Bauhaus-Universität Weimar

limits, but they will never actually touch them. A chess 
board has eight squares in a row, and eight pieces may be 
arranged in order on any one row, each piece occupying 
the centre of a square. Let the divisions in the row be 
graduated, calling the boundary to the extreme left, 
0°. Then the successive divisions between the squares 
will be 1°, 2°, 3°, up to T, and the boundary to the 
extreme right will be 8°. It is clear that the position of 
the first piece lies half-way between the grades (in a 
scale of eight grades) of 0° and 1° ; therefore the grade 
occupied by the first piece would be counted on that 
scale as 0-5° ; also the grade of the last piece as 7'5°. 
Or again, if we had 800 pieces, and the same number 
of class-places, the grade of the first piece, in a scale 
of 800 grades, would exceed the grade 0°, by an amount 
equal to the width of one half-place on that scale, 
while the last of them would fall short of the 800th 
grade by an equal amount. This half-place has to be 
attended to and allowed for when schemes are con¬ 
structed from comparatively few observations, and 
always when values that are very near to either of the 
centesimal grades 0° or 100° are under observation ; 
but between the centesimal grades of 5° and 95° the 
influence of a half class-place upon the value of the 
corresponding observation is insignificant, and may be 
disregarded. It will not henceforth be necessary to 
repeat the word centesimal. It will be always implied 
when nothing is said to the contrary, and nothing 
henceforth will be said to the contrary. The word will 
be used for the last time in the next paragraph.


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