Additimal Notes. 475 



person, though, as the motions of the moon and variation 

 of the angle is but slow, it may be brought to exactness by- 

 several trials in the intervals of direction. The instrument, 

 as above described, will not take an angle of much above 

 50 degrees, which, for the purpose intended, may be fully- 

 sufficient. But if the speculum K F be made to take off and 

 put on, and the end of the index at K be so notched as to 

 turn that speculum from its first perpendicularity, to make 

 an angle of about 25 degrees, it will then take any distance 

 to 1 00 degrees. 



By this description it may be thought that the utmost accu- 

 racy will be required in making the instrument : yet, of all that 

 ever have been invented of so curious a kind, it will probably 

 be found to demand the least; for, provided the speculums are 

 good, on which the whole depends, if the first E F be set 

 truly over the centre, the limb well graduated, and the other 

 speculum be also set perpendicular, there can, I think, be 

 no other error but what the instrument itself will easily rec- 

 tify: for if it be directed to one star, and that be taken, at 

 the same time, both by a direct ray through the glass G H, 

 and by a reflection from E F, both exactly coinciding at O, 

 it is evident that then the speculums are exactly parallel. And 

 if this falls not precisely when the index cuts degrees, if 

 the variation be noted, this constantly added or subtracted, 

 according as it falls, will fully rectify all other errors. So ia 

 fixing the speculum E F to another angle, as has been pro- 

 posed, the like method may or must be taken, viz. to observe 

 two stars at the distance of about 45 or 50 degrees, by the 

 speculum, in its first situation, and then the same stars by it 

 again in its second, and the difference of the intervention of 

 the index on the limb being noted, and constantly added ta 

 the arches taken in the second situation, will give the true 

 distance. This method of observing one and the same star, 

 in the first manner, or two stars in the second, as has been 

 mentioned, will also rectify errors even in the speculums; for 

 the line of the ray K O is in all cases constantly the same; 

 and, upon the whole, I may safely say the instrument will 

 be found much more certain in practice than at first it may 

 appear in theory, even to some good judges. But I am now 

 -sensible I have trespassed in being so particular when writing 

 to Dr. H ALLEY; for I well know that, to a gentleman noted 

 for his excellent talent of reading, apprehending, and greatly 

 improving, less would have been sufficient; but as this pos- 

 sibly may be Coiumuaicated by thee, I sliali crave leave fur- 



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