138 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
Similarly, if either Mocho or Mount Diablo had moved on April 18, 1906, in such a 
direction as to increase (or decrease) the distance between them, the effect upon the com- 
putations of apparent displacements would have been to produce a set of red arrows on 
maps 24 and 25, all pointing toward (or from) Mocho and Mount Diablo, the lengths of 
the arrows being proportional to their distances from Mocho and Mount Diablo. No 
such systematic relation appears among the arrows. 
Another item of evidence is still available which indicates that the absolute displace- 
ment of points far to the eastward of the fault was zero on April 18, 1906. From 1899 
to date a series of observations of latitude by observations upon the stars has been in 
progress continuously for the International Geodetic Association at Ukiah, California. 
The purpose of these observations is to detect variations in latitude due to any cause. 
The observations are of an extremely high grade of accuracy and they are made on every 
clear night. Dr.S. D. Townley, in charge of these observations, made a special study of 
the 233 observations made during the interval April 4—May 4 inclusive, 1906, to deter- 
mine whether any sudden change of latitude took place on April 18.'. He found no such 
change. The observations are competent to determine with reasonable certainty any 
change as great as 0.03”, corresponding to 1 meter (3 feet). It is therefore reasonably 
certain that the southward component of the motion, if any, of the pier on which Dr. 
Townley’s latitude instrument was mounted at Ukiah, was less than one meter on April 18, 
1906. Ukiah is about 42 kilometers (26 miles) from the fault and to the eastward of it. 
Mocho and Mount Diablo are much farther from the fault (53 kilometers). It is important 
to note that latitude observations determined the absolute displacement rather than the 
relative displacement and that they are independent of observations at any other station. 
For the reasons set forth above, it is believed to be certain that the permanent dis- 
placement, if any, of either Mocho or Mount Diablo on April 18, 1906, must have been 
extremely small. 
During verbal discussions of the earthquake of April 18, 1906, it has been suggested 
more than once that one of its possible effects may have been to change the position of the 
earth with relation to its axis of rotation and so produce a change of latitudes. If an 
appreciable effect of this kind were possible, the validity of the above reasoning in regard 
to the latitude observations at Ukiah would be questionable. Accordingly, a computa- 
tion of this possible effect has been made.” It was found that if it be assumed that the 
mass displaced in a northerly direction to the westward of the fault comprized 40,000 
square kilometers (15,600 square miles) of the earth’s crust, having a mean latitude of 38° 
and thickness or depth of 110 kilometers (68 miles), that this material had an average 
density of 4.0 and that the northerly component of the displacement was 3 meters (10 
feet), the position of the pole of maximum moment of inertia would be displaced by 
0.0007”, corresponding to 0.002 meter (0.006 foot). This is a limiting value certainly 
much larger than the actual value, for all assumptions entering the computation as to 
the area, depth, density, amount of displacement, and mean latitude have been made 
such as to make the computed value certainly too great. Moreover, the similar dis- 
placements of contrary direction to the eastward of the fault would partially cancel those 
on the westward side which have been considered. When the pole of maximum moment 
of inertia is displaced, the pole of rotation is not immediately changed with reference to 
the earth. The pole of rotation tends always to seek the pole of maximum moment of 
inertia and travels around it in an irregular path. It is the instantaneous position of the 
pole of rotation with reference to the earth which fixes the latitude at any instant. Hence 

_ + This investigation is published in the Publications of the Astronomie Society of the Pacific, Vol. 
ans yeas Aug. 10, 1906, under the title The Latitude of the Ukiah Observatory before and after 
pri , 1906. 
* The formula and method of computation is shown in Traité de Mécanique Céleste, par F. Tisserand, 
Paris, 1891, Gauthier-Villars, Tome II, pp. 485-487. 
