and Results of Harmonic Motion. 191 
by wot. The study of the various correlations which flow 
from this integral involves the following considerations:— 
(1) The principle of Galileo, that the total effort is equiva- 
lent to the effective sum of the causes which are operating. 
This is illustrated at sun’s surface, which is the region of 
greatest energy in our system, by the cyclic equation 
Sedu. 
(2) The equality of pressures or resistances to opposing 
forces, in all equilibrating tendencies. In consequence of this 
equality, every interruption or prevention of the free action 
of any force may be measured as a rate of change of momentum ~ 
in the opposite sense. 
(3) The invariability of the sum of kinetic and potential 
energies. 
(4) The maximum of kinetic energy in all cyclical motions, 
at the point of the trajectory which is nearest to the centre of 
force, and the maximum of potential energy at the point . 
which is most remote from that centre. At the origin of 
luminous radiation, where }y=vy, the reaction of gravitating 
resistance is all kinetic; after a haif-rotation it becomes all 
potential, but it is then combined with a new reaction which 
is all kinetic. 
(5) The evidences of local ethereal stress, which is opera- 
tive in various forms of gravitating, thermal, electromagnetic, 
and chemical attraction and repulsion. 
(6) The indestructibility of energy, which requires, as 
Maxwell has stated, that energy must exist in the ether 
during the interval of its transfer from one body to another. 
(7) The strong reasons for believing that the media for 
luminous, gravitating, thermal, electromagnetic, and chemical 
interactions, occupying the same space and represented by the 
same cyclical velocities, are identical. 
(8) The counteraction of stress by obvious elasticity, as in 
a spring, or by probable intermolecular elasticity and orbital 
motion, as in the resistance of solids. 
(9) The principle of Fourier, that any complex periodic 
motion must be compounded of a definite number of simple 
harmonic motions, of definite periods, definite amplitudes, and 
definite phases. 
(10) The application of “ Laplace’s Coefficients,” or sphe- 
rical harmonic analysis, to the explanation of cyclical waves 
and vibrations in spherical elastic masses. 
(11) Cumulative and progressive undulating tendencies, 
resulting in complex harmonic motions of various kinds. 
The evidences and consequences of harmonic motion in 
