352 Mr. Ivory on the Thcori/ of the Ast ronojnical Ilefiactio7is. 



Having said so much on the theory of the French table, it 

 may be proper to add a word on its accmacy. If it be com- 

 pared from 80° to 88° of zenith distance with BesseVs ob- 

 served refractions, there will be foimd a small error in excess, 

 continually increasing, and amounting at last to 4". This 

 shows that, in combining the two atmospheres, too mnch 

 weight has been given to that with a density varying in geo- 

 metrical progression, in consequence of which the air is not 

 rarefied enough in the interpolated atmosphere. With re- 

 spect to the two degrees of altitude next the horizon, no ac- 

 curate judgement can be formed, for want of observed refrac- 

 tions that can be depended on. 



The astronomical refractions have also occupied the atten- 

 tion of the astronomer of Kcenigsberg, who has contributed 

 so laro-ely to the improvement of every part of astronomical 

 science. For the purpose of representing the observations 

 of Bradley with all the accuracy possible, Bessel investigated 

 a table of refractions which appeared in the Fundamenta 

 Astro7iom uv lu ISIS. He assumes a theoretical formula; but 

 as every arbitrary quantity is determined by a careful com- 

 parison with real observations, what is supposititious may be 

 considered merely as an instrument of investigation, which is 

 finally laid aside, leaving the result to rest on the foundation 

 of fact. He returned to the subject in his Tahidce Regiomon- 

 taiia, published in 1830. In this last work he retains only 

 that part of the table of 1818 which extends to 85° from the 

 zenith, many corrections being applied irom recent observa- 

 tions made with improved instruments. In order to supply 

 what is wanting in the new table, Bessel has added a sup- 

 plemental one containing the refractions at every half degree 

 for altitudes less than 15" : which supplemental table is inde- 

 pendent of theory, being deduced from observations alone. 

 These two tables form together a real table of mean refrac- 

 tions, independent of all suppositions respecting the constitu- 

 tion of the atmosphere; and no other similar table of nearly 

 equal authority is to be found in the astronomy of the present 

 day. What Bessel has accomplished on the subject of the 

 refractions is not the least important part of his labours for 

 the advancement of astronomical science : it is precious to 

 the practical astronomer ; and it is necessary to the theore- 

 tical inquirer, for enabling him to confront his speculations 

 with the phaenomena to be accounted for. 



[To be continued ] 



