188 
CHARLES L. PARMENTER 
to approximately zero. This error is, of course, inherently 
included as a part of the personal error discussed below. 
Personal errors. Probably the greatest personal error was 
due to inaccuracies in making camera-lucida drawings. To 
reduce this error to a minimum, each chromosome, as stated 
above (p. 186), was drawn three times with extreme care. These 
sketches were made at the same point on the drawing-board so 
that any error due to different drawing distances and consequent 
differences in magnification was eliminated. The estimated 
median line of the sketch, upon which the measurement was 
made, was indicated with a lead pencil. The average deviation 
from the mean of the nine measurements is 0.6 mm. and the 
standard deviation, computed from combined measurements of 
several drawings, is 0.37 mm., which indicates that the instru¬ 
mental and personal errors in the average of these measurements 
are practically zero for relative purposes. 
Errors due to conditions inherent in the material. This class 
of errors is much more important than the preceding. The 
errors of this kind are an unequal shortening of the whole chro¬ 
mosome and a foreshortening of parts or all of the chromosome. 
Measurements made without very careful attention to fore¬ 
shortening are of questionable value, for small amounts can 
give rise to large errors, especially in short chromosomes. Shorten¬ 
ing is caused by a twisting of the chromatids about one another 
(figs. 1 to 8, 27 to 30). The amount of shortening in each twist 
of the chromatids, as determined by computation, 4 at the mag- 
4 The amount of shortening in each twist of a chromosome was determined 
by adding together the separately computed amounts of shortening due to the 
lateral deviation of the chromatids and that due to the vertical deviation of 
the chromatids. The shortening in each twist due to the lateral deviation was 
computed by averaging the lengths of the two chromatids of a chromosome and 
substracting the length measured upon the median line of the whole chromo¬ 
some. This total difference divided by the number of twists is 0.2 mm., which 
is approximately the amount of shortening due to the lateral deviation in each 
twist. In determining the amount of shortening due to the vertical deviation 
of the chromatids, the width or thickness of the chromatid, as determined with 
an ocular micrometer was assumed to be the amount of vertical sag of the chro¬ 
matid in each twist. ' This thickness multiplied by the magnification amounted 
to 1 mm. This was used as the altitude of a right triangle, the base of which 
represented half of the measured longitudinal length of the shortened part, and 
the hypotenuse of which then represents very closely one-half of the true length 
