Propagation of the' Charleston Earthquake. 9 



From these we rnay form trie following equations. 



"Weight. Residuals. 



x + Oy = 2 — 1-6 



x _j_ 438y =144 1 - 9-8 



X + 488,y =155 1 — 5-3 



x + 490y =144 1 -f 6-3 



x -f- 545// =174 1 — 6 '6 



x + 604y = 174 2 -j~ir6 



x + 620// =174 \ +16-6 



a -j- 622y = 174 1 -\-\1-2 



x + 645y =204 1 - 5-6 



a: + 765y = 294 f -58'4 



a; + 770y =234 1 -f- 3-1 



The normal equations are : 



12 x + 5898-5 y = 1811. 

 5898-5^ + 3577366-5 y = 1100677. 



The solution gives x = — l-6s. =fc 7 "Ys. y = 0*31 ± 0-014s. 

 The resulting speed is, 3-22.6 d= 0-147 miles or 5192 ± 236 

 meters per second. 



Group III consists of reports which fail to give either the 

 means of judging of the comparative accuracy of clocks and 

 watches or of determining to what phase the observation re- 

 fers. Many and indeed the majority of them are defective in 

 both of these respects. Quite probably some of them are good 

 observations but fail to give the evidence of it. So far as 

 errors of clocks and watches are concerned the errors may be 

 considered as belonging to the accidental class. But all errors 

 as to the phase must be systematic. That some of them refer 

 to more or less advanced phases is certain, and it becomes 

 difficult to determine how many of them do so, and how 

 great is the average tardiness. It is obvious that the effect of 

 all such errors is to make the time too late and the resulting speed 

 too slow. The general indications are, however, that this system- 

 atic error is not a large one. By comparing miscellaneous 

 reports from those cities which have also given better verified 

 reports belonging to groups I and II there seems to be a ten- 

 dency of the average value of this error to fall between one- 

 tenth and one-twentieth of the mean value of the time-interval. 



In discussing this group it seems unnecessary to go to the 

 length of formulating a hundred equations of condition, and an 

 equally good result or even a better one may be obtained by the 

 following more summary process. We may take them in sets, 

 the first of which shall comprise all times within 200 miles of 

 the centrum, the second set all between 200 and 300 miles, the 

 third all between 300 and 400 miles, and so on until the last, 



