M.-P — Vol. I.] DAVIDSON— APPARENT PROJECTION, ETC. IOI 



the inequality (125". 5) by the comparison of its extreme 

 observed effects on the Moon's right ascension, any error in 

 the adopted semidiameter will affect the result by its full 

 amount. This suggests that this gravitational method of 

 determining the Solar Parallax would be more accurately 

 employed by observing occultations of stars large enough 

 to be seen through the spurious bright limb of the Moon. 

 Moreover, the observations themselves would afford some 

 data for the elimination of the error depending upon a fac- 

 titious limb. 



Nearly all Measured Diameters Too Large. 



In all instrumental observations for the right ascension of 

 the Sun or Moon, and for their declination and diameter, 

 it must be evident that the observer obtains accurate meas- 

 ures only when the disc of either body is sharply defined, 

 devoid of tremor or unsteadiness, and unaffected by irregu- 

 lar and extraordinary refraction, without reckoning diffrac- 

 tion at the spider line, unknown instrumental errors, and 

 peculiarities of observation. As these supreme conditions 

 of steadiness are seldom obtained, it necessarily follows that 

 the mean of any number of observations taken under differ- 

 ent atmospheric conditions (say for example the diameter 

 of the Sun, Moon, or planets) must be too large. The 

 diameter can only be too small through error of observation, 

 instrumental errors, diffraction of the spider line, or abnor- 

 mal refraction. 



With a disturbed atmosphere in observations for the deter- 

 mination of the right ascension of the Moon during the first 

 half of a lunation, the observed A. R. of the limb will be 

 too small and for the second half too large. Similar results 

 will follow from observations of the I and II limbs of the 

 Sun and planets. Therefore all published diameters of the 

 Sun, Moon and planets derived directly from actual obser- 

 vations must be too large. Moreover, this presents a case 

 where the mean of measured quantities is not the most 

 probable value. The mean of all the minimum measures 

 would be nearer the truth. 



