NOVEMBEE 19, 1915] 



SCIENCE 



715 



stands for tlie morning and P for the after- 

 noon running. The discrepancies are given in 

 millimeters. 



MORNING AND AFTERNOON RUNNINGS COMPARED, 

 "WEATHER CONDITIONS IGNORED 



Steep Grade Low Grade 



Number of sections 188 761 



P-A, total, positive + 496.4 + 1,645.1 



Mean discrepancy + 2.64 + 2.16 



Number of sections 144 629 



P-A, total, negative — 340.4 — 1,277.8 



Mean discrepancy — ■ 2.36 — 2.03 



Number of sections 332 1,390 



Mean discrepancy 2.52 2.10 



Accumulated discrepancy . . + 156.0 + 367.3 

 Mean accumulation per sec- 

 tion + 0.47 + 0.26 



For both classes the sections with positive 

 values of P-A predominate while the mean 

 accumulated discrepancy per section for the 

 low grades is only 0.55 of that for the steep 

 grades. 



The next table includes the morning and 

 afternoon runnings, which were made in sun- 

 shine. 



MORNING AND AFTERNOON RUNNINGS, ALL IN SUN- 

 SHINE 



Steep Grade Low Grade 



Number of sections 131 529 



P-A, total, positive -|- 358.6 + 1,140.8 



Mean discrepancy + 2.74 -f- 2.15 



Number of sections 87 456 



P-A, total, negative — 203.0 — 935.5 



Mean discrepancy — 2.33 — 2.05 



Number of sections 218 985 



Mean discrepancy 2.58 2.11 



Accumulated discrepancy . . -f 155.6 + 205.3 

 Mean discrepancy per sec- 

 tion -I- 0.71 + 0.21 



The evidence here is similar to that of the 

 preceding table but the accumulated discrep- 

 ancy for the steep grades is three and one half 

 times as great as that for the lower grades. 



The investigation does not indicate whether 

 the morning or the afternoon running gives a 

 value nearer the truth, but it is the speaker's 

 opinion that the afternoon is freer from error 

 than the morning running. 



It is the speaker's opinion that the after- 

 noon running gives on an average a difference 

 which is closer to the truth than the morning 

 running. In the afternoon the temperatures 

 of the ground and of the air are more nearly 

 the same and a layer of air of uniform density 

 should be concentric or nearly so with the sea- 

 level surface. If this is true the refraction on 

 the front and back sights should be about the 

 same. The leveling of the U. S. Coast and 

 Geodetic Survey is seldom done after 5 o'clock 

 in the afternoon. So the afternoon running 

 is not materially affected by the abnormal re- 

 fraction of the late afternoon when a line of 

 sight on a grade would pass through layers of 

 colder and denser air which would tend to be 

 concentric with the surface of the ground. In 

 the late afternoon the earth cools more rapidly 

 than the air and the air near the earth's sur- 

 face becomes colder than the air above and 

 consequently denser than normal. 



In the morning on a clear day the air is re- 

 ceiving radiated heat from the earth's surface. 

 This decreases the density of the air close to 

 the ground, and forms layers which tend to 

 be concentric with the surface of the ground 

 rather than with the sea level surface. (The 

 air near the earth is of course not at rest but 

 tends to rise, owing to the decreased density.) 

 It may be assumed that the line of sight to 

 the observer from the rod held down the grade 

 is not affected abnormally while the sight to 

 the rod held up the grade is usually close to 

 the ground and must pass through the layers 

 of lower density near the earth's surface. This 

 sight would be less refracted than the one 

 down the grade and may even be negatively 

 refracted, therefore the morning running 

 would give too small a difference between the 

 zeroes of the rods sighted on from one station. 

 It is the speaker's belief that, other things be- 

 ing equal, a line of levels run over steep grades 

 in two directions in the afternoon, from noon 

 to about one hour before sundown, will give 

 results closer to the truth than levels with both 

 runnings in the forenoon or with one leveling 

 in the forenoon and the other in the afternoon. 

 It is believed that this also applies to leveling 

 over slopes of moderate grade. 



