DIAMETERS. 



14.-DIAMETERS. 



The values of the semidiameters of Mars and Venus at the unit of distance, which have been 

 assumed in the foregoing computations are as already stated in 4. 



Mars, e = 4."6639 ; (OUDEMANS, Aslr. Nachr. XXXV, 351.) 

 Venus, f = 8."6625 ; (WICHMANN, Aslr. Nachr. XXXII, 74.) 



Both these determinations are free from any error due to the thickness of the micrometer- 

 threads, being derived from heliometer-observations. 



That for Mars was derived from a careful discussion of the measurements of Bessel from 1830 

 to 1837, published in the XXIII. part of the Kiinigsberg observations. The observations, 

 having been made under a great variety of circumstances, and at greatly different distances, 

 seemed well adapted for avoiding the influence of any constant of irradiation upon the result, and 

 for detecting its amount. Prof. Oudemans found it impossible to bring the ellipsoidal form 

 of the planet into the investigation, and the deduced value rests, therefore, upon the hypothesis 

 of sphericity. Assuming a constant error in the measured diameter, and introducing this as au 

 unknown quantity into the equations of condition, he found this error (which has been denoted 

 by u in the present discussion) to be 0".0267; and thence inferred both that no such influence 

 of irradiation had affected the observations, and that no other essential constant error existed 

 in them. The probable error of the semidiameter came out as less than one hundredth part of a 

 second, or only one half as much as if the supposed irradiation had been ignored ; that of the 

 deduced constant error was about one-third greater than its whole amount. The probable error 

 of a single setting was 0."2975. 



The adopted value for the semidiameter of Venus was deduced by Prof. Wichmann from his 

 own measurements, which had been also made with the Konigsberg Heliometer. The circum- 

 stances under -which he observed were quite various, although the greater portion of the 

 measurements were included within a period of two months. Some of the observations were 

 made in broad daylight, some in the twilight, others still by night ; and the conditions were 

 yet further varied by the employment of different magnifying powers, and sometimes of shade- 

 glasses. Out of the eleven groups of comparisons the discordance of the extremes was but 

 O."51 for the entire diameter, and the resultant mean, derived from sixty-four settings, appears 

 entitled to much weight. No decided influence of irradiation was detected. 



In the Astronomical Journal III, 9, Prof. Peirce gives the results of a discussion of the semidi- 

 ameters of Mars and Venus from the published observations with the Mural Circle of the Naval 

 Observatory at Washington, in 1845 and 1846. His especial motive in the computation was 

 to investigate the probability of the existence of any constant and spurious enlargement of the 

 apparent disc, in consequence either of irradiation or of any other cause. He arrived at the 

 curious inference that the constant quantity t was essentially the same for each of the two 

 planets. His figures are as follows, Jf denoting the correction to the value in the Nautical 

 Almanac. 



For Mars, t = 0."596 O."167 4 O."0375 O."0086 

 For Venus, t = 0."554 O."107 J( = O."1397 O."0257 



