36 REPORT—1858. 
sions; we will restrict ourselves to the observation, that, in order to repre- 
sent the result of his work, he has employed a formula of interpolation of 
this kind :— 
“¢=M-+A sin (¢+a)+B sin (2+ 8)+C sin (3¢+y)+..-. in which M, 
A, B, C, &e. are always coefficients of the same nature as ¢; a, ps ¥> &e., 
are always angles, and ¢a variable angle dependent on the lunar motion, which 
_will be equal to 0 degree for the new moon, to 90 degrees for the first 
quarter, to 180 degrees for the full moon, &c. He then adapts this for- 
mula to the numerical tables deduced from observation, and determines the 
particular truths which it contains. By means of the formula thus ob- 
tained, the author was enabled to draw up numerical tables corresponding 
to those deduced from observation alone, and in which the law of the phe- 
nomena appears disconnected from the principal anomalies which tended to 
obscure it in the first tables.) The numbers contained in these new tables 
are carefully arranged, and form regular curved lines, in which the law is 
clearly manifest. These curves have a marked resemblance to each other, 
although they are not entirely alike—which could not be, for they are only 
approximative—and each bears the stamp of the group of figures which it 
represents. The resemblance of these curves is essentially increased by the 
fact that each presents two principal maxima corresponding to the Syzygies, 
and two principal minima corresponding to the Quadratures. We are thus 
brought back to the conclusion so evident by M. A. Perrey’s toil,—that, for 
half a century, earthquakes have been more frequent at the Syzygies than at 
the Quadratures. 
“The Academy fully conceives the importance of this conclusion, and 
appreciates the labour the author has taken to collect nearly 7000 observa- 
tions on the first half of this century. This number, however, is very small 
for the solution of a question of this nature ; and it is very desirable to have 
it increased, either by collecting all future observations from year to year, 
a by going back to past centuries, as the author has already commenced 
oing.” 
These views of Perrey have found support in the opinions enunciated 
by M. Zantedeschi as to the probable existence of a terrestrial as well as 
an oceanic tide, one in which the solid mass of the earth’s crust, and the 
liquid or semiliquid nucleus beneath (if indeed it exist in any such state) is 
supposed to be an ellipsoid, with a major axis perpetually following the move- 
ments of the moon and sun. To what extent such a change of form is possible 
in the solid material of our planet under the constraint of the same forces that 
produce the oceanic tides (and whose elevations must in so far act against 
such change of form), it is for physical astronomy to determine. But even 
if its existence be admitted, and the change of level of a given point on the 
earth’s surface were proved to amount to many feet—to far more, in fact, 
than the total elevation of the greatest ocean tide-wave, it is difficult to con- 
ceive how it even then could be a direct or immediate cause of earthquakes. 
Such change of form would be probably quite insignificant as compared 
with the earth’s total mass; so that the flexures or changes of form produced 
by it in the solid crust would probably be far within the elastic limits of its 
materials, and, hence, the occurrence of fractures or dislocations due to such 
a train of causes impossible. 
If it ultimately prove a fact that there is a real relation in epoch between 
earthquakes and the ocean tides, or the moon’s and sun’s position in respect 
- 
to the earth, the phenomena will probably be found in relation, only through | 
the intervention of changes in terrestrial temperature, or in the great circu 
