of Bessel's Astronomical Observations. 431 



1. Determination of the Magnifying Powers. 



I have founded this investigation on the same principle which 

 is the basis of Ramsden's dynameter; but I have employed the 

 divisions of the circle for measuring the diameter of the image of 

 the cell of the object-glass formed by the eye-glass. With this 

 view a compound microscope was' horizontally placed before 

 the telescope, which was likewise in a horizontal position, so as 

 to show distinctly the wires in the focus, after the eye-glass 

 of the telescope was taken out ; this microscope was furnished 

 with a wire, which, by being made to bisect the interval be- 

 tween the two horizontal wires in the telescope, might be easily 

 placed horizontal and consequently parallel to the axis of the 

 instrument. Then the eye-glass was put in, and the micro- 

 scope drawn back until it showed distinctly the image of the 

 cell of the object-glass, after which the angle was observed 

 which it was necessary to turn the circle, in order to produce 

 a contact of both the limbs of this image with the wire of the 

 microscope : this angle was found for the different eye-glasses, 

 6'29''-00; 4' 4"-08 ; 3' 23"-58 ; 2' 25"- 17, from which the 

 magnitude of the image may be found, if its distance from the 

 axis of rotation of the instrument be known. In order to find 

 this distance, I made at random a dot on the microscope, the 

 distance of which from a dot on the telescope situate in the 

 plane of the wires, was found without the eye-glass 40*3 lines, 

 and with the four eye-glasses =58 '4; 52-6; 50*5; 47*3 lines; 

 from which it follows that the four images of the eye-glass are 

 distant from the plane of the wires 18*1; 12*3; 10-2; 7*0 lines, 

 or from the axis of rotation 387*6 ; 381-8 ; 379-7 ; 376-5 lines; 

 the latter being distant from the wires 369*5 lines. The 

 diameter of the cell of the object-glass is 48*2 lines, and 

 therefore the ratio of its magnitude to those of its images 

 before the eye-glasses 65-94 ; 106-69; 128-62; 181-90. 



These numbers would denote the magnifying powers of the 

 four eye-glasses, if the latter were so placed that parallel rays 

 falling on the object-glass likewise issue from them parallel; but 

 they require a small correction when the observer has placed the 

 eye-glasses according to his own sight. Let the diameter of 

 the object =0; that of the image before the eye-glass =0; 

 the focus of the object-glass =P; that of the interior eye-glass 

 = f the exterior/' ; the distance of the two eye-glasses =d, 

 that of the object-glass from the interior eye-glass =F+d, 

 that of the image from the exterior one =8', that of the eye 

 from the point of distinct vision =f, and we have 



