8 



Proceedings of the Royal Irish Academy. 



or practically insensible, as might have been expected from the sraall- 

 uess of the residuals. 



The next part of the instrument to be specially investigated was 

 the glass scale. Of this only a length of about 40 mm. (from the line 

 marked 8 to that marked 16) has been used, or is likely to be used, 

 and I have therefore confined my attention to this part. The division 

 errors of the lines marked 7 to 17, distant from each other 5 mm. or 

 25 revolutions of the screw, were determined by Hansen's third 

 method.^ This involved the comparison of the intervals of the scale 

 with test-intervals of an auxiliary scale ; and as the scale as supplied by 

 the makers had the divisions marked along the centre of a glass plate 

 3f cm. in breadth, so that an auxiliary scale could not be seen beside 

 it in the microscope, Messrs. Troughton and Simms, at my request, 

 cut the glass plate lengthways in two, so that the division lines now 

 appear at the new edge of the glass plate, and supplied an auxiliary 

 scale 30 mm. in length, divided to 5 mm., which by a coarse screw can be 

 moved along the principal scale. I rather regret this alteration, as 

 the new edge was at first full of small fractures, which had to be 

 ground out, and the result of all this work was, that in one way or 

 other the edges of the division lines became so polished that it is 

 very difficult to get the lines properly blackened, and they are 

 therefore not quite as distinct as originally. Ey taking care to 

 have the mirror, by which the daylight is reflected through the 

 scale, moving along, so as to be always exactly opposite the micro- 

 scope, I believe, however, that I have obtained good light without 

 any danger of an apparent shifting of the lines due to excentric 

 illumination. It would obviously have been much better to have 

 left the scale as it was, and to have placed the auxiliary scale under 

 another micrometer-microscope, substituted for the viewing micro- 

 scope. In comparing the intervals of the two scales, no attempt was- 

 made to get the lines to coincide, lest systematic errors should be 

 introduced in that way ; the lines at one end of the interval were put 

 very close to each other, and independent settings were then made on 

 them with the screw. In this way intervals of 5, 10, 15, 20, and 

 30 mm, were compared, three complete series of measures being 

 taken. The following errors of division were found, expressed in 

 revolutions of the screw (Ir = 16"*4), and in millimeters. According 



1 P, A. Hansen, Von der Bestimnnmg der Theilungsfehler eines gradlinigen 

 Maasstabes, p. 608 (Abhandl. d. math. phys. Classe d. K. Sachs. Ges. d. Wiss. X.^ 

 Leipzig, 1874), 



