30 
down to either two only or four only, and this, without our 
being made aware that any such process was in operation. 
A little later on the writer elects to work further with the 
second term of equation (8) only, expressly setting aside the 
subject matter of the third term, as a detail which it was 
not his intention then to enter into. And yet, in the mean 
diurnal variations of declination for the year, the amplitude 
of the element which has half a day for its period is to that 
which has a full day for its period, — at Greenwich as 1’96 
to 2*88, and at Bombay as 1 to 1. Hence, as the East com- 
ponent of the horizontal variation, in fact, differs in this 
respect, very slightly from the declination, it is likely that, 
in throwing out from consideration the element of the po- 
tential that has half a day for its period, he discards quantities 
of the same order as those that he retains, and his hypo- 
thetical potential must, consequently, differ largely from that 
of nature. 
But the appearance of generality of the assumed time- 
function (T) would seem to have deceived even the writer 
himself. The function cannot, we see from equation (8), 
have any other form than either sin(0 + £ + sin2(0 -f- £ -f X) 
where £ is a constant,^ and, consequently, in comparing with 
observation his conclusion from equation (9), that X should 
be a maximum or minimum when Y vanishes, the writer 
should have chosen only the single- wave elements of the 
observed variations which have the full day for their period, 
or the similar elements which have half a day for their 
period but his description of the comparison]; refers to the 
whole complex variations, and it is obvious that he did not 
recognise how greatly his previous assumptions had put 
restrictions on the generality of form of T. At least it 
might be taken as obvious until it is found, a little further 
* That is, unless the potential is carried beyond terms of the second degree. 
t And a pair even of these elements is fit for the comparison only on the assumption 
that it belongs wholly to the first or second degrees of the potential of nature. 
. X Pages 124 and 125 of the paper. 
