VOL. XLVIII.] PHILOSOPHICAL TRANSACTIONS. 467 



let another object-glass, uncut, be fixed within the tube, of a proper degree of 

 convexity, to shorten the focus of the other as much as may be required ; sup 

 pose to 12 feet: by what has been just now observed, this glass will represent the 

 two images in the same form which would have been exhibited by the divided 

 glass, if this other glass had not been there. For though the images are not 

 yet formed, when the 2d glass receives the rays ; yet, as those rays are converg- 

 ing towards it, the 2d glass must represent those images in the same position, 

 and form, as the tendency of the rays requires. For while the segments are 

 fixed in their position to each other, their images will also be fixed in their po- 

 sition ; and let them be repeated ever so many times, by refraction through sphe- 

 rical glasses, or by reflexion from spherical mirrors, they can suffer no alteration 

 in their position to each other. By this means the telescope may be shortened at 

 pleasure, though the scale for the measure of the angles will remain the same. 

 The only inconvenience which the shortness of the telescope introduces, is a want 

 of sufficient distinctness ; which will so far hinder the exactness of the observa- 

 tion, as the contact of the edges cannot be so accurately determined, as they 

 might be with longer telescopes. 



This difficulty is entirely removed by fixing the divided glass at the end of a 

 reflecting telescope : for the reflections and refractions, which the rays must un- 

 dergo in passing through the telescope, will no way alter the position of the 

 images which the rays, that have passed through the segments, are tending to : 

 for, as has been already observed, a number of reflections and refractions may 

 repeat the images, and alter their magnitudes ; but can make no alteration in 

 their proportions. 



Therefore this way of fixing the divided glass to a reflecting telescope, which 

 was the 3d method proposed, is by far the best ; as such telescopes of moderate 

 and manageable lengths, when well made, are capable of magnifying conside- 

 rably, and showing objects to great advantage. This micrometer's being appli- 

 cable to the reflecting telescope with so much certainty, is no inconsiderable ad- 

 vantage : for any one will easily understand, that to measure the diameter of a 

 planet exactly, it is necessary that the planet be magnified, and shown distinctly, 

 which could not be obtained in the common way without very great lengths ; 

 such as rendered it very difficult, not to say impracticable, to take exact mea- 

 sures. Besides, the common micrometer is limited in this respect on another 

 account ; viz. because the diameter of the planet cannoi be measured without 

 having the whole planet within the field of the telescope, which confines the 

 magnifying power within very narrow bounds ; whereas, by this method, nothing 

 more is required, than to see the contact of the edges, which allows the magni- 

 fying power to be increased at pleasure. 



In the common micrometer, the object is to be taken between 1 wires, so 



3 o2 



