The re Places of the Planets 79 It is obvious that when the mean distance of a planet from its conjunc. tion is less than a quadrant in either direction, as at M, the ba8e Ea is greater than yodius ; when that distance is moze than 4 quadront, as at M', the base Ext is less than thdius: the cosine is to be added to radius in the one c£s, and subtracted from it in the other. Whis is the mean ing of the rule in vorse 40: compare the notos to i. 58 88 if 80. In illustration of the process, we will calculate the equation of the conjunction of Mercury for the given time, or for midnight preceding January 3, 1860, at Washington Since the Kind systemlike the Greek, interchanges in the case of the two inferior planets the motion and place of the planet itself and of the Sun, giving to the former as its moan notion that which is the mean apparent; motion of the sum, arud assigning to blhe conjunction (ethnvocc०) n . revolution which is tually }na of the planet in its orbit, the mean prsition of Mercury it the ven im is that found above (undex v. ) to be bhat of he sun t. the same irwhile to find that of its conjunc . ion we have to add the con ion for difference of meridian (centra. pat?g. f. 6, 61), to the lowig ude j«on under 58 a% +hat of the planet. annight, at jjayinf 4 * 13° 18 8* Lo ike of Mercury's conjunction (gfgrocco) add is difference of critium 1 44 1 4 16 57 22 Longitude cf conjunction at required time, Mam lot!itude of Bercury, 818 18 18 Man cormutation ¢grayadro) | 28 44 g The position of Mercury writh reference to the conjunction is accord. ingly very nearly that of M, in Fig. 5. The aro which determines the bake-sine (bajrjya), F OM', is 58° 44, while MD, its complement, from which the perpendicular-sine (Hotijyi) is taken , is 81° 18. The corresponding inex, ME and Mi and 2988" until 1784 respectively 'The epicycle of Mercury is one degree less at D than at . Hence the proportion B438 : 80; : 238: $1 gives 51 is the diminution at M : the circumference of the epicycle at M', then, is 182° 9. 'he two proportions 880° : 182० 9 ' : : 238 : 1078, anil B€0° : 182° 3':: 1784 : 655, give us the value of an's y as 1078, and that of 'M' 28 855'. The commutation being more than three and less than nine signs, or in the half-orbit beginning with Cance, the fourth sign, 4/M" is to be 89b
