THE PERSONAL EQUATION. m 



we have seen, to reduce the observations of A to what they would 

 have been if B had made them, it is simply necessary to know how 

 much later B is in the habit of observing than A, and to apply this as 

 a constant correction to A's work. 



This may be done in practice by A and B observing the same star 

 in the same telescope; A over the first ten wires (see Fig. 1), and B 

 over the second ten. 



A knowledge of the distances of the various wires from the middle 

 wire enables us to compare A's work with B's, and A B is the rela- 

 tive personal equation. 



There is, however, a strong objection to this process : if personal 

 equation is any thing, it is the difference between established habits y 

 and, if A observes over ten wires, and then hastily rises to allow B to 

 take his place at the instrument, both A's habits and B's are broken 

 in upon, and the resulting personal equation is likely to be affected by 

 this fact. In general, the way adopted is to allow A to observe sev- 

 eral stars leisurely, and from them to determine the error of the clock; 

 B does the same, and from his observations also a clock-error is found; 

 the difference of these clock-errors, reduced to the same epoch, gives 

 the relative equation of A and B. 



Now if, instead of A registering his own observations on the chrono- 

 graph (for example), we could have the star register its own transit, 

 then B's observation, compared with this, would give at once an abso- 

 lute equation. We cannot use the real star for this purpose ; but sev- 

 eral attempts have been made to construct an apparatus which should 

 register the transit of an artificial star, which star could, at the same 

 time, be observed. The principle of all of these machines is, in gen- 

 eral, the same, and we will merely give a brief account of one which 

 is now under trial by the Coast Survey. 



The artificial star is produced by lamp-light falling upon a small 

 hole in a blackened plate ; this plate is given a motion laterally, and 

 the small point of light passes from one side to the other of a plate of 

 ground glass, upon which lines are ruled to represent the spider-lines 

 of the reticle. As the artificial star passes each wire, an electric signal 

 is recorded on the chronograph, and the observer can also record his 

 signal ; and thus on the same chronograph-sheet many observations 

 of absolute personal equation can be permanently recorded. Any 

 velocity can be given to the star, so that it may pass through the 

 field of view as slowly as the pole-star, or as rapidly as a star at the 

 equator. 1 



1 The chief objection to this apparatus is, that there is a constant error in its indica- 

 tions ; i. e., it can never be adjusted so as to give its signal at the exact moment of tran- 

 sit, but it is always too soon or too late. This is sought to be eliminated by allowing the 

 artificial star to travel first from right to left, and then from left to right, and using the 

 mean of the two determinations. It is still a question whether the observer's habit is the 

 same no matter which way the star is moving. 



