VOL. XC.] 



PHILOSOPHICAL TRANSACTIONS. 



797 



to be always cautious to adjust the level ; and also to insert the state of the air, as 

 to temperature and density, by noting the thermometer and barometer. 



The height of the transit telescope above the ground was always 5± feet ; there- 

 fore, an allowance must be made, at each station, for the angle which that space 

 subtends at its corresponding one ; this premised, the refraction will be found from 

 one of the two following rules, viz. if a be the contained arc, and d, d, the ob- 

 served depressions, the quantity answering to the refraction r, will be expressed by 



-D-d 



or, if one of the angles should be an elevation, e, then r = 



a + e — d 



these rules give the refractions in the following table. 



On examining the refractions obtained on the first arc, we perceive them to have 

 been tolerably regular from 3 o'clock till 8 ; the mean being -j-l T part of the con- 

 tained arc. The height of Whiteham Hill is 576 feet, and that of White Horse 

 Hill 893 feet, above the level of the sea : the ray passes therefore through a 

 tract of air considerably elevated, as the country between the stations is, for the 

 most part, flat and low. The air is not often clear enough, or sufficiently free 

 from tremulous motion, for these delicate observations. On the present occasion 

 however, the state of it was highly fit for the purpose ; and as care was taken, I 

 am of opinion an error of more than 3", taking that of the arch of altitude into the 

 account, cannot have obtained in any of the angles. The refractions at 9 and 10 

 o'clock are less than at the preceding hours ; but this does not appear to have been 

 owing to any change in the refractive power of the air throughout the whole ex- 

 tent of the ray, because the depression of Whiteham Hill, from the other station, 

 varied little at those hours. These changes in the observed angles of elevation at 

 Whiteham, 44" and 42" being the differences, without corresponding ones at 

 White Horse Hill, prove that some partial alteration, from floating strata, had 

 taken place in the refraction near the former station. It will be perceived that a 

 case may be constructed in which this will take place, causing a great variation in 

 one of the angles, while the other apparently remains the same : and this suggested 

 the idea, that to afford any accurate conclusions in this way, a long series of obser- 

 vations would be necessary. It further appears that dew could not have caused these 

 differences at Whiteham Hill, since the same cause would equally operate to vary 

 he observed angles at White Horse Hill ; but these remained nearly the same. 



