VOL. LXXVI.] PHILOSOPHICAL TRANSACTIONS. 3/ 



and which being carried by him to a great pitch of perfection, the Commis- 

 sioners of Longitude did themselves the credit, by a handsome reward, 

 to induce him to publish to the world his particular method of dividing 

 astronomical instruments; which being drawn up by himself, in the year 1767, 

 this matter is fully set forth to the public : I shall therefore only take this oppor- 

 tunity of observing, that there seems to be one article in which Mr. Bird's me- 

 thod may be still improved. 



I apprehend that no quadrant, which has ever undergone a severe examina- 

 tion, has been found to form a perfect arch of QO" ; nor is it at all necessary it 

 should : the perfect equality of the divisions throughout the whole is the first 

 and primary consideration ; as the proportion of error, when ascertained by 

 proper observations, can be as easily and readily applied, when the whole error 

 of the rectangle is 15", as when it is but 5. In this view, from the radius 

 taken, I would compute the chord of l6° only. If I had an excellent plain 

 scale, I would use it ; because I should expect the deviation from the right angle 

 to be less than if taken from a scale of more moderate accuracy ; but if not, the 

 equality of the divisions would not be affected, though taken from any common 

 diagonal scale. This chord, so prepared, I would lay off 5 times in succession, 

 from the primary point of O given, which would complete 80°. I would then 

 bisect each of those arches of 16°, as prescribed by Mr. Bird, and laying off 1 

 of them beyond the 80th, vv^ould give the S8th degree : proceeding then by bi- 

 section, till I came to an arch of 2°, laying that off from the 88th degree, 

 would give the point of 90°. Proceeding still by bisection, till I had reduced 

 the degrees into quarters =15' each, I would there stop ; as from experience I 

 know, that when divisions are too close, their accuracy, even by bisection, , 

 cannot be so well attained, as where they are moderately large. If a space of 

 tV of an inch, which is a quarter of a degree, on an 8 feet radius, be thought 

 too large an interval to draw the index over by the micrometer screw, this may 

 be shortened, by placing another line at the distance of -^ of a division on each 

 side of the index line ; in which case the screw will never have to move the 

 index plate more than 4 of a division, or 5'; and the perfect equality of these side 

 lines, from the index line, may be obtained, and adjusted to 5' precisely, by 

 putting each of the side lines on a little plate, capable of adjustment to its true 

 distance from the middle one, by an adjusting screw. The above hint is not 

 confined to the chord of 16*^, which prohibits the subdivisions going lower than 

 15': for if it be required to have divisions equivalent to 5' on the limb itself; 

 then I would compute the chord of 2\^ 2V only ; and laying it off 4 times from 

 the primary point, the last would mark out the division 85° 20', pointed out by 

 Mr. Bird ; supplying the remainder to a quadrant, from the bisected divisions as 

 they arise, and not by the application of other computed chords. 



