218 M. Frauenhofer's Description of a new Micrometer. 



rallel with d e stand nearly vertical upon the parallel circle of 

 the star ; the lines running in the direction fg would therefore 

 be inclined thereto. From the times of transit of the stars 

 through the vertical and those through the inclined parallel 

 lines, the difference of right ascension and declination can be 

 derived with accuracy. To place the lines running in the di- 

 rection d a exactly vertical upon the parallel circle, might not 

 well be accomplished, even if still another line was drawn, of 

 which one knew that it cuts these parallel lines exactly under 

 a right angle. As the distance of the vertical lines from each 

 other, and also that of the inclined ones, in the same manner 

 as the angle under which they cut each other are exactly 

 known, the proportion of the times of transit of a star through 

 the vertical to those of the inclined parallel lines, will make 

 us correctly acquainted with the position of these lines with 

 regard to the parallel circle. The calculation of these obser- 

 vations will always be still more simple, than what is made 

 with the circular micrometer. Even at a transit of both the 

 stars we always obtain several observations, which on an ave- 

 rage give declination and right ascension equally exact, whe- 

 ther their difference of declination be great or small. Where 

 the difference of right ascension is small, as for instance in 

 double stars, the transit of both, indeed, could not be observed 

 through one and the same vertical line; but the observer would 

 for instance observe one at the first vertical line, the other 

 at the second, &e. This lamp «<tf-micrometer has, amongst 

 others, this advantage ; viz. that an alteration of the instru- 

 ment, during the transit of both the stars, can be detected pre- 

 vious to the calculation. I have given to the parallel lines 

 such a distance from each other, that the distance of the in- 

 clined to those of the vertical ones bears about the same pro- 

 portion, as the cosines of the inclined angle to the radius, in 

 order that about as many transits of the star, through the in- 

 clined as well as through the vertical lines, may be observed. 

 Five lines always have an equal distance only ; the 5th is one 

 half more distant from the 6th, than the rest amongst them- 

 selves. From this it is easy for the observer to know with 

 which line he is occupied. 



I have constructed an engine, with which straight lines can 

 be cut exactly parallel, and to *0001 of an inch at equal di- 

 stances. This engine is at the same time so contrived, that 

 the parallel lines can be cut through the others under any 

 given angle, exactly to a minute of a degree. For this net- 

 micrometer the same lamp and the same eye-glasses are 

 used, as to the above-described circular micrometer ; and it 

 is only necessary to screw on the frame with the net, in- 

 stead of that with the circular lines. 



