ox DISPLACEMENTS OF THE ROTATIONAL AXIS OF THE EARTH. 477 



The true law and explanation of these wanderings of the pole remained, 

 nevertheless, a deep mystery till Copernicus lifted the veil by showing 

 that they were only the celestial image of real displacements of the 

 rotational axis of the earth in space, and until Newton came and, com- 

 bining his discovery of universal gravitation with his deduction of the 

 ellipsoidal figure of the earth, proved that these displacements are due to 

 the actions of the moon and the sun on the earth. 



The mathematicians of the eighteenth century completed this explana- 

 tion by profound researches embracing the full theory of free rotation of a 

 solid system of masses, under the action of various disturbing influences, 

 not only those acting from outwards on the rotating body (as in the case 

 of the sun's and the moon's attractions on the earth), but also those 

 depending upon the condition or changes within the rotating system 

 itself. 



Among several interesting results, these investigations pointed out an 

 essential difference between the development of the disturbed rotation in 

 the first and in the second case. 



Ul3on the supposition, corresponding to the real terrestrial conditions 

 of the problem, namely, that all the disturbing influences are relatively 

 small in comparison with the amount of energy represented by the primary 

 rotation of the earth itself, the following distinctions were demonstrated. 



Exterior disturbing influences will mainly produce displacements of 

 the axis in space, and corresponding wanderings of the pole among the 

 stars ; whilst the simultaneous displacements of the axis in the earth itself, 

 in consequence of the particular conditions of their evolution, remain 

 insensible. 



On the contrary, interior conditions and distui'bing influences, as those 

 contained in the configurations of the masses, or in changes of the dis- 

 tribution of the masses composing the rotating system, will mainly produce 

 displacements of the rotational axis in the rotating body itself, whilst in 

 this case the simultaneous displacements of this axis in space and the 

 corresponding variations of the position of the pole among the stars remain 

 insensible. 



Very soon after these deductions had been made from theory, astro- 

 nomers began to inquire if also effects of the latter type — that is to say, 

 displacements of the rotational axis in the earth — really existed. 



According to theory, such displacements ought even to exist when the 

 distribution of the masses composing the earth is not in the slightest 

 degi'ee variable. 



It is sufficient for producing such displacements that the position of 

 the rotational axis of the earth is actually not in perfect coincidence with 

 one of its principal axes of inertia, known as the principal axis. 



The slightest deviation of tlie rotational axis from the principal axis 

 has the consequence that the pole of the rotational axis begins and con- 

 tinues to describe a small circle around the pole of the principal axis. 



The velocity of this movement depends upon the law of the figure and 

 of the distribution of the masses composing the earth, and the best 

 numerical data for this dependence had given the result that the dis- 

 placement in question would probably have a period of nearly ten months. 



Now all such displacements, possibly measurable with reference to 

 fixed directions in the earth, and insensible with reference to fixed direc- 

 tions in space, could be found in the most favourable way by measuring 

 as exactly and continuously as possible the distance of the pole from the 



