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,* at the mag- 



* The amount of shortening ia 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 



