28 Transactions of the Society. 



has a maximum value if the apex coincides, by reflexion, with the 

 exact centre of the circle. It is thus seen that deviations of the 

 apex within the upper surface of the disk will change the angle by 

 quantities of " second order " only ; and such deviations could be 

 increased up to 2 mm. without any appreciable fault remaining in 

 the middle of both readings. The single readings may differ one 

 from the other by some degrees, but the mean will yield the 

 correct value; and as the observer must always make both 

 readiugs, and take the mean, the difference is absolutely unim- 

 portant. For my own use I often apply a disk without any 

 central mark ; the silvered glass with the circular hole on the disks 

 made by Mr. Zeiss being intended principally not for centring, 

 but for preventing measurement with incorrect adjustment of the 

 objective. 



There is no other mechanical condition for the correct perform- 

 ance of the disk, but that the line of intersection between the inclined 

 surface and the upper surface of the disk must pass through the 

 exact centre of the circular division ; the angle does not need 45° 

 exactly. Just the same condition must be fulfilled with Dr. Wood- 

 ward's apparatus; and as it is not more difficult to grind an 

 inclined face than it is to grind a plane surface, it follows that the 

 convenience of manipulation afforded by the reflecting surface in 

 my arrangement is not obtained by a sacrifice of accuracy. 



In engraving circular divisions of unequal intervals by means 

 of a dividing machine, according to a calculated table, there is 

 no greater source of error, provided the maker is not a dunce; 

 and if the index of the glass plate has been correctly measured, the 

 reliability of such a scale will not be inferior to that of a division 

 into degrees. Whether the scale has been made on the base of 

 the right refractive index may be ascertained by the observer by 

 precisely the same method which Dr. Woodward suggests for 

 observing the index of a disk divided into degrees. He may 

 ascertain that any immersion lens with an ajDcrture exceeding 

 unity, yields exactly the unit by the mean of both readings, 

 when it is applied to the apertometer as a dry lens; and this, 

 indeed, is the method used by Mr. Zeiss for testing every plate 

 before sending it away, in order to prevent accidental use of a 

 wrong crown. In order to have the front lens separated from the 

 disk by an infinitely thin film of air only, and to prevent the pro- 

 jecting brasswork of the objective {]r) from stopping-off the utmost 

 oblique rays, a drop of soft balsam is placed on the disk, and after 

 it has dried superficially the objective is slightly pressed down 

 upon it. 



The divisions of the scale on the apertometer disk go from 

 • 05 to • 05 of the numerical unit. The intervals being equal to 

 2 mm. on the average, no observer will find any difiiculty in esti- 



