704 



PHILOSOPHICAL TRANSACTIONS. 



[anko 1672, 



ness. And for all objects, the same charge I believe may with advantage be al- 

 lowed, if the steely matter, employed at London, be more strongly reflective 

 than this which I have used. 



The performances of one of these instru- 

 ments, of any length, being known, it will ap- 

 pear by this lateral table, what may be expected 

 from those of other lengths by this way, if art 

 can accomplish what is promised by the theory. 

 In the first column is expressed the length of 

 the telescope in feet, which doubled gives the 

 semidiameter of the sphere, on which the con- 

 cave metal is to be ground. In the second co- 

 lumn are the proportions of the apertures for 

 those several lengths. And in the third column 

 are the proportions of the charges, or diameter 

 of the spheres, on which the convex superficies 

 of the eye-glasses are to be ground. 



The use of this table will best appear by example: suppose therefore a half 

 foot telescope may distinctly magnify 30 times with an inch aperture, and it be- 

 ing required to know what ought to be the analogous constitution and perform- 

 ance of a four- foot telescope: by the second column, as 100 to 47 6, so are the 

 apertures, as also the number of times which they magnify. And consequently, 

 since the half foot tube has an inch aperture and magnifies 30 times; a four-foot 

 tube proportionably should have 4-,^ inches aperture, and magnify 143 times. 

 And by the third column, as 100 to 168, so are their charges; and therefore if 

 the diameter of the convexity of the eye-glass for a half foot telescope be i of 

 an inch, that for a four- foot should be -fg-s-, that is, about ^ of an inch. 



In like manner, if a half foot telescope may distinctly magnify 36 times with 

 li of an inch aperture, a four-foot telescope should, with equal distinctness, 

 magnify 17 1 times with 6 inches aperture; and one of six-foot should magnify 

 232 times, with 8f inches aperture; and so of other lengths. But what the 

 event will really be, we must wait to see determined by experience. Only this 

 I thought fit to insinuate, that those who intend to make trials in other lengths 

 may more readily know how to design their instruments. Thus for a four-foot 

 tube, since the aperture should be 5 or 6 inches, there will be required a piece 

 of metal 7 or 8 inches broad at least, because the figure will scarcely be true to 



