892 Transactions of the Amebic an Institute. 



Let us consider the larger circle as the earth's orbit, with the sun 

 in the center, the lesser circle is the moon's orbit, with the earth in 

 the center. Now let us suppose that the diameter of the lesser circle 

 is one and the diameter of the greater circle is twelve, then the lesser, 

 revolving about the greater, will make twelve revolutions. Then 

 divide the number of revolutions, twelve, into six, the radius of the 

 earth's orbit, the result is five, which is the radius of the moon's 

 orbit. Again, if you know the moon's distance, and multiply it by 

 the number of revolutions required to pass round the sun, it will give 

 you the sun's distance or the radius of the earth's orbit. And if you 

 know the moon's distance, you can calculate the circumference of her 

 orbit, and, multiplying that by the number of revolutions required to 

 pass round the sun, it will give you the earth's orbit. If you know 

 the moon's distance, and divide it into the radius of the earth's orbit, 

 it will give you the number of revolutions of the moon in her orbit 

 required to pass round the sun, and these are just the things which 

 the earth and the moon together perform every year in the fulfillment 

 of their respective journeys round the sun. 



Hence, it will be seen, accepting these premises to be true, it will 

 result that the earth's daily progress in her orbit round the sun is 

 exactly equal to the circumference of the moon's orbit round the 

 earth, viz., it is exactly 1,518,343 miles, such as compose the earth's 

 diameter reckoned at 7,912 miles. Reduced to time, the daily motion 

 is as follows : Revolution of the earth on her axis, twenty-four hours ; 

 in the meantime the moon has advanced, in her orbit round the earth, 

 52' 30" + , sidereal time, to which you must add the difference between 

 a solar day and the revolution of a circle in space, 8' 36" + . 



If it is objected that neither the earth nor the moon revolve in a 

 circle, and therefore these things cannot be true, the answer is, that 

 if we suppose either the earth or the moon to revolve in a circle, the 

 area of which is equal to the area of the ellipse in which they do 

 actually revolve, then the radius of the circle is exactly the mean dis- 

 tance of either the earth or the moon from the center around which 

 they revolve ; and it is precisely the same thing whether they revolve 

 in a circle by an equal motion, or in an ellipse by an unequal motion ; 

 in either case they fulfill the law of passing over equal areas in equal 

 times. 



Divested of the lumber which science has given these questions, it 

 looks too simple to be believed, but you may alter your proportions 

 and carry your numbers and diameters to hundreds of millions, as 



