the New Talle.i of Ftmis. A^ 



S. Tlie same argument a|)i)lied to Table XII, obtains the 

 planet's heliocentric latitude*. 



To find the Radius Vector. 



9. With the mean anomaly found by precept 4, enter Ta- 

 ble VIII. for the elliptic radius vector ; underneath which write 

 the several corrections of the 5ame taken from Tab. IX. bv 

 means of the six Jirsl arguments of perturbation. To the sum 

 of the seven quantities, apply the secular equation, and the re- 

 sult i>< the true radius vector, corresponding to the mean distance 

 0-7233316ti. 



To find the Geocentric Longitude and Latitude. 



10. Calculate the earth's longitude and radius vector for the 

 given time from the solar tables. 



11. To the logarithm of the planet's radius vector, add the 

 logarithmic cosine of its heliocentric latitude, either from Tab. XI. 

 or from the common trigonometrical tai)les; the sum, rejecting 

 10 from the index, will be the logarithm of the planet's curtate 

 distance. 



12. Then, in the plane triangle formed by the sun, earth, and 

 planet's ecliptic place, we have given two sides, viz. the earth's 

 radius vector, and the planet's curtate distance, with their in- 

 cluded angle, called the angle of commutation. This latter is 

 found by subtracting the earth's longitude from that of the pla- 

 net (increased by 12 signs if necessary). From these data the 

 other two angles are found by the operations of trigonometry f. 

 The angle at the earth is called the elongation, and, in the case 

 of an inferior planet, it is always the least of tlie two. 



\'.i. When the angle of commutation is greater than six signs, 

 add the elongation to the sun's longitude, the sum is the planet's 

 true geocentric longitude reckoned from the mean equinox : but 

 if the angle be less than six signs, the elongation is to be sub- 

 tracted. 



14. Add together the log. tan. heliocentric latitude, log. sin. 



• In the Introduction to the original Tables, the secul.^r variation of 

 greatest latitude is stated to be — 7"'24 cos. inclin. but in the Tables them- 

 selves the co-eflicient seems to be -f B"'4. On account of this discordance, 

 and the siiiallnes» of the correction, it was thouglit proper in Tab. XII. to 

 omit altogether the column of secular variation. 



+ There are two fonnuLx adapted to the solution of this case. The one 

 employed in the following example, has generally been adopted in calcula- 

 tions of this kind ; but since the introduction of equations of perturbation 

 into Astronomical Tables has rendered it necessary to give the radius vector 

 in natural numbers instead of logarithms, perhaps the more common for- 

 mula would now be found preferable in practice. In that case, however, 

 there miist be substituted for Table XI. one of double entry for obtaining 

 thti cuitute distance in natural numbers. 



elongation, 



