208 PHILOSOPHICAL TRANSACTIONS. [aNNO 1771. 



that the southernmost limb of the northernmost image of the sun runs along the 

 same. Half the difference of these two measures, if taken immediately after 

 one another, is equal to the dift^erence of the declination of the centres of the 

 sun and planet at the intermediate time, without any regard to the quantities of 

 the diameters of the sun or planet, or the error of adjustment of the micro- 

 meter. The difference of the transits of the eastern or western limbs of the 

 sun and planet will give the diflference of right ascension, as in the common 

 micrometer. 



Instead of differences of right ascension, distances of the planet from the 

 sun's limb, in lines parallel to the equator, may be more accurately observed as 

 follows. The glasses being separated to a convenient distance, turn both the 

 wires and micrometer about, so that the two images of the planet may both run 

 along the wire ew, fig. 1 1, and separate the glasses so that v, one of the images of 

 the planet, may touch the limb of the sun to the east or west, or rather both 

 alternately. Or perhaps the following method may be preferable: separate the 

 two images of the sun to any convenient distance, so as to produce a consider- 

 able angle of intersection of the circumferences at i and t; turn the wires about, 

 so that the planet's centre, north, or south limb, may run along the wire ew ; 

 then turn the micrometer about till the two intersections i, t, pass the horary wire 

 NS at the same instant, and the micrometer will be in a proper position for 

 measuring distances in a line parallel to the equator; and the distance of the 

 planet from the sun's limb in a line parallel to the equator will be obtained by 

 only bringing the glasses nearer together, or separating them further, till the 

 planet's limb is in contact with the sun's limb. If distances of the planet's near 

 limb from the sun's limb be thus taken to the east and west alternately, and 

 reduced to a given time, by allowing for the motion of the planet by calculation, 

 half the difference of the two reduced measures will be the distance of the 

 planet's centre from the middle of the chord of the sun's disk passing through 

 the planet's centre parallel to the equator at the given time, without any regard to 

 the quantities of the diameters of the sun or planet, or the error of the adjust- 

 ment of the micrometer. It may be proper to remark, that when the planet 

 is brought to touch the sun's limb, the point of contact will be north or south of the 

 planet's centre, according as the planet itselfis north or south of the sun's centre. 



In like manner, distances of Venus or Mercury from the sun's limb may be 

 measured in lines perpendicular to the equator, see fig. 12, (the micrometer 

 being brought into the proper position, in the very same manner as for measuring 

 the difference of declination from the sun's north or south limb, before 

 described) ; and if the planet be brouglit into contact with the sun's limb to the 

 north and south alteinately, half the difference of the measures, reduced to a 

 given time, by allowing for the motion of the planet by calculation, will be the 



