732 PHILOSOPHICAL TRANSACTIONS. [aNNO I79O. 



the centre of the scheme of course is the planet Saturn, and its ring, expressed 

 by a line which represents the direction of its ansae; or the ring itself, as it ap- 

 peared in the telescopes during the months of July, August, September, Octo- 

 ber, and November, 1789. The 5 lines which are carried on parallel to each 

 other serve to convey the measure of the planet, and its ring, to the orbits of 

 the satellites, as will be seen in several instances that occur hereafter. The gra- 

 duated circle is divided into degrees, and begins to count from that part of every 

 satellite's orbit beyond the planet, which is intercepted by a plane passing from 

 the eye of the observer, at rectangles to the ring, through the centre of Saturn. 

 Hence it follows, that the point of zero, or 36o°, is the same with the geocen- 

 tric place of the planet in those 4 parts of the orbit of the satellite where the 

 eye is in the plane of the ring, and where it appears the most open; and that, 

 in other places, it may be had by solving one spherical triangle. This is to be 

 understood as relating only to the inner satellites; the 5th, or outermost, re- 

 quiring a different reduction, on account of its deviation from the plane of the 

 ring. But Dr. H. is inclined to believe, that the surest way of observing the 

 5th, is to trust only to measures, taken with micrometers which give the dis- 

 tance and angle of position, except in such cases when the eye is nearly in the 

 plane of this satellite's orbit, where the different reductions may be neglected, 

 without bringing on any considerable inaccuracies. 



The calculations of the places of all the satellites have been made according to 

 tables which are given at the end of this paper. Their form being very simple. 

 Dr. H. thought it not amiss to communicate them, for the use of those who 

 may wish to enter into a more particular examination of the following obser- 

 vations; or to follow the satellites in their orbits at any future time. Dr. H. 

 has deduced the epochae of all the 7 satellites from his own observations, and 

 they will be found to differ considerably from those given by De la Lande, in the 

 Connoissance des Temps for 1791. But he has not attempted to extend them 

 further than a few years backwards or forwards, as he is not in possession of any 

 observations that could authorize him to undertake such a work. On the con- 

 trary he is well convinced, that no tables will give the situation of the satellites 

 accurately, till we have at least established the dimensions of their elliptical 

 orbits, and the motion as well as the situation of their aphelia. The epochae 

 for 1789 therefore must be considered not as mean ones, but such as respect the 

 orbits of these satellites in their situation during the time of the following ob- 

 servations; and the 2 preceding and 2 following years must be already a little 

 affected with those errors which are the necessary consequence of our not know- 

 ing the required elements. Dr. H. flatters himself however, that the observations, 

 which are delivered in this paper, will serve as a beginning to a proper foundation 

 for investigating them. The many conjunctions between the satellites, for in- 



