198 
rOPULAR SCIENCE REVIEW. 
tlie solar-spot period, Dr. Auwers has also examined the Greenwich observa- 
tions of Bradley and Maskelyne, and their assistants, as well as some of 
those made at Konigsberg by Bessel, and at Dorpat by W. Struve ; but his 
result is a negative one. He has also compared the Greenwich solar diame- 
ters observed from 1851 to 1870 with Dr. It. Wolf’s relative number of 
the solar-spot conditions ; and his conclusions are that, 1 in the fluctuations 
of the observed values, both for the horizontal and vertical diameters, and 
the difference between the two, no dependence upon the variations of the 
degree of activity, and therefore no indication whatever of the reality of 
these fluctuations, can be perceived.’ 
11 The evidence thus far seems to negative the existence of any periodical 
changes in the sun’s diameter of sufficient magnitude to be detected from 
the ordinary meridional observations of the different limbs of the sun. This 
negative evidence is much strengthened by the results of an extensive com- 
parison, by Professors Newcomb and Holden, of the horizontal and vertical 
diameters deduced from the observations of the sun at Greenwich and 
Washington from 1862 to 1870, the transits of the first and second limbs 
having in this interval been registered on the chronograph. The total num- 
ber of observations discussed amount to 1,813 of the horizontal diameter, 
and 1,826 of the vertical diameter. The principle of the method is given 
as follows : — ‘ Suppose we have two series of observations of the sun’s di- 
ameter made simultaneously at two different observatories, so that each ob- 
servation of the one series is accompanied by a simultaneous one of the other 
series. Then, if the outstanding difference between each measure, and the 
mean of the whole series to which it belongs, is due entirely to the acci- 
dental errors of observations, there will be no relation between the differences 
of the two series. But if a portion of the difference is due to an actual 
change in the sun itself, the differences which are positive in the one series 
will be accompanied by a preponderance of positive differences in the other 
series. For on the days when the sun is larger than the average, the prob- 
ability of finding a positive correction will be more than ^ at each observa- 
tory, and hence the probability of an agreement of sign will be greater than 
a. If the probability in each case be ^ + «, it is easy to see that the prob- 
ability of an agreement will be | + 2a 2 . Our results should, however, 
depend not on a simple enumeration and comparison of the signs of the 
residuals, but also on the magnitude of the latter, and we may secure this 
dependence by taking the algebraic product of each residual of the one 
series by the corresponding one of the other. If the residuals are purely 
accidental, the mean value of these products should approximate to zero as 
the number of observations is increased ; while, in the case of actual vari- 
ability, it will approximate to some positive limit.’ 
11 As many observers were engaged in these observations, it was found 
necessary to correct the apparent error of the ephemeris diameter for the 
personal error of the observer, and tables are given containing the adopted 
errors for each year for each observer, both at Greenwich and Washington. 
The conclusion to which Professors Newcomb and Holden have arrived seems 
to be that, whatever apparent variations of a periodic nature in the sun’s 
diameter occasionally occur, they are probably the result of chance ; and 
that it is clearly shown by their investigation, based upon so large a number 
