354 



SCIENCE 



[N. S. Vol. XXXIII. No. 844 



series when arranged in correct order. This vir- 

 tually amounts to distributing the objects prop- 

 erly along some numerical scale taken as a scale 

 of excellence. Each student's arrangement of the 

 objects is then penalized in proportion to the dif- 

 ference in excellence of the objects exchanged and 

 to the number of exchanges necessary to bring 

 about the correct arrangement. The penalty can 

 be placed upon a percentage basis, if desired, by 

 determining the ratio of any observed errors to 

 that represented by completely inverting the 

 series. The system can be applied to any series 

 either with uniform or nou- uniform intervals; it 

 requires no tables, and it can be used with any 

 number of objects. 



The Measurement of Two Primary Base Lines 



with Invar Tapes: Mr. William Bowie, of the 



Coast and Geodetic Survey. 



There are several types of base apparatus which 

 have been used successfully in recent years by the 

 Coast and Geodetic Survey. They are: (1) the 

 secondary apparatus, a monometallic multiple bar 

 system; (2) the duplex apparatus, a bimetallic 

 multiple bar system; (3) steel tapes of 50 and 

 100 meters in length, and (4) nickel-steel or invar 

 tapes of 50-meter lengths. 



The secondary bars and the duplex bars gave 

 very accurate results, yet their operation was 

 more expensive than tapes. Tests made at the 

 Holton base in 1891, by Professor R. S. Wood- 

 ward, indicated that primary base lines could be 

 successfully measured with steel tapes, and they 

 were used in connection with the duplex bars in 

 1900 in the measurement of nine bases along the 

 98th meridian. In 1906 six primary bases were 

 measured with both steel and invar tapes. It was 

 found that the measurement of a base with tapes 

 occupied about twenty days, while the measure- 

 ment of a base with the bars had usually taken 

 several months. 



As the nickel-steel or invar base tapes were 

 satisfactory in the measurement of bases in 1906 

 it was decided to use them in measuring two 

 primary bases, one at Stanton, Tex., and the other 

 at Deming, N. M., on the Texas-California arc of 

 primary triangulation in 1909-10. These bases 

 were measured by the triangulation party working 

 in the vicinity. Owing to the small coefficient of 

 expansion of the invar metal, it is possible to do 

 the measuring in the hours of daylight. The 

 coefficient of expansion of the tapes used on the 

 primary bases by the Coast and Geodetic Survey 

 is only about one twenty-fifth that of steel. 



Four invar tapes, each 50 meters in length, were 



carried to the field and three of them were used 

 in the measurement. One was held in reserve for 

 use in case of accident to one of the other three. 

 The tapes were standardized at the Bureau of 

 Standards before and after the measurement of 

 each base. The Stanton base has a length of 

 13,193 meters. The size of the party on this base 

 was two observers and seven other men. One of 

 the observers was Mr. J. S. Hill, the chief of 

 party. During the actual measurements only six 

 persons were engaged. 



A very simple tape stretcher was used on the 

 measurements of the Stanton and Deming bases, 

 its weight being only eighteen pounds. The adop- 

 tion of this simple and light stretener is a step 

 in the right direction, for the amount of meas- 

 uring accomplished by a party in any one day 

 depends largely upon the endurance of the man 

 carrying the forward stretcher. 



A base 15,554 meters in length was measured 

 in the vicinity of Deming, N. M., in 1910, by tne 

 same party that measured the Stanton base in 

 the previous year. The measurement of the Stan- 

 ton base occupied the party seventeen days, while 

 thirteen days were required for the measurement 

 of the Deming base. The probable error of the 

 measurement of the Stanton base was one part in 

 ii,560,000, and the probable error for the Deming 

 base was one part in 1,960,000. 



Some of the conclusions which were drawn from 

 the measurement of these two bases are : ( 1 ) the 

 50-meter tape was found to be both convenient 

 and satisfactory, confirming the conclusions based 

 upon previous tape work by the Coast and Geo- 

 detic Survey; (2) invar tapes with measurements 

 made in daylight or at night give results which 

 are as accurate as those obtained by the duplex 

 base bars; (3) it is not necessary to standardize 

 the invar tapes in the field; (4) owing to their 

 small coefficients of expansion invar tapes give 

 more accurate results than steel tapes; (5) with 

 proper care during measurements in the field, the 

 invar tape does not change appreciably in length. 

 While not so elastic as steel, yet it is sufficiently 

 strong to withstand the ordinary shocks due to 

 excessive tension. 



It is possible that the invar tape will not find 

 favor with the surveyor and engineer, for general 

 use, on account of its low elasticity, but it has 

 proved to be a most satisfactory apparatus for the 

 measurement of primary base lines by the Coast 

 and Geodetic Survey. 



E,. L. Fabis, 

 Secretary 



