130 PHILOSOPHICAL TRANSACTIONS. [aNNO 1704. 



pole, the distance of the sight being radius; and the diameter of the outermost 

 circle, equal to double the tangent of the distance of the next star to the pole- 

 star, from the pole. The instrument thus prepared, if you look through the 

 sight, and bring the two circles to the two stars, whose distances from the pole 

 they represent; a line passing through a sight and centre of the circles, is the 

 elevation of the pole : and two plumb-lines hung up, one over the sight, the 

 other over the centre of the two circles, will lie exactly in the meridian of the 

 place. Mr. Gray's ingenious Contrivances are in the Phil. Trans. N° 268 

 and 270. 



The last instrument is what I have made use of for several years, and 

 which I can recommend on my own experience, for a ready way to find the 

 meridian of any place, and to see the transits of the celestial bodies over it, 

 either northward or southward. The instrument is thus made of wood, or 

 rather iron, or brass, to indure the weather, without swelling or contracting, 

 viz. prepare a small flat iron bar, as cc in fig. 21, pi. 3. At each end of 

 which rivet on two upright sights, to turn stiffly, at the joints 11. Let one of 

 the sights, cd, have a perforation, large enough to see the pole-star through 

 it ; the other sight, ab, a very small perforation, to see the sun through. Just 

 behind the joints fix two upright arms cd and cd, but to bend off, so as to be 

 out of the way of the sights, when you look through them. These arms 

 ought to be long enough for the plumb-lines to reach the pole-star, on 

 one side; and the sun at his greatest height, on the other side, when you 

 look through either of the sights. The plumb-lines therefore are tangents to 

 their opposite sights, and their lengths may be found by a table of natural 

 tangents, making the distance of the two sights radius. Thus, in the latitude 

 of London, if the instrument be two feet from sight to sight, the southern 

 plumb-line should be near 4 feet, and the northern one about 2 feet 10 inches. 

 On the tops of these two arms, place two small cross pieces de and de, to turn 

 with a joint at d; which cross pieces are to hold the plumb-lines ep and ep, 

 and to turn off and on, so as to bring the plumb-lines exactly to the sights. 

 Place this instrument on a pedestal h, to turn round on it stiffly at the pin g. 



The instrument being thus prepared, the way to set and use it is thus: plant 

 it in a convenient place, where the pole star may be seen by night, and the sun 

 by day. When that star is on the meridian, is the time to set the instrument, 

 which is thus to be done; viz. through the sight with the larger hole, cd, look 

 at the pole-star, and turn the whole instrument about, till you see the opposite 

 plumb-line nicely to intersect the pole-star. Or when you have brought the 

 plumb-line near the star, you may more easily bring the plumb-line to intersect, 

 by moving the sight cd backward or forward, at the joint i, instead of moving 



d 



