Observed Variations in the Dip of the Horizon. 181 



feet as against 1016 feet as determined by spirit levelling. These 

 altitudes are computed with co-efficient of refraction = 0"083. 

 Using the lower values quoted by American writers tliese 

 altitudes would be increased by two feet. Reference may be 

 made to Appendix XVI. " U.S. Coast and Geodetic Sui'vey 

 Report for 1876" for interesting information about somewhat 

 similar observations. The American observations, as well as 

 the writer's, give for observations taken from the lower station a 

 difference of elevation greater than the true one. This can be 

 explained on the assumption that the path of the ray between the 

 stations is not a circular curve but one whose radius of curvature 

 is greater at the higher station than at the low^er one. As the 

 air is denser at the lower station this is to be expected. 



Attention may be directed to the remarkably small variations 

 in the observed angles of elevation to Arthur's Seat compared 

 with the large variations in the dip of the horizon. 



The observations support the following deductions, which are 

 not however advanced as new : — That under abnormal conditions 

 the dip may differ greatly from the ordinary tabular value, that 

 it may be unequal in different parts of the horizon, and that it 

 may vary very rapidly especially in the afternoon. That at 

 comparatively moderate angles of elevation the abnormal refrac- 

 tion is greatly diminished and that under unfavourable conditions 

 of the atmosphere, altitudes determined by angles of elevation of 

 about one degree observed front moderate distances are quite as 

 reliable as elevations determined from a few barometric observa- 

 tions. 



