VL—THE FREQUENCY-DISTRIBUTION. 7) 
The numbers of rays range from 6 to 20,—12, 13, or 14 rays 
being the most usual. 
4. To expand slightly the brief description given in § 2, tables 
like the preceding are formed in the following way :—(1) The 
magnitude of the class-interval, 7.e. the number of units to each 
interval, is first fixed ; one unit was chosen in the case of Tables 
I. and IIL, five units in the case of Table II. (2) The position or 
origin of the intervals must then be determined, e.g. in Table I. 
we must decide whether to take as intervals 12-13, 13-14, 14-15, 
ete, or 125-135, 13-5-14'5, 14'5-15'5, ete. (3) This choice 
having been made, the complete scale of intervals is fixed, and the 
observations are classified accordingly. (4) The process of 
classification being finished, a table is drawn up on the general 
lines of Tables I.-III., showing the total numbers of observations 
in each class-interval. Some remarks may be made on each of 
these heads. 
5. Magnitude of Class-Interval.—As already remarked, in cases 
where the variation proceeds by discrete steps of considerable 
magnitude as compared with the range of variation, there is very 
little choice as regards the magnitude of the class-interval. The 
unit will in general have to serve. But if the variation be con- 
tinuous, or at least take place by discrete steps which are small 
in comparison with the whole range of variation, there is no such 
natural class-interval, and its choice is a matter for judgment. 
The two conditions which guide the choice are these: (a) we 
desire to be able to treat all the values assigned to any one class, 
without serious error, as if they were equal to the mid-value 
of the class-interval, e.g. as if the death-rate of every district in 
the first class of Table I. were exactly 13-0, the death-rate of 
every district in the second class 140, and so on; (2) for con- 
venience and brevity we desire to make the interval as large as 
possible, subject to the first condition. These conditions will 
generally be fulfilled if the interval be so chosen that the whole 
number of classes lies between 15 and 25. A number of classes 
less than, say, ten leads in general to very appreciable inaccuracy, 
and a number over, say, thirty makes a somewhat unwieldy 
table. A preliminary inspection of the record should accordingly 
be made and the highest and lowest values be picked out. 
Dividing the difference between these by, say, five and twenty, we 
have an approximate value for the interval. The actual value 
should be the nearest integer or simple fraction. 
6. Position of Intervals.—The position or starting-point of the 
intervals is, as a rule, more or less indifferent, but in general it 
is fixed either so that the limits of intervals are integers, or, as in 
Tables I. and II., so that the mid-values are integers. It may, 
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