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HISTORY OF PHYSICAL ASTRONOMY.

of the earth’s mass, the particles composing the latter will all in con-sequence approach nearer to the axis. Now, it follows immediately froma well-known principle in Mechanical Science, that when a body is enduedwith a rotatory motion, and is not exposed to the action of any extraneousforces, the principal moment of inertia, or, in other words, the sum of theproducts formed by multiplying each particle into its angular velocity andthe square of its distance from the axis of rotation, is a constant quantity.The number of particles then remaining the same, if their distances fromthe axis be diminished, their angular velocities must be increased, andvice versa. Hence, if the dimensions of the earth be in a state of con-traction from cooling, the velocity of rotation must be increasing, and thelength of the sidereal day must be diminishing. It is not difficult, how-ever, to show that if the earth is really becoming cooler, the diminutionof temperature must be proceeding at a very slow rate. We have seenthat, during a period of 2500 years, the sidereal day has not been shortenedby so much as the ten-millionth part. Now, the principles of Mechanicsteach us that this result would ensue if the earth’s radius experienced adiminution of only one twenty-millionth part of its length. It follows,then, that during the period which has elapsed since the earliest Chaldeanobservations, the mean temperature of the earth has not varied to such anextent as to cause the terrestrial radius to contract by one twenty-millionthpart of its length.

The important question of the Tides has recently attracted consider-able attention in this country. The Encyclopcedia Metropolitana con-tains a valuable essay on the mathematical part of the subject, by Mr.Airy, founded on the theory of undulations. Sir John Lubbock and Dr.Whewell have been engaged during many years in determining the lawsof the tides by observation, and in tracing their connexion with the placesof the sun and moon. The results to which they have been conductedby their researches are contained in a series of admirable papers, whichcontinue to be published from time to time, in the volumes of the RoyalSociety . These distinguished philosophers are now endeavouring to dofor the theory of the tides what astronomers had done for the lunartheory previous to the establishment of the theory of Gravitation. Let ushope that their efforts will be attended with similar success, and that theday is not very remote when this important branch of Physical Astronomywill be in a condition to invite the researches of the geometer, and toreward him with a rich harvest of results.

It is clear that if the sun and moon by their action on the earth occa-sion oscillations in the waters of the ocean, they ought to produce asimilar movement in the atmospheric fluid. Laplace investigated thetheory of this subject upon a somewhat restricted hypothesis*, and Bouvardundertook an extensive series of observations of the height of the baro-meter, with the view of detecting periodical oscillations depending on theplaces of the disturbing bodies. The effects, however, were so very minuteas to be almost entirely masked by irregularities arising from other causes,and no satisfactory conclusion could be deduced from the observations.

The oscillations of the atmospheric tide will manifestly be greatestnear the equator, and the most favourable station for detecting them would

* Mee. Cel. liv. iv. chap, iv., liv. xiii. chap. vii. The temperature of the atmospherewas assumed to be uniform, and the density at each point proportional to the compressingforce.