100 
those of solar activity, so that to analyse the former is 
probably equivalent to analysing the latter. 
2. Our method of analysis is not new. The system 
pursued by us is, in fact, that which has been pursued by 
Baxendell, and probably other astronomers, with obser- 
vations of variable stars, and it has already been applied by 
one of us in a preliminary manner to magnetic declination 
ranges (Pro. Lit. and Phil. Society, Manchester, February 
24, 1880). 
S. The observations at our disposal are those which have 
been used by Prof. Elias Loomis in his comparison of the 
mean daily range of the magnetic declination with the 
extent of the black spots on the surface of the sun* These 
observations are recorded as monthly means of diurnal 
declination range, and we found it necessary to multiply 
each by a certain factor, firstly, on account of the 
well-known annual inequality of declination range, and 
secondly, to bring them all to the standard of the Prague 
observations. We have applied for this latter purpose pre- 
cisely the same corrections as those made by Professor 
Loomis. 
4. The result of an analysis of these observations has 
been to indicate the existence of three inequalities; two 
dominant ones with periods of about 10J and 12 years, 
and a subsidiary one with a period of about 16 £ years. By 
these means we have been enabled to reproduce the 
observed annual values of declination range with an average 
difference of S9". The amount of agreement between the 
observed and calculated values will be seen from a diagram 
which accompanies this note. We are, however, of opinion 
that the series of observed values at present obtainable is 
too short to render this analysis a very accurate one. It 
will certainly not bear carrying back forty or fifty years 
beyond its starting poiut, which was in 1784, and it would 
* American Journal of Science and Arts, Yol. L., No. CXLIX. 
