellent oppor- 
tunities to young men engaged during the day for obtaining a 
good education, literary and scientific, and for intellectual im- 
provement in various ways. 
THE Times of India says that a scientific geographical survey 
of native Sikkim is in contemplation by the authorities. 
THE Geological Magazine announces the death of Prof. Dr. 
Kemp of Darmstadt, a distinguished zoologist and palzeontologist, 
whose name is well known in connection with the discovery of 
the Dinotherium. 
HERR SCHLOENBACH, proprietor of certain salt works at 
Lieberhall, in Hanover, has instituted a foundation of 12,000 
florins, the interest of which is to be devoted to assist geologists 
who may undertake journeys of exploration beyond the Austro- 
Hungarian empire. This is intended as a memorial tribute to 
his son, a young German geologist of much promise, recently 
deceased. 
THE additions to the Zoological Society’s Gardens during the 
last week include an Arctic Fox (Canis /agopus) and an Iceland 
Gull (Zarus leucopterus), European, presented by Mr, B. L. ~ 
Smith ; a Black-handed Spider-monkey (A¢e/es melanochir) from 
South America, presented by Mr. B. Went; an African Civet 
Cat (Viverra civetta), presented by Lady Cust ; a Macaque Mon- 
key (Macacus cynomolgus) from Africa, presented by Capt. 
Denison ; a Raccoon (Procyon lotor) from North America, and a 
Vulpine Phalanger (Pialangista vulpina) from Australia, pre- 
sented by Miss Breach, 
THE ERITISH ASSOCIATION 
SECTIONAL PROCEEDINGS 
SECTION A.—MATHEMATICS 
On the Introduction of the Decimal Point into Arithmetic, by 
J. W. L. Glaisher, B.A. 
The following is an extract from Peacock’s excellent History 
of Arithmetic, in the ‘‘ Encyclopsedia. Metropolitana,” which 
forms the stanndard (not to say the only) work on the subject. 
Speaking of Stevinus’s ‘‘ Arithmélique,” Peacock writes: ‘* We 
find no traces, however, of decimal arithmetic in this work, and 
the first notice of decimal, properly so called, is to be found in 
a short tract, which is put at the end of his ‘ Arithmétique,’ in 
the collection of his works by Albert Girard, entitled ‘La 
Disme.’ It was first published in Flemish, about the year 
1590, and afterwards translated into barbarous French by 
Simon of Bruges. . . . Whatever advantages, however, this 
admirable invention, combined as it still was with the addition 
of the exponents, possessed above the ordinary methods of cal- 
culation in the case of abstract or concrete fractions, it does not 
appear that they were readily perceived or adopted by his con- 
temporaries. The last and final improvement in this 
Decimal Arithmetic, of assimilating the notation of integers and 
decimal fractions, by placing a foint or comma between them, 
and omitting the exponents altogether, is unquestionably due to 
the illustrious Napier, and is not one of the least of the many 
precious benefits which he conferred upon the science of calcu- 
lation. No notice whatever is taken of them in the ‘ Mirifici 
Logarithmorum Canonis Descriptio,’ nor in its accompanying 
tables, which was published in 1614. In a short abstract, how- 
ever, of the theory of these logarithms, with a short table of the 
logarithms of natural numbers, which was published by Wright, 
1616, we find a few examples of decimals expressed with refer- 
ence to the decimal point ; but they are first distinctly noticed in 
the ‘Rabdologia,’ which was published in 1617. In an *‘ Admo- 
nitio pro decimali Arithmetica,’ he mentions in terms of the 
highest praise the invention of Stevinus, and explains his nota- 
tion; and without noticing his own simplification of it, he 
exhibits it in the following example, in which it is required to 
divide 861094 by 432. . The quotient is 1993,273, or 
1993,2'73'", the form under which he afterwards writes it, in 
partial conformity with the practice of Stevinus. The same form 
is adopted in an example of abbreviated multiplication, which 
subsequently occurs. . . . The preceding statement will suffi- 
ciently explain the reason why no notice is taken of decimals in 
the elaborate explanations which are given by Napier, Briggs, 
and Kepler, of the theory and construction of logarithms ; and 
indeed we find no mention of them in any English author be- 
tween 1619 and 1631. In'that year the ‘ Logarithmicall Arith- 
