Page:Great Neapolitan Earthquake of 1857.djvu/171

And for those to the east of the same $\tau =t-\mu -\mathrm {T}$

(III.)

While for those to the north or south of the seismic vertical or in the same meridian with it… $\tau =t-\mathrm {T}$

(IV.)

Add the respective velocities therefore

${\frac {\alpha }{\tau }};{\frac {\beta }{\tau ^{\prime }}};{\frac {\gamma }{\tau ^{\prime \prime }}}$ . . . . . . . . . . ${\frac {\nu }{\tau ^{n}}}$

(V.)

Obtaining an average transit time per second for three adjacent places, situated in one radius of surface, from the seismic vertical, Dr. Schmidt then applies the method of least squares to the discussion of all the remainder, and with a result undoubtedly important, where, as in his example, he has had thirty distinct observations of time, at as many different stations; but which, when the number of stations is very limited in which any real confidence can be reposed, possesses no advantage over a simple choice from the whole of the most trustworthy, and the reduction from these of the mean.^[1]

The question of transit velocity, however, although of great physical interest, and destined, no doubt, ultimately to connect itself in an important way with that of the velocity of the wave particle (or wave itself), is, as respects seismometry viewed as a branch of physical geology, of subordinate importance at present.

1. Or, as suggested to me by Dr. Robinson, giving each observation weight proportional to the length of its own wave-path, which gives the formula—

   $\mathrm {V} ={\frac {\alpha ^{2}+\beta ^{2}+\gamma ^{2}\mathrm {\&c.} }{\alpha \tau +\beta \tau '+\gamma \tau ''\mathrm {\&c.} }}$

   or, what is the same in result, though perhaps more convenient—

   $\mathrm {V} ={\frac {\alpha \tau +\beta \tau ^{\prime }+\mathrm {\&c.} }{\tau +\tau ^{\prime }+\mathrm {\&c.} }}$