DIURNAL MOTION OF THE EARTH. 



18$ 



essays living received the approbation of many gentlemen 

 well acquainted with the mathematical and physical sciences, 

 I was induced to enter into a farther investigation ot the 

 effects arising from this principle of cycloidal motion. The 

 result of this investigation is contained in the work above- 

 mentioned : and to give you a general idea of the principles 

 on which my theory is founded, I shall recite those propo- 

 sitions of my work, which appear to me most important. 



Prop. 8, Book I. If the semicycloid Aa^be described Prop. *• I 

 by the point A of the circle A D B E, PI. V, fig. 7, revolv- 

 ing from B to A ; and the semicycloid B b B be at the same 

 time described by the opposite point of the generating cir- 

 cle ; then the cycloidal arcs A a and B b, described in 

 equal times, will be to each other as the chord A. F of the 

 circular arc A F to the difference between the diameter A B 

 of the generating circle and the chord B H of the supple- 

 ment of the same arc. 



Prop. Q. The velocity of the point A at a is to the velo- Prop. 8. 

 city of B at b, as a/B L io \/ A L. 



Prop. 12. If the circle A D B E move from B to A with *f°P-3» 

 two uniform motions, a rotatory motion and a progressive 

 motion, so that the two opposite points A and B describe 

 two semicycloidal curves A a A and B b B, and the pro- 

 gressive velocity be to the rotary velocity as n to 1 : then the 

 velocity of the point A in any place, a, will be to the velocity 

 •f the point B in any place, b, as 



Si 



1 , n x AC + AC-AL' 

 2 AC x AL-AL 5 



i/ r ,,n x AC + A C — BL' 



is to W i + 



2.AC + BL-BL' 



In order to apply this formula to the motion of the Earth, 

 I suppose it to move along the chord of an elliptical arc every 

 twenty-four hours, instead of the arc itself, over which it 

 really moves : and having shown, that the velocity of any 

 part on the surface of the globe, except at the poles, is 

 greatest at noon, and least at midnight, I prove, that the 



velocitiei 



