138 PHILOSOPHICAL TRANSACTIONS. [aNNO 166/. 



To Measure the Diameters of the Planets, and the Parallax of the 

 Moon. By M. Auzout. iV° 21, p. 373. 



I applied myself last summer to measuring the diameters of the sun, moon, 

 and the other planets, by a method which M. Picard and myself have esteemed 

 the best of all that have been practised hitherto ; since we can take the diame- 

 ters to second minutes, being able to divide one foot into 24,000 or 30,000 parts, 

 scarce failing as much as in one part only, or to three or four seconds. I can 

 well assure you, that the diameter of the sun, taken in his apogee, has not 

 been much less than 31 m. 37 or 40 sec. and certainly not less than 31 m. 35 

 sec. and that at present in his perigee it does not exceed 32 m. 45 sec. but may 

 be less by a second or two. What is at present troublesome is, that the ver- 

 tical diameter, which is the most easy to take, is diminished, even at noon, by 

 eight or nine seconds, 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 A5 

 sec. and I have not seen it exceed 33m.^or if it has, it was only by a few se- 

 conds. But I have not yet taken her in all situations of the apogees and peri- 

 gees which happen, with the conjunctions and quadratures. I have found a 

 way to know the parallax of the moon, by the means of her diameter: viz. 

 if on a day when she is to be in her apogee or perigee, and in the most 

 northerly signs, 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 six or seven hours, the difference of the diameters 

 will show the proportion there is of her distance, with respect to the semidia- 

 meter of the earth. The same would yet be practised 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. If one were under the 

 same meridian, or the same azimuth in two very distant places, and took at 

 the same time the diameter of the moon, it would effect the same tiling, 

 though not so exactly. 



From what has been said may be collected the reason of the observation 

 which M. Hevelius has made in an eclipse of the sun, touching the increase of 

 the moon*s diameter near the end. For the moon's diameter must change in 

 the eclipses of the sun according to the places where they happen, and accord- 

 ing to the hour and height of the moon. And had the eclipse been in the 



