JANUARY 19, 1912] 
The probability that a student be in the 
first year of the course is 0.43, from the data 
of the Bureau of Education; the probability 
that German will be offered in that year is 
(1904) 0.23 for a 4-year course and 0.24 for a 
3-year course, or 0.47 for both; the desired 
probability is then 0.43 < 0.47 =0.202.2 The 
probability that a student be in the second 
year is 0.26; the probability that German 
will be offered in that year is 0.29 for a 2-yea1 
course begun that year, 0.24 for a 3-year 
course begun in first year, 0.23 for a 4-year 
course, 0.12 for a 3-year course begun in sec- 
ond year. The resulting probability that a 
student be taking German, if it were a required 
study in second year, is 0.26 (0.29 + 0.24 + 
0.23 ++ 0.12) = 0.232. Similarly for the other 
years. Then the total probability that a ran- 
dom student be taking German in 1904 is 
0.654. Computations like this carried out for 
the studies in Dexter’s tables result in the 
following table. 
SCIENCE 
97 
With regard to some of the other subjects 
tabulated by the Bureau of Education, I am 
not able to draw any conclusions from Dex- 
ter’s tables and other data. Some of his facts 
may be quoted as supplementing the table 
above. 
This goes far to explain the increase in the 
percentage of students studying foreign his- 
tory, as tabulated in the commissioned report 
and shown on the curve-sheet. 
Table III., in spite of the very inadequate 
data on which it is in part based, is capable 
of giving us a certain amount of information 
about the relations between election and 
schedule alteration and the data of the 
Bureau of Education. The columns headed 
“ver cent.—if required ” give in per cents. the 
probabilities for each study that a random 
student would be taking the subject if there 
were no elective system, as derived from Dex- 
ter’s data, and hence also the percentages of 
students in the mass who would take the sub- 
TABLE III * 
Actual 
Per Cent.—if Required Per Cent.—Actual 
Study Required 
1894 1904 Ratio 1894 1904 Ratio 1894 1904 
69.2 91.4 1.32 43.59 49.96 1,23 0.63 0.55 
64.8 66.0 1.02 10.31 11.15 1.08 0.16 0.17 
72.0 65.4 0.91 12.78 18.98 1.49 0.18 0.29 
47.7 63.1 1.11 52.71 56.23 1.07 1.10 1.06 
Geometry, plane............ 24.2 30.4 1.26 
3 solid .. 8.0 10.5 1.31 
ns both... 32.2 40.9 1.27 25.25 27.30 1.08 0.78 0.67 
Physics.............. 21.3 22.0 1.03 24.02 15.90 0.66 1.13 0.72 
Chemistry........... 11.5 10.2 0.89 10.31 7.08 0.69 0.90 0.69 
Geology cess. -ee-nerece cress 11.0 5.6 0.51 5.525 2.79 0.51 0.50 0.50 
Physical geography and | 
physiography............ 29.8 27.0 | 0.91 22.445 21.26 | 0.95 0.75 0.79 
*Tm this it is assumed that all schools dealt with ject under these conditions. In a way they 
are of the same size, which is inaccurate, but 
unavoidable. 
* Results computed from the articles of Hunter, 
Weckel, Ramsay and Whitney, published in School 
Science and Mathematics during the last two 
years, supplement the above table in part. But 
they depend on limited or fragmentary data. A 
complete census by the Bureau of Education would 
be of great value. 
51894-5 data. 
measure the average opportunity for a stu- 
dent to take the subject. The column 
“ratio” gives the quotient of the per cent. 
for 1904 by that for 1894. It measures the 
extent of schedule change. The columns 
headed “per cent.—actual” are quoted from 
the commissioner’s table. The “ratio” col- 
umn is found in the same way. The columns 
headed “ actual/required ” check the accuracy 
