39 
where, even according to Mr. Chambers’ high standard of 
accuracy, “ the variations do, in a rough manner, conform to 
the rule laid down.” The second part of the assumption in- 
volved in (1) is more doubtful, though Mr. Chambers does not 
criticise it. If that equation was strictly correct, the type 
of the diurnal variation in diderent latitudes would be the 
same, the amplitude only varying. As this is not strictly 
true, we. cannot expect equations (2) to be rigorous, and I 
never implied that they were. But if we can put the 
potential into the form of a product of a time function into 
a latitude function, it is clear that nothing can restrict the 
generality of those functions, for the value of a potential at 
the different points of a closed surface is quite arbitrary, and 
is subject to no condition. I may therefore choose any 
functions T and U, which best accords with observation. 
Being unable to discover the “ delusion ” in my own vfork 
I naturally look into Mr. Chambers’ paper to see in what 
way he supports his charge. Supposing, at any time, 
the variable part of the magnetic potential to be expanded 
into a series of a spherical harmonics; we may obtain 
according to the assumption I have made, the potential at 
any future time (t) by simply writing (X-f-Q for X the long- 
titude. Mr. Chambers does this in a roundabout way in 
his equations (6), (7), and (8). Each term of the series thus 
obtained, consists of the product of a function of (X + 0 into 
a latitude function ; but we can combine only those tesseral 
harmonics which are of the same type, so as to appear for a 
given longitude in the form TU. From this, Mr. Chambers 
seems to conclude that if the potential, which has been 
expanded, is of the form TU, all coefficients must vanish 
except those belonging to some one single type. The con- 
clusion is wrong, for we can expand any function of a 
latitude and longitude into a series of surface harmonics, and 
it is impossible to say, ch priori, whether any coefficients in 
