88 CALIFORNIA ACADEMY OF SCIENCES. [Proc. 3D Ser. 



Errors of Observation. 



It is therefore astonishing to note that under such adverse 

 conditions for accurate observation the times of contacts 

 are noted to tenths of seconds. As two seconds of time 

 mark the apparent relative movement of the bodies about 

 one-tenth of a second of arc, we need not wonder that some 

 of the observers were not sure of the minute; and in one 

 case an error of three minutes could not be fixed. This 

 occasional and accidental distortion of the planet's disc 

 in such transits had called for the determination of the 

 epoch of the geometrical contact of the limbs of the images 

 of the two bodies and for other appearances ; but under 

 such unfavorable conditions the judgment of the best ob- 

 server may reasonably have been at fault, and his recorded 

 epoch of contact very wild. This is shown by many illus- 

 trations of the distortion where the outlines of the "black 

 drop" are drawn with a hardness and positiveness that are 

 certainly uninstructive, and unsuggestive of the cause. 



The difficulty of observation is made painfully manifest 

 in the experiments at Washington early in 1874, when most 

 of the observers practised upon an artificial transit of 

 Venus to determine the times of the four contacts. The 

 observations range from four seconds before the first con- 

 tact to twenty-eight seconds after; and even at the second 

 and third contacts, from twenty-one seconds before to sev- 

 enteen seconds after the epochs. These extraordinary per- 

 sonal equations must surely have been due in part to inex- 

 perience, and mainly to the disturbed conditions of the at- 

 mosphere. And yet the mean value of a series of such 

 observations was applied to the actual observations in 

 the field upon the Sun and planet, to reduce them to 

 a systematic series. Had these preliminary observations 

 been made in a serene atmosphere, the apparent per- 

 sonal equations would have been brought to normal and 

 reasonable limits, notwithstanding one observer declares 

 that "the optical edge of a bright body is not, and in the 

 nature of things, cannot be, absolutely sharp in the eye or 

 in the telescope." The great discrepancies arose in large 



