ght to be avoided between "graduation" and "rank,"
though it leads to no sensible error in practice. The first of the
"park palings" does not stand at A, which is 0 deg., nor does the
hundredth stand at B, which is 100 deg., for that would make 101 of them:
but they stand at 0 deg.5 and 99 deg.5 respectively. Similarly, all
intermediate _ranks_ stand half a degree short of the _graduation_
bearing the same number. When the class is large, the value of half
a place becomes extremely small, and the rank and graduation may be
treated as identical.

Examples of method of calculating a centesimal position:--

1. A child A is classed after examination as No. 5 in a class of 27
children; what is his centesimal graduation?

_Answer_.--If AB be divided into 27 graduations, his rank of No. 5
will correspond to the graduation 4 deg.5; therefore if AB be graduated
afresh into 100 graduations, his centesimal grade, x, will be found
by the Rule of Three, thus--

x : 4 deg.5 :: 100:27; x = 450 deg./27 = 16 deg.6.

2. Another child B is classed No. 13 in a class of 25 _Answer_.--If
AB be divided into 25 graduations, the rank of No. 13 will
correspond to graduation 12 deg.5, whence as before--

x : 12 deg.5 :: 100 : 25; x = 1250 deg./25 = 50 deg.; _i.e._ B is
the median.

The second method of comparing two statistical groups, to which I
alluded in the last paragraph but one, consists in stating the
centesimal grade in the one group that corresponds with the median
or any other fractional grade in the other. This, it will be remarked,
is a very simple method of comparison, absolutely independent of any
theory, and applicable to any statistical groups whatever, whether of
physical or of mental qualities. Wherever we can sort in order,
there we can apply this method. Thus, in the above examples, suppose
A and B had been selected because they were equal when compared
together, then we can concisely express the relative merits of the
two classes to which they respectively belong, by saying that 16 deg.6
in the one is equal to 50 deg. (the median) in the other.

I frequently make statistical records of form and feature, in the
streets or in company, without exciting attention, by means of a
fine pricker and a piece of paper. The pricker is a converted silver
pencil-case, with the usual sliding piece; it is a very small one,
and is attached to my watch chain. The pencil part has been taken
out and replaced by a fine short needle, the