Astronomical and Nautical Collection^. 435 



and parallaxes, as I have several times remarked in cases 

 which have actually occurred. 



2. The affection of the parallactic angle is sometimes am- 

 biguous, as noticed in Remark 1 . 



But, in the corrected rules, these imperfections are avoided 

 by computing the parallactic angle by Napier's analogies. 



3. By the rules in the N. A. the parallactic angle is di- 

 rected to be reckoned sometimes from the North, and some- 

 times from the South Pole. But by the corrected rules, this 

 angle is always reckoned from the North Pole, whereby the 

 precepts are simplified. 



Other changes have been made ; and, if you think proper, 

 the corrected rules may be published in such manner as you 

 may deem suitable. And 1 am, with respect, 



Dear Sir, 

 Your very obedient humble servant. 



Thomas Henderson. 



Rules for computing an observed Occultation. 



1. Find half the sum and half the difference of the north 

 polar distance of the zenith (corrected on account of the 

 spheroidal figure of the earth), and the north polar distance 

 of the star ; and to the logarithmic cosecant of the half sum 

 add the log. sine of the half difference, and the log. cotangent 

 of half the star's horary angle ; the sum is the log. tangent 

 of an angle A always less than 90°: and to the log. secant 

 of the half sum add the log. cosine of the half difference, and 

 the log. cotangent of half the horary angle, the sum is the 

 log. tangent of an angle B, which is greater or less thai) 90°^ 

 accordingly as the half sum is greater or less than 90°. If 

 the north polar distance of the zenith be greater than the 

 north polar distance of the star, the sum of A and B, other- 

 wise their difference, is an angle C, to which prefix the sign + 

 when the star is east of the meridian, and — when west. 

 When the orbital angle has N. prefixed, its complement to 90^ 

 will have the sign— , and + when S. The sum of this com^ 



