Astronomical and Nautical Collections. 321 



the sun and moon inclined to the horizon, occasioned by refraction. 

 An easy and simple method of estimating the correction proceeding 

 from this cause was given in the second number of the Astronomi- 

 cal and Nautical Collections, Journal, No. XVII. The two examples 

 computed above, being further corrected in this manner, are reduced 

 to 41° 18' 18% and 30° 2' 28". If neither of the several correc- 

 tions had been attended to, these distances would have been found 

 to be 41° 18' 54", and 30° 1' 34". 



iv. Correct Formula for the Nutation. By Professor Bessel. 



Astr. Nachr. 83. 

 AL={- 18",0377 sin. & + 0",21720 sin. 2& - 0",21633 



sin. 2 D } (1 + i) - (1",1 3640 — 2",86868 i) sin. 20 ; 

 A u a= {+ 9",6480 cos. ftj- 0",09428 cos. 2& + 0",09391 cos. 



2 D } (1 + + (0",49330 — 1",24527 i) cos. 20 : 

 Or, iff 2= -0,069541; 

 AL=- 16",78332 sin. & + 0",20209 sin. 2fc - 1",33589 



sin. 20 - 0",20128 sin. 2 J, 

 A u = + 8",97707 cos. & - 0",08773 cos. 2 Q + 0",57990 cos. 



20 + 07)8738 cos. 2 $ . 



v. Remarks on the Principles of Algebraical and Fluxional 

 Notation. By the Editor. 



It is extremely desirable that the mathematicians of Europe, 

 who may have to make public any new investigations, or to reprint 

 any of their former labours, should adopt, as much as possible, a 

 uniform symbolical language ; and in order that the language may 

 be uniform, it is required that it should be deduced from some fixed 

 principles, or should have at least a certain regularity of plan 

 which would ensure its elegance and symmetry, as well as its pre- 

 cision and distinctness. In the Article Fluents, of the Supple- 

 ment of the Encyclopoedia, and in several parts of the Illustrations 

 of the Celestial Mechanics, an attempt has been made to intro- 

 duce some improvements, which will here be repeated, with a few 

 further elucidations. 



1. " The earlier letters of the alphabet, as far as q, and some- 

 times r, are commonly employed to denote constant quantities ; 





