THE EARTH MOVEMENT ON THE FAULT OF APRIL 18, 1906. 123 
actual case, neither of these ideal conditions is found. Each triangle has a closing error, 
and the lengths computed along different paths thru the triangulation show discrepancies. 
These closing errors and discrepancies are a measure of the accuracy of the triangulation. 
The triangulation, both old and new, was adjusted by the method of least squares. 
This method of computation, as applied to triangulation, takes into account simul- 
taneously all the observed facts in connection with a group of triangulation stations and 
also all the known theoretical conditions connecting the observed facts; such, for example, 
as those mentioned in the preceding paragraph, in regard to closures of triangles and dis- 
crepancies in length. It is the most perfect method of computation known. The results 
of the computation are a set of lengths and azimuths (true directions) of lines joining the 
triangulation stations and of latitudes and longitudes defining the relative positions of 
the stations which are perfectly consistent; that is, contain no contradictions one with 
another and are the most probable values which can be derived from the observations. 
In such a computation, the measures of the accuracy of the computed results appear in 
the form of corrections to observed directions from station to station, which it is necessary 
to apply in order to obtain the most probable results given by the computation. The 
greater the accuracy of the observations the smaller are the corrections to directions. 
In the problem in hand, in which, at least for some points, the observed apparent dis- 
placement is of about the same magnitude as the possible error in the apparent displace- 
ment due to accumulated errors of observation, it is necessary to make a careful estimate 
of the errors of observation and of the uncertainties of the computed displacements. 
This has been done and the estimates are given in general terms in the following text and 
are indicated in the last column of the tables. These estimates will help the reader to 
avoid drawing conclusions in detail not warranted by the facts. 
Group 1. Northern part of primary triangulation. — In this group, as shown by tables 1-3 
(see also map 24), there are 11 points of which the positions were redetermined after the 
earthquake of April 18, 1906. Of these, 9 had been determined before 1868 and 7 
between 1868 and 1906. 
There is about 1 chance in 3 that each of the two apparent displacements of Rocky 
Mound, 0.50 meter (1.6 feet), in 1868 (table 2), and 0.34 meter (1.1 feet), in 1906 (table 1), 
is simply the result of errors of observation. Similarly there is about 1 chance in 3 that 
the apparent displacement of Red Hill in 1868, 0.65 meter (2.1 feet), is the result of 
errors of observation. The chances are about even for and against the apparent dis- 
placement of Red Hill in 1906, 0.30 meter (1.0 foot), being simply the result of errors of 
observation. The effect of errors of observation upon the apparent displacements are 
larger at these two points than they otherwise would be on account of the difficulty in 
this vicinity of separating the triangulation into two complete schemes, one before 1868 
and one after that date, each strong and complete. 
According to the evidence furnished by the triangulation, the apparent displacement 
of Ross Mountain in 1906, 0.53 meter (1.8 feet) in azimuth 309° (51° E. of S.), is prob- 
ably the result of errors of observation. This apparent displacement as computed depends 
on the accumulated errors of the two triangulations from Mount Diablo to Ross Mountain, 
a distance of 130 kilometers (81 miles). The apparent displacement of 0.53 meter almost 
directly toward Mount Diablo corresponds to a shortening on the line Ross Mountain- 
Mount Diablo by 1 part in 250,000, too small a change to be detected with certainty 
by the triangulation. 
On the other hand, there is about 1 chance in 15 that the apparent displacement of 
Ross Mountain in 1868, 1.70 meters (5.6 feet), is due to errors of observation. It is 
reasonably certain that this is a real displacement. 
The chances are about even for and against the apparent displacement of Point Reyes 
Light-house in 1906, 1.09 meters (3.6 feet), being due simply to errors of observation. 
