the northern and southern hemispheres. But if we sub- 
stitute, in the extract, for “ in the morning and “ in the 
afternoon ” the hours 8 a.m. and 8 p.m., as the formula 
requires, we shall see that such terms as — exactly happens — 
and— ^surprising representation— -have no relation, in a 
matter of this kind, to the approximation of the hour 11 
a.m. to the hour 8 a.m. Similarly, the maximum of Z is 
required by equation (10) (the writer s own) to be at 8 p.m., 
both at Greenwich and Bombay; the maximum of the 
simple-wave element that has the one day period does 
actually occur at Greenwich at 8h. Im. p.m., but at Bombay 
not till llh. 7m. p.m.— a greater discrepancy even than 
before. 
But, as we have said before, the element of the observed 
variations that has half a day for its period is of the same 
order of magnitude as the element that has the full day for 
its period; and we see even from the restricted values of 
X^, of equations (7) and (8) that there is in the potential 
a term of the second degree which is proportional to 
sin 2 t(.sin 2 ( 0 -l- 7 -HX). It is, however, to pairs of values of 
— -f^and — ^ derived from each of the terms of the 
aclu dr 
potential of a single degree (or of the corresponding nega- 
tive degree), equally with those derived from any single 
term, that the test applied by the writer to the relations 
between the derived north force and vertical force properly 
applies ; and little value can be attached to the comparison 
of pairs of values derived from a single term, as indicating 
which of the two values of Z — that corresponding to ex- 
ternal forces or that corresponding to internal forces — best 
accords with observation. Moreover, as the results derived 
from the terms of each degree of the potential, taken 
separately, should concur — when the method is applied in a 
systematic manner — in attributing the forces to external or 
