182 
From answers to question 8 it was ascer- 
tained that the following elements, of those 
listed, are omitted from courses given in the 
number of schools indicated. 
Antimony ........ Atl \Goldl ia Pele seteia eels ee 16 
Arsenic ........... US} UGCHN Gee ouodGdaao 3 
Barium ........... 10 Manganese ......... 7 
Bismuthi<s.\cies 22'V Nickel! £.0..8 0's cfle ess 12 
Boron ............ 18 Phosphorus ......... 2 
Bromine .......... 4 Radium ............ 49 
Cadmium ......... 32) Silicont (is vss. eevee 11 
Chromium ........ 16 Strontium .......... 27 
Cobalt ane. chicas. POULIN ee eieveheiel<eleterelevenelene 5 
Fluorine .......... 10 
In answer to question 9 it was found that 
the following theories, laws and principles are 
omitted by the number of schools indicated. 
Law of constant proportions—3, combining 
weights—2, Boyle’s law—2, kinetic molecular hy- 
pothesis—26, Avogadro’s law—3, Gay-Lussac’s 
law—5, catalytic agent—3, allotropism—16, os- 
motic pressure—21, freezing and boiling point ef- 
fects—7, gram molecular volume law—21, Du- 
Long and Petit’s law—51, periodic arrangement 
of elements—15, Moseley numbers—99, electron 
theory—19, structure of atom—27, ionization—2, 
Faraday’s law—25, equilibrium—8, thermal equa- 
tion—45, colloids—45. 
_ Question 15 is answered in Tables IV., A, 
B and C. 
TABLE IV 
(a) Number of Lectures per Week per Instructor 
Number | Number | Number | Number | Number | Number 
of 0! O) of of 
Lectures | Schools | Lectures | Schools | Lectures | Schools 
1 25 ¢ 4 3 6 2 
2 9 5 2 7 2 
3 7 8 2 
(6) Number of Recitations per Week per In- 
Structor 
Number | Number | Number | Number | Number | Number 
of Reci- of of Reci- of of Reci- of 
tations Schools tations Schools tations Schools 
1 17 i 2 16 1 
2 24 8 6 18 al 
3 24 9 2 20 1 
4 16 12 6 21 1 
5 6 14 3 25 1 
6 3 15 3 26 1 
With reference to question 18 it is gratifying 
to note that most of the science teachers in 
high schools are graduates of reputable col- 
leges and universities. The writer has a list 
SCIENCE 
[N. S. Von, XLVIII. No. 1234 
showing the number from each institution. 
This list is available for any one who may be 
interested. It would seem unnecessary to in- 
clude the institutions here, because of the 
large amount of space required for the pur- 
pose. Seventy-four institutions are included 
in the list already compiled. 
(c) Number of Hours of Laboratory per Week per 
Instructor 
Number Number Number 
Number Number Number 
Tong [ofSchools| > 22° |orschools| % 282: | of Schools 
1 11 6 6 12 5 
2 22 ce at 14 1 
3 21 8 ff 15 3 
4 11 10 6 16 3 
5 7 17 1 
It is evident from the variety of answers al- 
ready received that standardization is neces- 
sary. For this purpose the state should have a 
permanent committee, as long as the United 
States Commissioner of Education is not em- 
powered to establish standards and enforce 
them. The latter procedure is naturally more 
desirable, as it would enable all colleges and 
universities to plan their courses as continua- 
tion courses instead of repeating much of the 
material which students in some high schools 
have already covered. 
The writer wishes to acknowledge valuable 
assistance rendered by Miss Marcella Schwer. 
ALEXANDER SILVERMAN 
ScHOOL oF CHEMISTRY, 
UNIVERSITY OF PITTSBURGH 
TWENTY-FIVE IMPORTANT TOPICS IN 
THE HISTORY OF SECONDARY 
MATHEMATICS 
THE rapid increase in the number of the 
historical ‘notes in our recent text-books on 
elementary and secondary mathematics raises 
the question, What should be the dominating 
motive in the selection of such notes? The 
history of mathematics is so enormous that 
it is clearly impossible to present a consider- 
able part of it in such notes, but it would be 
possible to select for them some of the central 
elements of this history, which ‘might become 
