Polytechnic Association. 891 



dozen years after the publication of my Quadrature that the change 

 was made in the estimate of the sun's distance, and then without 

 credit to my earlier demonstration. 



But we need not wait for the transit to learn the truth. The 

 mechanical properties of numbers, which Archimedes threw away, 

 and which all astronomers now throw away as useless, will help us 

 out of the difficulty. If we admit the hypothesis that the earth 

 revolves about the sun on the value of the circumference of the 

 moon's orbit (and I do not see how we can help admitting it, unless 

 we first deny the unity of the earth and the moon as constituting a 

 perfect and distinct system, and unless we deny also the well estab- 

 lished truth that the heavenly bodies are goverened by laws that 

 regulate their distance and motion relative to each other precisely 

 according to their relative magnitudes, density, etc.), then it will fol- 

 low, from the mechanical properties of numbers, that knowing how 

 many revolutions of the earth and moon are performed (381,895) in 

 the passage over the earth's orbit, if we divide that number into the 

 sun's distance (which is the radius of the earth's orbit), the product 

 will be the radius of the moon's orbit. 



If, then, we want to know whether the sun is 95,000,000 of miles 

 distant from us, we will divide 95,000,000 by 381,895, the number 

 of revolutions of the earth and the moon, and that will give 248,759 

 miles as the moon's distance ; and Ave know from observation, aside 

 from our own theory, that it is not 248,759, miles and that it does not 

 differ much from 240,000, and by the same means we then know, also, 

 that the sun is not 95,000,000 of miles from us. Again, knowing 

 approximately the moon's distance to be about from 240,000 miles, if 

 we take that as radius, and multiply it by the number of revolutions 

 which the earth and the moon perform (381, S95) in passing over the 

 earth's entire orbit, the product will be the sun's distance, or the 

 radius of the earth's orbit. And here again we see that the sun is 

 not 95,000,000 of miles from us, and, moreover, that its distance is 

 not greater than the sum we have given it, viz., 92,285,568 of those 

 parts of which the earth's diameter is 7,912, which we call miles. 

 Again, knowing the moon's distance, we can calculate the circum- 

 ference of her orbit, and, multiplying that by the number of revolu- 

 tions; will give us the earth's orbit round the sun. 



These truths are all so perfectly simple as scarcely to need a dia- 

 gram to illustrate them, but as all may not see the truth quite clearly, 

 I have prepared here a diagram to illustrate the power of numbers 

 as applicable to our theory. 



