M. Fraueiihofer's Description of a new Micrometer. 215 



nomena produced by the mutual action of bent rays *, so that 

 their exactness cannot be questioned. By the same microscope 

 I also ascertain whether the circular lines be exactly round and 

 concentric. It is only wanted to determine the proportion of 

 the diameters with the microscope. This proportion, and at 

 the same time the value of the dimensions, could be derived 

 with sufficient precision from the transit of a star near the 

 pole, if the telescope was set sufficiently firm. If the propor- 

 tion of the dimensions was determined by the microscope, 

 then it is required only to determine the value of the dimen- 

 sion of one of the largest circular lines, in order to know also 

 the value of the remaining ones. As the circular lines are 

 exactly concentric, the values of their dimensions, which they 

 have at the focus of any object glass, can be determined in 

 many different ways. If the telescope were placed extremely 

 steady, and could be at the same time very sensibly moved, 

 then the determination of the values of the dimensions might 

 be the most simple, by means of the pole-star. For it is only 

 necessary to place this star in the middle of the smallest cir- 

 cular line, and to observe the time of its transit throuo-h the 

 other circular lines. But this transit requires much time, for 

 which reason a telescope might not be easily placed sufficiently 

 firm ; nor is it easy for the motions of the telescopes to be suf- 

 ficiently sensible, in order to place a star exactly in the centre 

 of the smallest circular line. If the proportion of the dimen- 

 sions of the different circular lines is known, then their value 

 can likewise be derived from the transit of a single determined 

 star, even if it does not pass through the centre. 



For a star therefore of small declination, if it passes through 

 the centre of the field of view, the greater part of the circular 

 lines in the above micrometer are distant from each other 

 about 10 seconds of time; which time might perhaps suffice 

 to note the observation. As this time is proportionally longer 

 for northerly stars, double the number of circular lines might 

 be made in the field of view, without incurring the danger of 

 being uncertain with which line the observer is occupied. 

 One might, for instance, give equal distances to the first 5 

 circular lines, from each other, then, for easier distinction, to 

 make the distance from the 5th to the 6th larger; then again 

 5 in equal distances, &c. With this micrometer one half of 

 these circular lines could only be made use of in stars of small 

 declination ; because the intervals of time for noting would be 

 too short. As the declination can only be exactly derived 

 from those observations where the star has cut a small segment 



* See New Modification of Light, &c., by M. Frauenhofer. 



of 



