VOL. LII.] PHILOSOPHICAL TRANSACTIONS. OSQ 



egress, because I have good reason to believe that tiie observation at the egress 

 at these two places vvas not correct, and the observation of the contact at the 

 ingress is more certain than that of the egress, and the observers at the ingress 

 at these two places agree to 2'^ . . 



«^ The elements I made use of in the preceding calculations are h^jtibf^-^ 



The sun's diameter . tp. y^Un'U •.] .-l' ^ 0^ 3 1 ' 3 r^ ' 



The diameter of Venus !..........= 59 



Horary motion of Venus in her path .* := 3 50.8 



Angle of the orbit of Venus with the ecliptic =8 30 10 ' 



Distance of the centres of the sun and Venus as seen from the ^ 



[ f centre of the earth .>. .suU. I*"* -v. . . . = o g 35 



Difference of the parallaxes of the sun and Venus . .'..'..■.' ....,= o O 21 35 



I shall now give the method I followed in these calculations. 



In pi. 15, fig. 2, let fg represent the horizon, zvh a vertical circle passing 

 through the centre of Venus, pvr a circle of declination, bv a circle of latitude 

 -EC the ecliptic, ovn the orbit of Venus, vl the parallax of altitude, vn the pa- 

 rallax of longitude, ln the parallax of latitude, zvp the angle of the vertical with 

 the circle of declination, bvp the angle of the equator with the ecliptic, zvb the 

 angle of the vertical with the circle of latitude, evo the angle of the orbit of 

 Venus with the ecliptic, zvo the angle of the orbit of Venus with the vertical 

 zp the complement of the latitude of the place, vp the complement of the decli- 

 nation of the planet, zpv the horary angle or distance of the planet from the 

 meridian, zv the complement of the altitude of the planet. 



In the triangle zpv, the sides zp and pv and the angle zpv are given, there- 

 fore the angle zvp may be found, and also the side zv; and as the parallax of 

 altitude is to the horizontal parallax as the cosine of the apparent altitude is to 

 the radius, therefore lv is found, bvp added to or subtracted from zvp as the 

 nature of the case requires, leaves the angle zvb; th6 angle zvb subtracted from 

 Bvo leaves zvo = to the angle of the orbit of Venus with the vertical zvo = 

 LVxV. Therefore in the right-angled triangle lnv, the angle lnv, the angle 

 lvn being given, and the side lv, the side vn, = the parallax of longitude, and the 

 side LN, = to the parallax of latitude, may be found. The parallax of longitude 

 is reduced to time by knowing the horary motion of Venus in her orbit or path 

 Thus the value of one second of longitude is known in time. But to reduce the 

 parallax of latitude to time, in fig. 3, let ecp represent the ecliptic, ors the path 

 of Venus over the sun as seen from the centre of the earth, lhd the path of 

 Venus as affected by parallax at any one place, or the nearest distance of the 



centres of the sun and Venus as seen from the centre of the earth cr thi- r.« 



. } ■"• "-tic near— 



est distance of the same centres as seen from the place of observation Rr or nv 

 the parallax of latitude, cs the sun's semidiameter, vs the semidiameter of Venus 



4 p2 ' 



