RECENT ADVANCES IN SCIENCE 199 



and that, if a telescope is used (one is not really necessary), 

 it should have a low power and a large field of view. The 

 graduations should be very clear, so .as to be easily read, and 

 a vernier can be dispensed with. When above flat land or 

 in sight of sea, observations on the natural horizon can be 

 made as easily as at sea, and almost with the same accuracy, 

 the best and most distinct horizon being provided by level 

 land. The value of the dip, of course, reaches remarkably 

 high values, but even up to an altitude of 10,000 feet it is 

 found that the relation holds that the dip in minutes is equal 

 to the square root of the height in feet. With a good horizon 

 the average error of one observation is only about two to 

 three minutes of arc, which fixes the Sumner line with sufficient 

 accuracy. 



Under average conditions, there is too much haze for 

 observations to be made on a land or sea horizon at a height 

 exceeding one or two thousand feet. Frequently the haze 

 has a sharp upper boundary at a definite level presenting a 

 definite " false horizon," which is usually sharp in a direction 

 opposite to the sun. Provided that the height above sea-level 

 of the top of the haze is known, which can be determined with 

 the aneroid during ascent or descent, observations upon such 

 false horizons may in general be used, and accurate results 

 obtained. Occasionally, however, very large errors were 

 obtained, the causes of which were investigated. It was found 

 that at times the surface of the haze was irregular, so that 

 instead of a true horizon being observed, the apparent boun- 

 dary was the top of a ridge of haze, rising above the general 

 level : thus, in one instance, the observations were in perfect 

 accordance with the existence of a ridge at a distance of 100 

 statute miles and at a height of 14,800 feet above the sea-level. 

 Since the earth's surface curves away from the tangent by 

 6,600 feet in 100 miles, the ridge was on the theoretical horizon 

 of the observer at a height of 8,200 feet, and at lesser heights a 

 negative dip was obtained. It is therefore of extreme impor- 

 tance to make certain that the haze is uniform : this can be 

 tested with a dip-measuring instrument, which permits a direct 

 determination of the amount by which the angular distance of 

 two opposite parts of the horizon differs by 1 8o°. 



Frequently, however, weather conditions are such that 

 observations, even on a haze horizon, are not possible. The 



