416 



Astronomical and Nautical Collections. 



CALCULATION. 



Mr. B. has rightly performed the first part of the calcu- 

 lation ; the other part should be as follows : — 



Difference of apparent altitudes by Mr, B. . 14' 20*" 



Add for augmentation 10 



Correct difference of apparent altitudes . . 14 30 



Star's altitude 47° 27 17 



Moon's apparent altitude 47 41 47 



The complementary orbital angle must be found for the 

 moon's apparent place. By the differential analogies of 

 spherical triangles, we have 



Cot. •)(- alt. : sin. comp. orbit, ang. :: +14' V : +1' 12" 

 Rad. : cos. comp. orbit, ang-. tang. alt. : : — 4 39 : — 5 3 



— 3 51 



4 29 



Comp. orbital angle for ]) 's apparent place ..425 



Log. secant D 's apparent altitude . . . . 0*17195 

 Prop. log. reduced hor. parallax .... 0*52167 

 Log. cosecant comp. angle 1*11346 



Prop. log. orbital parallax . . + 2' 48" 1*80708 

 Log. tang. comp. angle . . . 8*88783 



Prop. log. perpendicular parallax —36 20 0*69491 

 Nearest distance . +50 31 



Sum +14 11 



}) *s hor. semidiameter 14' 46" 

 Augmentation lOj 



D's augmented semidiameter . 14 56^ 



Sum 29 7J P.L. 0*79100 



Differ 45j P.L. 2*37541 



2)3*16641 



Side +4 42 P.L. 1*58320 



Orbital parallax . . +2 48 

 + 7 30 

 in place of 7' 31", as by the other method. The difference 

 is occasioned by the minute quantities omitted in the arith- 

 metical operations, which, in this instance, have a sensible 

 influence upon the result. 



