326 PROCEEDINGS OF THE AMERICAN ACADEMY 



(2.) By the use of two microscopes. 



It will be seen in Fig. 1 that there are two carriages, S and S^ 

 which traverse independent ways. S^ is supposed to be in front of S. 

 Two arms are attached to the upper surface of table S-^ (not shown in 

 the figure), which project about half-way over the surface of S, allow- 

 ing a sliirht clearance between the two surfaces. The standard whose 

 subdivisions are to be compared is placed upon the table S, and a bar 

 having upon its surHice a graduated space, X, approximately equal to 

 one of the subdivisions of the first bar, is placed upon the projecting 

 arms attached to S^. Both microscopes are now secured to the car- 

 riage K. M^ is adjusted for coincidence with the initial line of the 

 standard, which is placed upon S, and M is adjusted for coincidence 

 with the corresponding line upon the other bar. The carriage K is 

 moved toward the left, and a second coincidence of M is made with 

 the other defining line. A comparison of the two readings of M^ for 

 the two positions of M will give the relation between the two spaces 

 compared. M^ is then adjusted for coincidence with the second line, 

 and the carriage S^ is carried back by the rack and pinion D till the 

 first line is again under M. The second subdivision can now be com- 

 pared with the same constant space, X, as before. It is obvious that, 

 by the proper disposition of the two bars with respect to M and M\ 

 subdivisions of any magnitude whatever can be compared. It is to be 

 noted, however, that the results obtained in this way are subject to 

 errors due to the horizontal curvature of the cylindrical ways. 



(3.) For long distances, and for any distance exceeding one decime- 

 ter, more i-eliable results can be obtained by the use of two micro- 

 scopes in a fixed position. The various adjustments required in order 

 to bring tlie defining lines of any subdivision into coincidence with M 

 and M^ have already been described. 



Description of Comparixg-Rooms. 



The comparator first described is mounted upon isolated brick piers 

 in the cellar of the Observatory. Through the liberality of the Di- 

 rector of the Observatory a small room in the shape of a trapezium 

 was partitioned off for this purpose. This comparator was at first 

 mounted upon stone piers mounted upon the clock pier in the prime- 

 vertical room of the Observatory. But notwithstanding the great size 

 and stability of this pier, it was found impossible to make comparisons 

 except very early in the morning before the disturbance from passing 

 teams began. This pier rests upon a layer of blue clay having a large 



