288 Tables hj the Board of Longitude. 



evaded by annihilating my objections to the PhiUiphn Theory, 

 with one grand sweep, on an erroneous principle, with an intent 

 to impose on the igiiorr.nt. Us remains particularly for Veri- 

 talis to prove the falsity of the three first deductions, as he says 

 my subsequent deductions are founded on my first : otherwise, 

 by the rules of logic, all my inferences are true, and the whole 

 of my reasoning correct ! ! 



Tliat the readers of the Philosophical Magazine may not again 

 be told that they are hoaxed at the expense of truth, under an 

 anonymous signature, I subscribe myself, 



Sir, yours truly, 

 Lynn Regis, Oct. 12, 1820. James U'lTlNG. 



P.S. — Vossixis too, and many others give partly into the Car- 

 tesian notion, and suppose gravity to arise from the diurnal ro- 

 tation of the earth round its axis. — Vide Hution's Diet. vol. i. 

 p. 548. 



XLIII. Tables ly the Board of Longitude. 



To Mr. Tilloch. 

 Y Oct. 20, 1820. 



Sir, — 1 HAVE just seen a six-penny pamphlet published, 

 during the course of last year, by order of the Commissioners of 

 Longitude relative to A rule for correcting observations of me- 

 ridian altitudes made with the repeating circle: and I must 

 confess that I am somewhat surprised that that learned body 

 should have considered it necessary to order the printing of so 

 useless and inaccurate a performance. I consider it useless, be- 

 cause the tables already given by Delambre, under the title of 

 Tables for the reduction to the meridian, are in the hands of 

 every person who has an opportunity of using the repeating cir- 

 cle: and such tables are more convenient and more accurate 

 than those which are the subject of this letter; although founded 

 on precisely the same principles. M. Delambre 's formula for 

 the correction of the meridional zenith distance, as given by 

 himself in the Base du systeme vielrique, and repeated by every 

 writer on the subject since that time, is as follows, viz. 



Ssin'^P cos L. cos D 2 sin* J P /cos L cos D\ * 



ihri"~ ^ ~5n (L-D)~ "" sin 1" ^ Vsin (L-D) / ^ 



cot (L — D): where L denotes the latitude of the place, D the 

 declination of the star, and P the horary angle. And, in order to 

 render this formula applicable to practical purposes, he has 

 thrown into two tables for general use, all the constant parts, viz. 



2 sin' i P 2 sin' ^ P 



— ^-■^,— and ■ — :r~i—; but, the variable part (depending on 



the 



