498 Mr. Ivory on the Theory of the Astronomical Refractions. 

 y 1 _ L(1 + /3t') _ 



8 ' p' 



^ 8 v' } 



f. ± <P' \ 



aj/) _ _«__ "^i 8 '7[ _ 



''' p' ~ i " L(l+ ^t') ~ ^' 



and further, it will appear that the same relation subsists be- 

 tween X and u in the atmosphere of moist air as between the 

 quantities represented by the same letters in the atmosphere 

 of dry air. The same procedure will therefore lead, in both 

 cases, to the same integrals extending between the same li- 

 mits. The only difference lies in the values of X and i, which 

 in the case of moist air acquire, as a multiplier or divisor, 



the small factor ( 1 — — . — j-] depending on the tension of 



the vapour at the earth's surface. If the hygrometer afforded 

 an easy practical method of ascertaining the tension of the 

 vapour, the minute variations of the refractions, arising from 

 moisture in the atmosphere, might be corrected by the me- 

 thod usually employed for compensating the small changes 

 which a difference of temperature causes in the mean con- 

 stants. 



Experience confirms what has been said; for all the astro- 

 nomers who have attended to aqueous vapour in the atmo- 

 sphere, agree in admitting that it either has no influence, or 

 but a very small and imperceptible effect, to alter the refrac- 

 tions. On this head it will be sufficient to cite the authority 

 of M. Biot*, who seems carefully to have studied this point, 

 on which he expresses himself very strongly. The very exact 

 coincidence of the theoretical with the observed refractions as 

 far as 88° or 88^° from the zenith, concurs to prove that the 

 variable quantity of vapour in the air has little influence so 

 long as it retains the gaseous form ; but at lower altitudes, 

 when the rays of light become almost parallel to the horizon, 

 it is very probable that particular and local causes may come 

 into play. 



11. Nothing is now wanted for completing the solution of 

 the problem, except the reducing of the expression (C.) to a 

 form fit for numerical calculation. 



• Precis Elem. de Phj/siquCf p. 229, torn. ii. edit. 2nd. Addit, a la Conr* 

 des Temps. 1839, p.. 36. 



