Tables hy the Board of Longitude. 289 



the latitude of the place and the declination of the star) he has 

 necessarily left to be calculated according to the circumstances 

 of the case. This is the proper and only correct mode of pro- 

 ceeding on such occasions: and the world is much indebted to 

 M. Delambre for the great labour which he has bestowed on this 

 and other branches of practical astronomy. But what has the 

 English computer done, under the sanction of our Board of 

 Longitude ?— He has garbled this very formula, and under the 

 disguise of a new dress and a new title, has given us the same 

 thing, or rather a part of the same thing, in a more clumsy and 

 incor.venient form. The rule given by this writer is expressed 



cos L. cos D. secA • p 



by the following formula: viz. ^.|^„ x ver-sin r, 



where A denotes the altitude of the star, and L, D, P, the same 

 as in Delambre's formula above mentioned. And it is a table of 

 the value of the versed sine of P only, for the first 7i degrees, 

 which constitutes the whole two leaves (for there are literally no 

 more) of this six -penny publication. The other part of the for- 

 mula, including the constant quantity -^r-^, he has left for cal- 

 culation, according to the particular circumstances of the case. 

 But let us analvsetliis formula, and reduce it to a more modern 

 appearance by getting rid of those antiquated terms secant and 

 versed sine (terms which are now necessarily discarded from 

 practical astronomy, since there are no tables by which their 

 adoption can be rendered of any use to the computer), and we 

 shall then see that this formula is precisely the same as the first 

 term of Delambre's. For, ver-sin P = 2 sin* \ ?, and sec A = 



J . consequently the English formula, translated into 



sin(L-D)' ^ ^ 



2 sin^ ' P C03 L. cos D ol^ovo 



French notation, becomes —^—[r, — x sirTcL-^rDT' ^' 

 mentioned. But, since A^c value of " ^^^ ^„ for every second 



has been already given, in several publications, and to a much 

 greater extent than the table of versed sines here alluded to, 

 there can be no hesitation which is the most convenient formula 

 to adopt : and the Board of Longitude would have chosen a better 

 ijart, to have reprinted those tables with an English introduc- 

 tion ; if indeed an English edition were called for. This however 

 is not the whole of the correction necessary ; for there is the 



. 2 sint § P /cos L. cos 1) \i . (L — D^ 



other term, viz. --",»- X (, li;7"(L-Dr/ ^ ^ 



which must be applied where great exactness is required : so that 



Vol. 5G. No. 270. Oct. IS20. O o the 



