( 467 ) 
of stars in the meridiancircle at Leyden in the illuminated field 
with the usual magnifying power of 200. Availing myself of these 
determinations I have, in the following accounts, expressed the different 
degrees of brightness in star magnitudes. 
During several days observations have been made with this apparatus 
in order to determine the personal error in the observation of the 
sudden appearance or disappearance of the artificial star in different 
positions of the Nicol, and the first question was: how are we to 
deduce from such a series the most probable result for that personal 
error? The result from each observation, obviously, depends on a great 
number of different quantities, among others on: A, the attentiveness 
of the observer; B, the sensitiveness of his eye, C, his tiredness, etc. 
which all will be different in different observations. If we assume 
that for a given series of observations it is as probable that A, B, C etc. 
are larger than 45, Bo, Co, as that they are smaller than these 
values, the personal error which belongs to the quantities 4, Bo, Co ete. 
will be called mean personal error 7. 
It is obvious that this value Z cannot be found by forming the 
arithmetical mean of the several values t, the distances of the two 
corresponding marks on the chronograph. With a small degree of 
attentiveness 4, for instance, t may become very large and t— 7’ may 
increase indefinitely, whereas with a high degree of attentiveness ¢ will 
become smaller, but not indefinitely, as the appearance of the luminous 
point can never be registered earlier (errors excepted) than the moment 
at which it has actually appeared. Hence the positive errors are 
sure to be larger than the negative ones. An approximate value of 
that mean personal error may be found by arranging the measured 
distances of the two marks in a series in the order of their values 
and by taking as the most probable value the middle quantity of 
this series. This may also be found followiug a more accurate method. 
I have found from a very long series of observations that the values 
log(t—ty’, where t) is a constant to be determined for each series, 
follow the ordinary exponential law of errors; the mean value of 
log (t—tp), log (T—t,) will then yield the most probable value 7 of the 
mean personal error. The constant quantity f introduced into this com- 
putation, represents the smallest possible value of the personal error 
with the maximum of attentiveness and sensitiveness, the minimum of 
tiredness etc. 
From the series of observations of the sudden appearance and 
disappearance of the artificial star, according to the latter method, 
the following values were found: 
