178 PHILOSOPHICAL TRANSACTIONS. [aNNO I675. 



The Extract of the other Letter. 



I think I have been since my last a little better employed than before. I found 

 it necessary to make new solar numbers, because in my old I had neglected to 

 apply refractions in all the altitudes above 30 degrees; wherein yet reason and 

 some little experience has showed me they are not insensible. I found Signor 

 Cassini's observations, which I took from Ricciolus's Astronomia Reformata, 

 much more accurate than Tycho's, and therefore sought out numbers that 

 might answer them. The apogaeum I found it necessary to promote 44 minutes; 

 so that anno ineunte l655, it might be in 25 7° 30' O'' ; and to make the great- 

 est equation only 1° 54' IS*^'; whereby I found, the phsenomena would be 

 answered much more accurately than I expected, and as near, all things con- 

 sidered, as I could desire. 



But still I was uncertain whether the refractions in the said Cassini's Tables 

 were just measures or not; and I had no conveniences for making trial. At last 

 I thought on this expedient, which fully satisfied me; viz. 



I considered that if some of those observations of the distances of 9 from 

 the O by day, the stars in the night preceding or following, were skilfully 

 examined, they might show me the true quantity of the equations of the sun's 

 orb, or rather the difference of his mean and equal motion. I turned over his 

 progymnasmata, and pitched on two. The first made anno 1582, the 5th of 

 March, hor. 4. 42', and hor. 7. 12' p. m. ; whereby I found the at hor. 4. 42' 

 was 94° 47' in antecedence of the lucida calcis H • The second made anno 

 ]585, the 15th Sept. hor. 5. 15', and hor. 6. 55' mane. Where from applying 

 and considering the refractions in both, I found the sun at hor. 6. 55' to be 74° 

 30' in consequence of the lower head of n • The difference of longitude 

 between these two stars is 17° SQ': and therefore now the sun in consequence 

 of the lucida calcis n 92° 29'. So that the sun's apparent motion between the 

 year 1582, the 5th of March at hor. 4. 42', and the year 1585, the 15th of Sept. 

 at hor. 6. 55' mane (besides the whole revolutions) was 187° 16': but the mean 

 motion is 191° 2'; greater than the apparent by 3° 46': which parted in pro- 

 portion to the equation of the earth's motion, collected for those times from my 

 new tables, gives the greatest equation of the orb, 1° 54' 1 5" ; consenting, to 

 my wonder, without any wresting of the observations, with that which I dedu- 

 ced from Cassini's correct meridional altitudes. 



I had not had time to examine any of those others he has related ; nor 

 indeed are they any ways convenient : but by this that I have done you may 

 see, that if once we get instruments to our purpose, that then it will not be 

 difficult to correct the sun's motions, without the consideration of the meri- 



