234 PHILOSOPHICAL TRANSACTIONS. [ANNO 1782. 



power gives 0".355 for the apparent diameter of aLyrae. The scale of the mi- 

 crometer, on this occasion, was no less than 8.443 inches to a second, as will 

 be found by multiplying the natural tangent of a second with the power and 

 radius in inches. Nov. 1781, I measured the diameter of the new star ; but the 

 air was not very favourable, for this singular star was not so distinct with 227 

 that evening as it generally is with 460 : therefore, without laying much stress 

 on the exactness of the observation, I shall only report it, to exemplify the use 

 of the micrometer. My radius was 35 feet 11 inches. The diameter of the 

 star, by the distance of the lucid points, was 2.4 inches, and the power I used 

 227 : hence the magnified angle is found to/, and the real diameter of the star 

 5 // .022. The scale of this measure .474 millesimals of an inch, or almost half 

 an inch to a second. 



XIV. A Paper to obviate some Doubts concerning the Great Magnifying Powers 

 used. By Mr. Herschel, F. R. S. Addressed to Sir Joseph Banks, p. 173. 

 Sir, I have the honour of laying before you the result of a set of measures I 

 have taken in order to ascertain once more the powers of my Newtonian 7-feet 

 reflector. The method I have formerly used, and which I still prefer to that 

 which I have now been obliged to practise, requires very fine weather and a 

 strong sun-shiny day ; but my impatience to answer the requests of Sir Joseph 

 Banks would not permit me to wait for so precarious an opportunity at this season 

 of the year. The difference in all the powers, as far as 2010, will be found to 

 be in favour of those I have mentioned ; and, I believe, a much greater concur- 

 rence could not well be expected, where different methods of ascertaining them 

 are used. The variation in the 2 highest powers is more considerable than I was 

 aware of; but still may easily be shown to be a necessary consequence of the dif- 

 ference in the methods. However, if on comparing together the methods, it 

 should be thought that the power 5786 is nearer the truth than 6450, I shall 

 readily join to correct that number. The manner in which I have now deter- 

 mined the powers is as follows: I took one of the eye lenses which magnifies 

 least, and measured its solar focus by the sun's rays as exactly as I could 5 times, 

 which proved to be 1.01, 1.04, l.OQ, 1.01, 1.05, in half-inch measure, a mean 

 of which is 1.04. The sidereal focus of my 7-feet speculum is 170.4 in the 

 same measure. Thence, dividing 170.4 by 1.04, we find that the telescope will 

 magnify 163.8 times when that lens is used. This power being found, I applied 

 the same lens as a single microscope to view with it a certain object, which was 

 a drawn brass wire fastened so as not to turn on its axis or change its position ; 

 for these wires are seldom perfectly round, or of an even size, and it is there- 

 fore necessary to use this caution to prevent errors : then, with a fine pair of 

 compasses, I took 4 independent measures of the image of the brass wire, 



