November 19, 1915] 



SCIENCE 



717 



SECTIONS WITH BOTH RUNNINGS IN THE MORNING OR 

 BOTH IN THE ATTEENOON 



Number of sections 85 



C-W, total, positive + 177.2 



Mean discrepancy + 2.08 



Number of sections 90 



C-W, total, negative — 222.3 



Mean discrepancy — 2.47 



Number of sections 175 



Accumulated discrepancy — 45.1 



Mean accumulation per section — ■ 0.26 



The effect of morning and afternoon condi- 

 tions being eliminated (but not the cloudy or 

 clear sky) we have a result which shows a 

 larger value on an average for the running in 

 wind than the one in calm. 



There are 495 sections, each of which had 

 one running in the morning and one running 

 in the afternoon with both runnings made 

 during calm. These sections should have 

 values for P-A which are free from the effect 

 of calm and wind. The data for these sections 

 are shown below. The grade is not considered. 



SECTIONS RUN IN BOTH DIRECTIONS DURING CALM 



Number of sections 259 



P-A, total, positive + 603.5 



Mean discrepancy + 2.33 



Number of sections 236 



F—A, total, negative — 497.5 



Mean discrepancy — 2.11 



Number of sections 495 



Accumulated discrepancy + 106.0 



Mean accumulation per section + 0.21 



The results in the above table are free from 

 the eifects of wind and calm, but may be and 

 probably are somewhat affected by cloudy or 

 clear sky. But the indication is that the after- 

 noon running is greater than the forenoon, on 

 an average. 



If it is assumed that the running in wind is 

 free from error, then the data for the sections 

 shown below should give an indication as to 

 whether an afternoon or forenoon running of 

 a section will give the greater difference in 

 elevation. The amount of grade is not con- 

 sidered. 



The term (O-W^A represents calm minus 



wind, with the calm running in the forenoon, 

 while (C-W)P is the same, except that the 

 calm running is in the afternoon. 



Mm. 

 Number of sections 256, total 



positive value (.C-W) A + 499.2 



Number of sections 330, total 



negative value (C-W) A — 759.0 



Number of sections 94, total 



positive value (C-W) P + 221.7 



Number of sections 87, total 



negative value (C-W) P — 182.3 



Mean accumulated discrepancy 



per section for (C-W) A — 0.44 



(C-W)P+ 0.22 



The indications from these data are that the 

 difference from the calm running in the fore- 

 noon is too small and from the calm running 

 in the afternoon too great, upon the assump- 

 tion that the running in wind is without error. 

 This bears out the conclusion stated earlier 

 in this paper that the afternoon running gives 

 a greater difference in elevation than the 

 morning running. 



CONCLUSIONS 



While the data used in the investigation 

 into the sources of error in precise leveling 

 are not sufficient to warrant any definite state- 

 ments, yet they seem to justify the following 

 conclusions as probable. 



1. The average size of the discrepancy be- 

 tween the values of the difference in elevation 

 determined twice under different conditions 

 does not give a clear idea of the magnitude of 

 the accidental errors which may be produced 

 by certain conditions, as the custom is to make 

 the length of sight as great as the conditions 

 will permit. Therefore, the extra length of 

 sight may offset otherwise favorable condi- 

 tions and give a large difference between two 

 runnings of a section. 



2. For sections run twice under different 

 conditions the average accumulated value of 

 the discrepancy is greater for the sections 

 with steep grades than with low grades; the 

 direction of the running being ignored and 

 only the actual difference in elevation be- 

 tween the ends of a section being considered. 



3. On all grades, but more especially the 



