Astronomical and Nautical Collections. 117 



iii. A Rule for clearing the Lunae Distance from the effects of 

 Parallax and Refraction. By Charles Blackburne, Esq. 



Let S and S' denote the true and apparent altitudes of or ^9 

 M and M', the true and apparent altitudes of the D , c? the diffe- 

 rence between the true altitudes, d' the difference between the appa- 

 rent altitudes, A the apparent distance of the centres. Then, 



Rule, 

 Add together the five following logarithms, VIZ. 1. sin. 4 A + cf ; the 

 I. sin. i . A«^d'; the 1. cosin. M; the 1. sec. M' ; the constant loga- 

 rithm 0.301150, and reject 30 from the index.* 



To the natural number belonging to this logarithm, add the v. 

 sin. d; the result will be the v. sin. of the true distance!. 



Z 



DEMONSTRATION. 



Let ZS, ZS\ be the true and apparent zenith distances of the sun 

 or a star ; ZM, ZM', those of the moon ; then SM will be the 

 true, and 5' M' the apparent distance of their centres. And by the 

 principles of trigonometry, 



sin nZrz ^^ ^ ^^°- ^ ^^^'^ ZM'+S'M') x sin. i{ZS^ZW^SM') 

 ' ^ sin. ZS' X sin. ZM' 



or sin 2 1 7 - /e^ Xsin.j.A +d' X sin, j A ^ 

 orsm.-^ z. 



^ ^ d' 



sin. S' X cos. M' 

 Again, 



cos. SMrz cos. ZS^ ZM- sin. ZS x sin. ZM>< sin.2 1 Zx ^ 



^ R3 



2 

 or cos, SM = cos d - cos. S x cos. M x sin.^ 4. Z x 



•The constant logarithm 0.301150 must be corrected, if necessary, by 

 Table X. or XI. in page 83 of the Requisite Tables. 



t If the index to the logarithm be 9, find the natural number to as many 

 places as the tables are calculated to; if it be 10, to one more ; if it be 8, to 

 one less; and so on. 



The rule requires no distinction of cases. 



