304. REPORTS ON THE STATE OF SCIENCE.—1912. 
13.° The Types for Mathematical Symbols should correspond with, 
or be larger than, the sizes of type recommended for the various ages. 
It is important that the smaller symbols should not be too fine, and 
it is advisable to employ the ‘ heavy’ type for fractions which is 
described by typefounders as ‘ heavy fractions.’ For children under 
twelve years no fractions should be employed less than 3°5 mm. in 
height of face; thus in ? the distance from the top of the 3 to the 
bottom of the 4 should not be less than 3°5 mm. For pupils over 
twelve the minimum face height for fractions should be 3 mm. If 
heavy fractions be not used, these heights should be increased to 4 and 
3°5 mm. respectively. It should be easy to discriminate between the 
numerals 3, 6, § and 9. 
14. Squared Paper.—Use of squared paper should be restricted to 
work for which it is really required. If this be done, and paper with 
rulings not less than one-tenth inch apart be used, there will be little 
danger to vision. The use of millimetre paper should be restricted to 
students over fourteen, and be only used by them in a good light—on 
exceptional occasions. 
15. Atlases.—It does not appear possible to avoid some use in 
atlases of type which is below the desirable standard of size, and the 
care which should be exercised by teachers in regard to the children’s 
eyesight needs to be specially emphasised in this connection. Their 
ase should be avoided when the illumination is below normal—the less 
they are used for home-work the better. Location by reference lines 
should be taught from the beginning, and children should not be 
allowed to hunt for a name in an undirected fashion, as they may thus 
have to read fifty names in finding the one sought. Atlases intended 
for use by children under nine should have no type smaller than ten- 
point, with minimum height of 16 mm. or one-sixteenth inch for the 
short letters. No school atlas should be printed with type smaller 
than eight-point, with minimum height of 1:2 mm. for the short 
letters. The type should be extended; italics should not be used more 
than is necessary, and should not have fine hair-lines. Type of display 
character may be used with advantage. 
It is not necessary that every map should be coloured. (It has 
already been pointed out that colour decreases legibility.) In the 
case of beginners, the colour helps the appreciation of area; but for 
this purpose the colouring should be pale, and few names inserted. 
For the portrayal of relief, the practice of block-shading the contours 
is better than heavy black hill-shading by hachures. Maps should be 
duplicated where it is necessary (e.g., Switzerland) to exhibit great 
variation of contour together with several place-names. In general it 
is better to multiply maps than to put much detail into one. 
If a system of inserting the names of every town of a certain 
population be .adopted, the result is certain to be overcrowding of 
those portions of the maps which represent highly-populated countries. 
It would Le better to avoid this overcrowding, even at some sacrifice 
of systematic uniformity. Modern methods in the teaching of 
geography are reducing the hunting for place-names, and thereby 
diminishing eye-strain. This advantage will be more general when 
