NUTATION OF THE EARTH'S AXIS, ^cc. 59 



fuppofe the place of the Moon's afcendine node to be at i, and 

 the pole of the Earth being 3' before the Moon's afcendmg node, 

 will be at 4' in the ellipfe : and the occult line 4 ff, at right 

 angles to the meridian of the ftar, v/ill be the nutation in right 

 afcenfion anfwering to 1% and 7% of the longitude of the Moon's 

 afcending node, but with contrary figns of application. The 

 diilance C a, or the occult line 4^, in the direction of the meri- 

 dian will be the nutation in declination. The diflance 4 a, mea- 

 fured on the fame fcale by which the projeftion is made, will 

 give 8". 44, and the diftance 4^ will give 3". 15 : But the firft 

 mufl be reduced to the equator, which is moil conveniently 

 done by multiplying it by the natural tangent of the ftar's de- 

 clination. 



When great accuracy is required, recourfe mufl: be had to 

 calculation, which may be done in the fame manner as purfued 

 in aberration. It has already been obferved that an ellipfe may 

 be confidered as a circle in the orthographical projeftion of the 

 fphere, and therefore the arc C 0, which is the meafure of the 

 angle C 3 0, will be had by adding 10, to the log. of 7.1, and 

 from that fum deducting the log. of 9.55 the remainder will be 

 the log. fine of the arc Co which will be about 48° 2'. Then 

 in the right angled fpherical triangles Co^, and Co^, right an- 

 gled at 0, it is required to find the angles C^o, Q.eo, and the 

 axis 0^, oe, the angle oQg being the right afcenfion of the 

 ftar, and the angle oQ.e its complement, and therefore both 

 given. The angle C^o will be 62" 28', the arc 0^^:35° 

 25', the angle C d'o:^ 61° 6', and the arc 06" ^: 37" 52 . Thefe 

 being the necefiJary requifites, the nutation in right afcenfion 

 will be had as follows 



To - 9 55 - Log. 0.9SC00 



Add angle Cj'or: 62° 28' - Log S. 994780 



Dedua 



10 927!: 



0.92780 Conftant Log. 



Conftant - - Log. o 927S0 



Addarc^ I = 5° 25' - Log. S. 8.97496 



9.9027^ 



As 



