the proportion of her distance to the sun's distance. If the sun's distance from the earth is not excessively greater than the moon's, then that angle SEM will be sensibly less than 90 degrees; but if the sun's distance from the earth is very much greater than the moon's, then that angle will be very nearly equal to 90 degrees. This observation, therefore, gives us, theoretically, the way to determine the sun's distance from the earth, if we can determine exactly the time when the moon is half illuminated. Unfortunately, the roughness of the moon's surface, which resembles very much a volcanic surface, makes it impossible to observe, with any degree of exactness, at what time the moon is half illuminated, and this principle fails totally in practice, from that cause.
The next method pointed out for ascertaining the distance of the sun from the earth, and which has been used with considerable success, is founded upon the observation of the planet Mars. Although the distances of the planets from the sun were not known to the ancient astronomers, yet the proportions of their distances were known to them. I have already pointed out to you that Venus is the planet which exemplifies this best. By observing how far Venus goes to the right and to the left of the sun, we can ascertain the proportion of the distance of Venus from the sun, to the distance of the earth from the sun, which is a proportion of 72 to 100 nearly; although we do not know the absolute distances at all The same remark applies to other planets; although we do not know their absolute distances, yet we can see or ascertain the proportions of the diameters of their orbits, which explain their different apparent movements. With regard to Mars, we are able to assert (knowing the proportion of the
