714 



SCIENCE 



[N. S. Vol. XLII. No. 1090 



act as accidental errors in a long line of levels. 

 The methods foUovced in the Coast and Geo- 

 detic Survey have this in view. One of the 

 most troublesome errors encountered in the 

 past was due to the changes in the relation 

 between the line of sight and the axis of the 

 bubble caused by rapid and unequal tempera- 

 ture changes in the different parts of the in- 

 strument. The older instruments were made 

 of metals having large coefficients of expan- 

 sion, and the bubble was at a considerable dis- 

 tance from the center of the telescope tube. 

 It was found that the error of a line was a 

 function of its direction or azimuth. This 

 error is probably eliminated in leveling run 

 with the Coast and Geodetic Survey level 

 which has been in use about fifteen years. It 

 is made of nickel-iron with a coefficient of ex- 

 pansion of only .000004 and its bubble is set 

 into the tube of the telescope near the line of 

 sight. 



We will not consider the sources of errors 

 which are well known and which are largely 

 eliminated by the methods employed, but wiU 

 confine ourselves to some interesting errors ap- 

 parently due to variations in the vertical at- 

 mospheric refraction on steep grades, and even 

 these can only be touched upon. They are 

 considered at some length in a recent publica- 

 tion of the Survey.^ 



All leveling by the Survey is run in both di- 

 rections, forward and backward, the line is 

 divided into sections approximately one kilom- 

 eter in length, and the two runnings of a sec- 



3 See Special Publication No. 22, of the 0. and 

 G. Survey. 



tion are made in different days in order to 

 vary the atmospheric conditions. Usually one 

 running is made in the morning and the other 

 in the afternoon. For a number of years the 

 observers have kept records of the time of day 

 of the runnings of the different sections and 

 the weather conditions which obtained. Five 

 lines of levels were selected for a study of the 

 possible relation between the errors of leveling 

 and the conditions of the weather, the time of 

 the observations and the steepness of the grade. 

 These lines are: 



Mean grade per section, steep slopes. 16.6 meters 

 Mean grade per section, low slopes. . . 3.4 meters 

 Mean grade per section, all sections. . . 6.4 meters 



The total length of these lines is 2,310 kilom- 

 eters. As it was impracticable to investigate 

 the relations between the size and sign of the 

 discrepancy between the results of the two 

 runnings of the sections and the many differ- 

 ent grades, the leveling was separated into 

 only two classes: First, those having grades 

 exceeding ten meters and, second, those with 

 smaller grades. As the average length of a 

 section is about one kilometer a ten-meter 

 grade corresponds to a grade of approximately 

 one per cent. The average grade for the first 

 class is 16.6 meters, for the second 3.4 meters, 

 and for all the sections 6.4 meters. 



We shall first see whether there is any dif- 

 ference in the elevation between the two ends 

 of a section by the two runnings where one 

 running is in the morning and the other in 

 the afternoon. The direction of the slope is 

 not considered. In the following table A 



