Life, Researches, and Discoveries of F. W. Bessel 313 



features of this second memoir, deserves to be noticed a happy 

 application of the general resolution, by continued fractions, of 

 an equation of finite differences of the second order, to the ex- 

 pression of the course of a ray refracted through any combina- 

 tion of spherical surfaces. The third of these memoirs relates 

 to the elimination of the influence of refraction ; and the fourth 

 to that of the several effects of precession, nutation, and aberration, 

 from measures so taken, and from micrometric measures generally. 

 The exceeding precision of micrometric measurement of which 

 the heliometer proved capable, was also brought to bear upon 

 other objects, such as the measurement of distances of the 

 Huyghenian satellite of Saturn from the ring, and those of 

 Jupiter from the limb of the planet, with a view to the more 

 perfect determination of the masses of these planets. The re- 

 sults of the latter observations, as compared with their theory, and 

 the improved tables of the motions of the satellites themselves, 

 concluded from the whole inquiry, are to be found in the Ninth 

 Essay, Vol. II. of the Astronomische Untersuchungen, already 



referred to. 

 In the year 1824, in a paper communicated to Schumacher's 



Astronomische Nachi 



peculia 1 



minatton of latitudes, and of the declinations of such stars as 

 pass near the zenith, offered by a mode of observation whose 

 first idea seems to have been due to the celebrated Romer, viz. 

 M the use of a transit instrument at right angles to the meridian, 

 and therefore describing the prime-vertical. By the use of this 

 method, the differences of declination of two stars passing near 

 the zenith of any given places, or the change of declination ot 

 one and the same star at different times, comes to be measured 

 upon a vastly increased scale by the interval of its two transits 

 over the vertical, expressed in time. It is therefore independent 

 of the errors of division of any circle, and, as Bessel has also 

 shewn, of a variety of other influential causes of error, ana is es- 

 pecially adapted for those inquiries in which the zenith sectoi 

 has been usually employed. A large instrument constmcted 

 «Pon this principle has been since erected in the Impe rial Obser- 

 v atory at Pulkowa, with the express object of affording normal 

 «*alts as to the constants of aberration, nutation, &c., ana me 



destination of parallax ; and from the terms in whiclr the Alas- 



tn^,~ . r . i -r *u~* ^f^uiiokmpnt sneaks ot its 



Performance, the views of M. Bessel 



eral adoption appear to be fully borne out. . .. A -.- n 



intent on fully providing the observatory under his direction 



witK a 3 i . . *„ ,„v,;„i, or* nan pTccute. rJessei 



i, Bessel 



-"v„ u , eu permission to oraer iui uw «™*« - — an im ~ 



Prcved meridian circle from the Brothers Repsold, of Hamburg, 



Sicosd Series, Vol. IV, No. 12.-Nov., 1847. 40 



