FORMATION OF EQUATIONS OF DISTANCE OF CENTERS, FOR MOKATTAM. 297 



EQUATIONS RESULTING FROM THE MICROMETRICAL OBSERVATIONS AT MOKATTAM. 



From the first series of Captain Browne's micrometric measures of the 

 double diameter of the planet are obtained the quantities 



rev. 



Diameter of Venus 4' 837 



Zero-reading 2 1 972 



From the final series are obtained 



r 



Diameter of Venus 4 '977 



Zero-reading 22 oo5 



The mean of the two determinations of the diameter, which are not in very 

 close agreement, is 4 r- 907, and taking the tabular diameter as 62"'84, the 

 value of one revolution of the micrometer-screw is 



1 2"-8o6 + 0-408 S r, 



where 8 r is the correction required to the tabular semidiameter, to be deter- 

 mined hereafter. 



It is essential in using the double-image micrometer of this construction 

 that the zero, or reading corresponding to the coincidence of the images, 

 be determined with the micrometer-screw in the same position angle, with 

 regard to its rotation around the axis of the micrometer itself, as it had 

 during the measures. There are no means of knowing the position of the 

 screw during the first series of measures of double diameters, hence the zero- 

 reading obtained from them should not be employed. 



The Zero proper to the measures of the distance of limbs is obtained by 

 comparing the measures themselves, before and after the change from the 

 negative to the positive side, with the computed tabular quantities. In this 

 way, using the five readings on each side of zero, between 12 h . 59 m . 53 s . and 

 13 h . 10. 25 s ., the zero 22 r> 152 is obtained, and has been applied to. all the 

 measures in order to obtain the observed distance of limbs in terms of the 

 revolution of the screw. This has been converted into arc by using the value 

 of one revolution given above. 



For the Cusp measures the zero proper to employ is that obtained from 

 the final series of double-diameter measures, viz., 22 rev> 005, the micrometer 

 not having been rotated in the interim. It will be seen that the last five or 

 six cusp measures are entitled to but little weight, they having been observed 

 more than five minutes after contact. 



