24 
On the Variatious in Personal liquation 
I. Introduction. 
Starting from Bessel's discovery, in the early part of the last century, of the 
existence of a definite relative personal equation for two observers recording 
transits by the eye and ear method, there has been a continuous discussion among 
astronomers on the errors which such personal equations may introduce, and on 
the methods of eliminating them or correcting for them*. In such discussions 
it has been the usual practice to take the yearly mean personal equation, whether 
relative or absolute, of different observers and to use this mean personal equation 
as the basis of any correction to be applied to observations made in that year. 
From a comparison of the yearly means it is aduiitted that there may be gradual 
secular changes in personal equation, but it is found that for experienced observers 
there is usually very little variation. In text-books on Practical Astronomy brief 
mention of the subject is usually made, and the conclusion drawn is that for an 
observer in normal health, the personal equation in any one type of observation 
will remain sensibly constant for " shoi't periods " of time ; an exact definition of 
the words "short period" is not and clearly cannot be attempted f. It is further 
assumed that variations from the personal equation ai-e due to accidental errors 
and may be taken as randomly distributed in accordance with the Gaussian Law. 
With the recent introduction of photography and mechanical methods of record, 
the interest of the astronomer in the subject has to some extent diminished, but 
there are many fields of scientific observation where the human element cannot be 
eliminated, and in the modern researches of the psychologist we find a study is 
made of problems of this type for their own interest and for the light which they 
may throw on the working of the human machine. 
One very important aspect of the problem of personal equation, and of par- 
ticular import to the astronomer, was discussed in detail in a paper entitled " On 
the Mathematical Theory of Errors of Judgment, with Special Reference to the 
Personal Equation," published in the Phil. Trans. (Vol. 198 a, p. 235). In this 
case various series c>f experiments were cai-ried out simultaneously by three 
observers under identical conditions and it was found that there was a marked 
correlation between the variations in absolute personal equation of the different 
observers. This in itself was sufficient to show that the judgments of any one 
observer were not randomly distributed about his mean personal equation. The 
purpose of tlio present paper is to discuss the variations in judgment of one ob- 
server, and to inquire how far the evidence of four or five experiments suggests 
that the theory of personal equation and of errors of judgment, as usually accepted, 
requires modification. 
The subject is a large one, and much beyond the scope of a single paper ; but 
by making careful inquiries of this type with the help of statistical methods, it 
* For example, Monthly Notices, Vol. xl. 1880, pp. 75, 165, 302 (Discnssion of Greeuwich Obser- 
vations of the Moon); Monthly Notices, Vol. xliv. 1884, pp. 1 and 39 (Greenwicb Observations of the 
Sun) ; Monthly Notices, Vol. lvii. 1897, p. 504 (General Discussion of relative personal Equations). 
t For example, in Campbell's Elements of Practical Astronomy, 1899, p. 157 ; Young's General 
A^tionomy, Revised Edn. § 114, and Chauvenet's Spherical and Practical Astronomy, 4th Edn. ii. p. 189. 
