An Extract of a Letter written Decemb. 28. 1666. by M. Auzout to the Publisher, concerning a way of his, for taking the Diameters of the Planets, and for knowing the Parallax of the Moon; as also the Reason, why in the Solar Eclipse above calculated, the Diameter of the Moon did increase about the end.
I did apply my self the last Summer to the taking of the Diameters of the Sun, Moon, and the other Planets, by a Method, which one M. Picard and my self have, esteem'd by Us the best of all those, that have been practis'd hitherto; since we can take the Diameters to Second Minutes, being able to divide one foot into 24000. or 30000. parts, scarce failing as much as in one only part, so as we can in a manner be assur'd, not to deceive our selves in 3. or 4. seconds. I shall not now tell you my Observations, but I may very well assure you, that the Diameter of the Sun has not been much less in his Apogee, than 31. m. 37. or 40. sec. and certainly not lesse than 31. m. 35. sec. and that at present in his Perigee it passes not 32. m. 45. sec. and may be lesse by a second or two. That, which is at the present troublesome, is, that the Vertical Diameter, which is the most easie to take, is diminisht, even at Noon, by 8. or 9. sec., because of the Refractions, which are much greater in Winter than Summer at the same height; and that the Horizontal Diameter is difficult, because of the swift motion of the Heavens.
As for the Moon, I never yet found her Diameter less than 29. m. 44. or 45. sec. and I have not seen it pass 33. m. or if it hath, it was only by a few seconds. But I have not yet taken her in all the kinds of situations of the Apogees and Perigees which happen, with the Conjunctions and Quadratures. I do not mention all, what can be deduced from thence, but if you have Persons at London, that observe these Diameters, we may entertain our selves more about this Subject, another time. I shall only tell you, that I have found a Way to know the Parallax of the Moon, by the means of her Diameter: Vid. If on a day, when she is to be in her Apogee or Perigee, and in the most Boreal Signes, you take her Diameter towards the Horizon, and then towards the South, with her Altitudes
above the Horizon. For, if the Observation of the Diameters be exact; as in these Situations the Moon changes not considerably her Distance from the Earth in 6. or 7. hours, the Difference of the Diameters will shew the Proportion there is of her Distance, with the Semi-diameter of the Earth. I do not enlarge, because that as soon as one hath this Idea, the rest is easie. The same would yet be practis'd better in the places, where the Moon passes through the Zenith, than here, for the greater the difference is of the Heights, the greater is that of the Diameters. I do not note (for it easily appears) that, if one were under the same Meridian, or the same Azimuth in two very different places, and took at the same time the Diameter of the Moon, one would do the same thing, though this Method goes not to preciseness.
From what has been said, may be collected the reason of the Observation, which M. Hevelius made in the last Eclipse of the Sun, touching the increase of the Moon's Diameter about the end. I am exceeding glad, that a person, who probably knew not the cause of it, has made the Experiment: but it is strange, that until now no Astronomer has foreseen, that that should happen, nor given any precepts for the Change of the Moons Diameter in the Eclipses of the Sun, according to the places, where they should happen, and according to the Hour and Height, the Moon should have. For, what hapned in that Eclipse of Augmentation, would have faln out contrarily, if it had been in the Evening; for, the Moon, which in that Eclipse, that began in the Morning, was higher about the end than at the beginning, was nearer us, and consequently was to appear bigger: But if the Eclipse should happen in the Evening, she would be lower at the end, and therefore more distant from us, and consequently appear lesser. So also in two different places, whereof one should have the Eclipse in the Morning, and the other at Noon, the Moon should appear bigger to him that hath it at Noon: And she must likewise appear bigger to those, who shall have a leser Elevation of the Pole under the same Meridian, because the Moon will be nearer them.
I wish, I could satisfie you about the Optick Glasses of Signior Burattini in Poland, which he hath sent hither; but I have not yet seen their performances my self. I only saw once the Glasses,
which are perfectly well wrought and well polisht. Those, that have tried them, find them very good; but they are only, the one of 10, the other of 8. foot. A good Astronomer told me, that they would bear a great Aperture in respect of their length.