C86 3 



V. A second Appendix to the improved Solution of a Problem in 

 physical Astronomy, inserted in the Philosophical Transactions 

 for the Tear 1798, containing some further Remarks, and 

 improved Formulae for computing the Coefficients A and B ; 

 by which the arithmetical Work is considerably shortened and 

 facilitated. By the Rev. John Hellins, B. D. F. R. S. and 

 Vicar of Potter's Pury, in Northamptonshire. 



Read December 12, 1799. 



.1. It was shewn, in Art. 9. of the first Appendix, that the 

 common logarithm of the fraction l+ , when c is ex- 



pressed in numbers, might be taken out from Taylor's excel- 

 lent tables, and converted into an hyperbolic logarithm by 

 means of table XXXVII. of Dodson's Calculator; which 



method of obtaining the H. L. — — - '~ ■■■ is undoubtedly easier 



and shorter than the more obvious one of first computing the 

 numerical value of that fraction, and then taking out the hyper- 

 bolic logarithm corresponding to it from a table. But yet, that 

 method of obtaining the value of a, easy as it is, requires, first, 

 a search in the table for the angle of which c is the sine, and 

 generally a proportion for the fractional parts of a second; 

 then, a division of the degrees, minutes, and seconds contained 

 in that angle, by 2 ; and, thirdly, another search for the loga- 

 rithmic tangent of half the angle, and another proportion to 

 find the fractional parts of a second. I was therefore desirous 



