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Proceedings of the Royal Society 
temperature, is undoubtedly much larger in all, or nearly all, places 
than the semidiurnal. It is then very remarkable that the semi- 
diurnal term of the barometric effect of the variation of temperature 
should be less, and so much less as it is, than the diurnal. The 
explanation probably is to be found by considering the oscillations 
of the atmosphere, as a whole, in the light of the very formulas 
which Laplace gave in his Mecanique Celeste for the ocean, and 
which he showed to be also applicable to the atmosphere. When 
thermal influence is substituted for gravitational, in the tide- 
generating force reckoned for, and when the modes of oscillation 
corresponding respectively to the diurnal and semidiurnal terms of 
the thermal influence are investigated, it will probably be found 
that the period of free oscillation of the former agrees much less 
nearly with 24 hours than does that of the latter with 12 hours ; 
and that therefore, with comparatively small magnitudes of the tide- 
generating force, the resulting tide is greater in the semidiurnal 
term than in the diurnal. How, if we look to the values of c 2 
in the table, we see that, with one exception (Sitka, a place far 
north, where R 2 is very small), they are all positive acute angles : 
and we find 61°*3 as the mean of all the 30. If we assign weights 
to the different values of c 2 , according to the corresponding values 
of K 2 , we should find a somewhat larger number for the true mean 
value of c 2 . It is enough for our present purpose to say that the 
mean is 60° or a little more. Looking now to the formula, we see 
that the meaning of this is that the times of maximum of the semi- 
diurnal variation R 2 are a little before 10 o’clock in the morning 
and a little before 10 o’clock at night (exactly at 10 o’clock if c 2 were 
exactly 60°). Without more of observation, or of observation and 
theory, than has yet been brought to bear on the subject, we cannot 
tell the law of variation of R 2 with the latitude. The observations 
in the table seem to show, what Laplace’s Tidal Theory prepares us 
to expect, that it diminishes more in the Polar regions than it would 
if it followed the elliptic spheroidal law of proportionality to the 
square of the cosine of the latitude. We may, however, take by 
inspection from the table P 2 = cos 2 lat x '032 inch as a rough esti- 
mate of a barometric variation distributed over the whole earth in 
the form of an elliptic spheroid, which would give the same resisting 
couple in the calculation of the solar gravitational influence on the 
