ii 



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 177 



at one end, to two shoulders or arms of brass, at the distance of 23° and -4. 

 from the poles of the ecliptic. These shoulders at the other end are strongly 

 fastened on to an iron axis, which passes through the poles of the ecliptic, 

 and is made to move round, but with a very stiff motion; so that when it is 

 adjusted to any point of the ecliptic, which you desire the equator may 

 intersect, the diurnal motion of the globe on its axis will not be able to 

 disturb it. 



When it is to be adjusted for any time, past or to come, bring one of the 

 brazen shoulders under the meridian, and holding it fast to the meridian with 

 one hand, turn the globe so about with the other, that the point of the ecliptic, 

 which you would have the equator to intersect, may pass under no degrees of 

 the brazen meridian : then holding a pencil perpendicular to that point, and 

 turning the globe about, it will describe the equator as it was posited at that 

 time; and transferring the pencil to 23-4-°, and 66-J° on the brazen meridian, 

 the tropics and polar circles will be described for the same time. 



By this contrivance, the celestial globe may be so adjusted, as to exhibit not 

 only the risings and settings of the stars, in all ages, and in all latitudes, but 

 the other phaenomena likewise, that depend on the motion of the diurnal axis 

 round the annual axis. 



The Solution of Kepler s Problem, by J. Machin, Sec. R. S. N° 447, p. 205. 



Many attempts have been made at different times, but Mr. Machin thinks 

 never any yet with tolerable success, towards the solution of the problem pro- 

 posed by Kepler : to divide the area of a semicircle into given parts, by a line 

 from a given point of the diameter, in order to find a universal rule for the 

 motion of a body in an elliptic orbit. For among the several methods offered, 

 some are only true in speculation, but are really of no service. Others are not 

 different from his own, which he judged improper: and as to the rest, they 

 are all some way or other so limited and confined to particular conditions and 

 circumstances, as still to leave the problem in general untouched. To be more 

 particular; it is evident, that all constructions by mechanical curves are seem- 

 ing solutions only, but in reality unapplicable; that the roots of infinite serieses 

 are, on account of their known limitations in all respects, so far from affording 

 an appearance of being sufficient rules, that they cannot well be supposed as 

 offered for any thing more than exercises in a method of calculation. And 

 then, as to the universal method, which proceeds by a continued correction of 

 the errors of a false position, it is, when duly considered, no method of solu- 

 tion at all in itself; because, unless there be some antecedent rule or hypothe- 

 sis to begin the operation, (as suppose that of a uniform motion about the 



VOL. vni. A A . 



