Page:Practical astronomy (1902, John Wiley & Sons).djvu/33

INTERPOLATION. 15 therefore E and are known : and we have A' = E - (360 -L)=E+L- 360. (37) To find the geocentric latitude, we have P = E tan B' = S tan 6 (38) tan 8' _ S sin E tanlT : Z ~EO ~sin~S ; whence tan 6 r = tan 6 Sm . (40) sin jy To find r", we have Z7 7 /") '/ /Jf a, u r cos c/ , > S0 = r' cos 0. In the triangle E S 0,we have r" cos 0': r' cos :: sin $ : sin E, whence . cos sin $ cos 0' sin E * With these data we can readily find the right ascension, decli- nation, horizontal parallax, and apparent diameter as in the case of the sun and moon. INTERPOLATION. Interpolation. Whenever the differences of the quantities re- corded in the Ephemeris tables are directly proportional to the dif- ferences of the corresponding times, simple interpolation will enable us to find the numerical value of the quantity in question. When this is not the case, the value is determined by the " method of in- terpolation by differences." BesseFs form of this formula, usually employed, is