them, as well as ambiguous or doubtful statements; so that out of a considerable number of such time-facts, obtained in a seismic-shaken country, probably not above two or three can be really relied upon. Were we in possession of a large number of time records of considerable accuracy, such even as rated chronometers at the distant stations but still more, self-registering instruments, would afford, it would then be important to apply the method of least squares to their discussion, in the way that has been done by Dr. Julins Schmidt, astronomer at Bonn, to the Rhenish earthquake of 1846 ('Das Erdbeben vom 29 July 1846, im Reingebiet,' &c., von Dr. Jacob Nöggerath. Bonn, 1847. Pamphlet, 4to).

If we denote by ${\displaystyle \alpha \beta \gamma .....\nu }$ the surface distances in geographical miles from the seismic vertical = ${\displaystyle \mathrm {Z} }$,

${\displaystyle \mu \mu '\mu ''.....\mu ^{n}}$ their respective differences of longitude in time from ${\displaystyle \mathrm {Z} }$,

${\displaystyle tt't''.....t^{n}}$ the observed times at ${\displaystyle \mathrm {A} \mathrm {B} \mathrm {C} ....\mathrm {N} \mathrm {T} }$, the moment that the wave reaches the surface at the seismic vertical ${\displaystyle \mathrm {Z} }$,

${\displaystyle \tau \tau '\tau ''.....\tau ^{n}}$ the transit periods or times of running over the distances ${\displaystyle \alpha \beta \gamma .....\nu }$, it is obvious that

${\displaystyle \tau =t\pm \mu -\mathrm {T} }$

and ${\displaystyle \tau ^{\prime }=t^{\prime }\pm \mu ^{\prime }-\mathrm {T} }$

and

${\displaystyle \tau ^{n}=t^{n}\pm \mu ^{n}-\mathrm {T} }$

(I.)

and that

For places situated to the west of the seismic vertical . . . . . ${\displaystyle \tau =t+\mu -\mathrm {T} }$

(II.)