44 R. S. Woodward — Iced Bar Base Apparatus. 



apparatus.* Intermediate stones dividing the kilometer into 

 four nearly equal sections were set on September 7, 1891. 

 Each of them consisted of a half cubic meter of concrete set 

 in the ground so that its upper surface was about even with 

 the ground surface. On the top of each stone was cemented 

 one of the Repsold cut-off plates which are provided with 

 spherical headed bolts for use with the cut-off cylinder previ- 

 ously described. 



When these intermediate stones were set, the ground along 

 the line was so wet that it was a matter of difficulty to keep 

 the water out of the excavations while the concrete was being 

 rammed into place. These stones did not become dry and 

 hard until deep trenches were dug about them on September 

 18, 1891. For this reason it is probable that these stones were 

 much less stable during the first two measures of the kilometer 

 (Sept. 10-15) than during the last two measures (Sept. 26-30). 

 Results erf' measures of 100 m comparator interval. — The 

 earliest experience with the iced bar apparatus showed that 

 the personal equation of the observers may cause appreciable 

 constant error, and hence the method of interchange of the 

 observers already explained was adopted. The first, five 

 measures of the comparator interval, however, were made 

 without interchange of the observers. In place of such inter- 

 change direct observations for relative personal equation were 

 made on the bar. 



The greater part of the measures of the comparator interval 

 were made by starting at the west end and moving the bar 

 toward the east. Some of the later measures were made in the 

 opposite direction and they disclose, apparently, a systematic 

 error depending on the direction of measure. The same kind 

 of systematic error is indicated also by the measures of the 

 kilometer referred to below. 



In order to explain the data of the comparator measures 

 clearly and fully let 



D = distance between spheres of comparator 



= 100 m + 39-5 mm approximately, 

 B lT = length of 5 m steel bar No. 1*7 in ice, 

 x = the relative personal equation of the two observers 



on the bar, 

 Q = quantity measured on cut-off scale, 

 v = the most probable correction to Q.f 



Then, for one position of the observers a measure of the 

 comparator interval gives an observation equation of the form 



* This is an end measure apparatus consisting of two steel rods encased in 

 wood, with mercurial thermometers to give their temperatures. 



f The quantity Q involves the error of measuring the line as well as the errors 

 in position of the first and last microscope with respect to the fiducial points. 



