VOL. LXl.] PHILOSOPHICAL TKANSACTIONS. 187 



used by Kepler as such ; however, it ought to be corrected by adding it to bd, 

 and taking an arch to this, in the proportion of the sine of bd thus augmented, 

 to the sine simply of bd ; and this last arch will be equal to the parallax in lon- 

 gitude without sensible error. 



Again, de, taken to the horizontal parallax as the sine of zb to the radius, is 

 considered by Kepler as the moon's parallax of latitude in eclipses ; but this being 

 deducted or added, as the case requires, gives eh, which being augmented in 

 the proportion of the sine of bd + dc to the sine of bd, gives truly the apparent 

 latitude without sensible error, when the latitude is small : but, when greater, 

 requires to be corrected by adding together the logarithmic sine of the latitude 

 now found, the sine of eh and the logarithm of D^ the sum of which is the 

 double of the correction required. mb d.r.n-. iii'i loiitsrt 



In the last place the moon's horizontal diameter augmented in the proportion 

 of the sine of bo to the sine of bd exhibits the moon's apparent diameter. And 

 here the calculation will proceed thus : in the example above chosen for com- 

 puting the nonagesime degree. 



The moon's longitude is given from T 62° 2' 38" 



The longitude of the nonagesime degree as found above .... 54 56 24 



Therefore bd = 7 6 14, its sine 9.09226 



Bz, as found above, 50° 2' 0", its cosine 9.80777 



The horizontal parallax in seconds 3.52387 



4 25 2.42390 



This added to BD gives 7 10 39, its sine 9.0y673 

 Difference from the first sine 44/ 



This added to the log. of 4' 25", gives the log. of 4' 28", for the moon's parallax 

 in longitude, such as is derived from the parallax in altitude by the parallactic 



angle 2.42837 



Again, 



The sine of zb 50° 2' 0" 9.88447 



Horizontal parallax 55' +1" = 3341 seconds 3.52387 



Their sum, rejecting the radius, gives de = 4'2' 40" 3.40834 



The moon's latitude 4° 50' 18" 



Their sum, (eh) the latitude being south 5 32 58, its sine 8.98546 b 



From the preceding calculation . .' .... 447 



For the apparent latitude, were the moon's lat. small 5 6 25^ 8.98993 



But the moon's lat. being here great, the numbers marked 



A, B, c, being added together, givetwice the correction. . 24 1,38373 



Its half 12 

 This deducted from N° c, the moon's lat. being south, gives 



for the apparent latitude 5 36 13j 



Lastly, 



From the moon's horizontal parallax her horizontal dia-\ 30 37 i 



meter it J or 1837| 



The number from the first calculation 

 The moon's apparent diameter 1856 J" or 30 56 J 



3.26423 



447 



3.26870 



Now, in solar eclipses, the most regular method of treating them, would be 

 to consider the visible way of the moon from the sun as a line of continued cur- 



B B 2 



