558 



SCIENCE 



[Vol. LVI, No. 1455 



The differential results of the triangulation of 

 the U. S. Coast and Geodetic Survey, covering 

 many points in the neighborhood of tiie 19'06 

 fault, appear to furnish a more precise cri- 

 terion. The closing error of each triangle 

 represents the errors of observation. No one 

 questions the usefulness of this device, nor its 

 validity, for the purpose of deriving the best 

 individual results available. We commonly 

 follow the same process in fundamental as- 

 tronomical work, when we derive systematic 

 eorreotions to right ascensions, by closing a 

 cycle of a year of continuous differential re- 

 sults. An apt illustration, also, is the measure 

 of graduation errors. The sum of the errors 

 of the divisions of one circle must be exactly 

 zero, when we arrive at the starting point of 

 the measures, having gone round the circle. 

 The average closing error for primary triangu- 

 lation work appears to be about two seconds. 

 Its proportional part must be assigned, as ac- 

 cidental error, to any absolute determination 

 of a point, by the triangulation. 



The probable error of an observed direction, 

 for primary work, appears to be less than one 

 second of arc. For secondary triangulation it 

 is between one and two seconds, and for terti- 

 ary work it may be as much as five seconds. 



One should guard against the assumption 

 that the probable errors are small for any 

 special triangle, when its closing error is small. 

 This error is made up of several constituent 

 parts, and they may balance in the sum of 

 their effects; just as we have zeros in any list 

 of residual eri'ors and also have some residuals 

 as large as three or four times the probable 

 error of the individual results. 



The following data have been taken from 

 the reports for 1907 and 1910. 



The test of changes in position at several 

 miles from the fault line may be assumed to 

 rest on the triangulation net from the base 

 line bet?ween Mocho and Mt. Diablo. This is 

 not a measured base, but has been connected 

 up with the Pulgas base, soilth of San Fran- 

 cisco. The base line is about 36 miles long, 

 and it lies 33 miles east of the fault, with which 

 it is approximately parallel. 



The changes of the tabulated latitudes of 

 41 stations, between wieasiires before and after 



1906, have been summarized below. Each 

 group includes points on both sides of the 

 fault at nearly the same distances. On the 

 east side the average change is 0.02" south, and 

 on the west the average is 0.05" north. The 

 average of all changes is 0.04", and all groups 

 show a plus relative displacement for west 

 minus east. The latitude of the center of the 

 base line is 37.7°. 



No. cp 



7 37.8° 



81 37.7° 



12 38.5° 



10 38.9° 



4 37.0° 



Prom Fault Eel. Dis. 



11 miles +0.03" 



3 miles -i-0.07" 



1 mile -i-0-09" 



3 miles -j-O-H" 



14 miles +0.03" 



The Mooho-Diablo base line, being 33 miles 

 from the fault, one second of arc in the ob- 

 served direction is represented by nearly a 

 foot lineal measure, (0.01"), at the fault line. 

 At 80 miles, a second of arc is represented by 

 two feet. The average displacements of the 

 groups are from two to eight times the lineal 

 measure of a second of arc, at the respective 

 distances. Farallon is the only station west 

 of the fault showing a sensible change 

 (0.027") at a relatively great distance, 22 

 miles. The change of 2.7 feet is quite precise- 

 ly twice the lineal measure of a second of are, 

 at its distance from the base line. 



No change of latitude was found for the 

 station, Mount Hamilton. This point is 12 

 miles southwest of Mocho, and at this distance 

 one foot on the surface is represented by over 

 three seconds of are, in the observed direction. 

 This result would indicate also that there was 

 no sensible change at the date of the 1903 

 earthquake, unless the station returned to its 

 original position by an almost equally precipi- 

 tate movement. 



These lineal equivalents are of course only 

 true for arcs measured at right angles to the 

 respective lines of sight. But the relative posi- 

 tions of the base line and points along the 

 fault are in general favorable for the measure- 

 ment of displacements in latitude, especially 

 for the stations between 37° and 38°. Farallon 

 lies almost due west from the center of the line, 

 but was not observed from either end, its posi- 

 tion being fixed by directions from stations 



1 One omitted, residual ten times the average. 



