12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



from assuming the rigorously permanent figure of a paraboloid of 

 revolution as it would do if the earth were immovable. 



(2) If the body moves along a given curve that is attached 

 firmly to the surface of the earth, the differential equation of its 

 motion does not contain the velocity of the rotation of the earth 

 and consequently this motion is the same as if the earth were at 

 rest. Thus, for any given value of gravity resulting from the 

 figure and the rotation of the terrestrial spheroid, the oscillations 

 of the pendulum are the same in all azimuths around the vertical; 

 a result that was important to demonstrate, considering the 

 degree of precision that we now attain in the determination of the 

 length of the seconds pendulum at different places on the earth. 

 But the diurnal rotation and the direction of the plane of oscillation 

 have a slight influence on the variable tension that the wire expe- 

 riences during the oscillations and which is not rigorously the 

 same in all azimuths. 



(3) Finally, when a projectile is sent into the air in any direction 

 whatever the rotation of the earth neither increases nor dimin- 

 ishes the distance that it attains at any instant from a plane 

 through the point of departure and parallel to the equator. 



Before seeking the integrals of the equations of apparent motion 

 in the general case of an initial velocity having any magnitude and 

 any direction whatever, I have considered the simpler special cases. 



The first case is that where the moving body starts from a point 

 situated at a given height above the ground without imparting 

 to it any initial velocity whatever and is left to the action of 

 gravity, so that it commences to fall vertically. The velocity [of 

 the eastward motion] at the point of departure, due to the rota- 

 tion of the earth in which it participates, being greater than that 

 which belongs to the foot of the vertical, we perceive that the 

 moving body when it has reached the earth must have departed 

 from the foot of the vertical line, to the eastward or in the direc- 

 tion of the true motion of the earth, but mathematics alone can 

 give the measure of this distance, especially when we consider the 

 resistance of the air; one can see that the deviation takes place 

 toward the east and that it is nothing in the direction of the 

 meridian. In order to compare with experience the formula which 

 expresses the amount of deviation, I have chosen the observations 

 of this phenomenon which were made in 1833 by Professor Reich 

 in the mines of Saxony. The height of the fall was 158.5 meters 

 and M. Reich concluded for the mean of 106 experiments 

 that there was a deviation to the east of 28. 33 mm . He also 



