TOL. XV.] PHILOSOPHICAL TKANSACTIOMS. 235 



distances from the axis of Jupiter may be found, to any given time, within the 

 compass of the year, and for any future year by the like tables. 



To make the catalogue of eclipses, as also the table of the parallaxes of 

 Jupiter, it was necessary first to make a table of Jupiter's heliocentric places, 

 to which the parallaxes being applied, give the geocentric. The common ephe- 

 merides are very faulty in this planet. 



The Solutions of three Chorographic Problems. By a Member of the Phil. Soc. 



of Oxford. N° 177, p. 123]. 



The three following problems may occur at sea, in finding the distance and 

 position of rocks, sands, &c. from the shore ; or in surveying the sea-coast ; 

 when only two objects, whose distance from each is known, can be seen at one 

 station : but especially they may be useful to one, who would make a map of a 

 country, by a series of triangles, derived from one or more measured bases ; 

 which is the most exact way of finding the bearing and distance of places from 

 each other, and thence their true longitude and latitude ; and may consequently 

 occur to one who would in that manner measure a degree on the earth. 



Prob. \. There are two objects, B and C, fig. 10, pi. 7, whose distance BC 

 is known ; and there are two stations, at A and E, where the objects B, C, be- 

 ing visible, and the stations from each other, the angles BAC, BAE, AEB, 

 AEC, are known by observation ; to find the distances or lines AB, AC, AE, 

 EC. 



Construction. — In each of the triangles BAE, CAE, two angles at A, E, 

 being known, the third is also known: then take any line a eat pleasure, fig. 11, 

 on which constitute the triangles bae, aec, respectively equiangular to the 

 triangles BAE, AEC ; join be. Then upon BC constitute the triangles BCA, 

 BCE equiangular to the correspondent triangles bca, bee, join AE, and the 

 thing is manifestly done. 



Calculation. — 'Assuming « e of any number of parts ; in the triangles abe, 

 ace, the angles being given, the sides ab, ac, eb,ec, may be found by trigo- 

 nometry: then in the triangle bac, having the angle bac, and the legs ab, ac, 

 we may find be. Then be : BC:: ba: BA::be:BKi:ca :CA:: ce:CE. 



Prob. •!. — Three objects, B, C, D, fig. 12, are given, or, which is the same, 

 the sides, and consequently the angles of the triangle B C D are given ; also 

 there are two points or stations A, E, such, that at A may be seen the three 

 points B, C, E, but not D ; and at the station E, may be seen A, C, D, but not 

 B ; that is, the angles BAC, BAE, A E C, A E D, and consequently E A C, 

 AEC, are known by observation : to find the lines A B, A C, AE, EC, ED. 



HH2 



