PRESIDENTIAL ADDRESS. 435 
This is surrounded on all sides but one (towards South America) by a zone of 
depression, the waist of the pear. This, again, is surrounded on all sides but one 
(towards Japan) by a zone of elevation, the protuberant part of the pear; and 
finally we find the nose of the pear in the central Atlantic between the Madeiras 
and the Bermudas. I do not, however, wish to emphasise the resemblance of the 
surface to a pear or any other fruit, but prefer to describe it as an harmonic 
spheroid of the third degree. Another way of regarding it would be as a surface 
with ridges and furrows.- From a place in the South Atlantic there run three 
ridges: one north-westwards across America, a second north-eastwards across 
Atrica and Asia, and the third southwards over the Antarctic continent, continu- 
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Fig.!2. 
ing northwards across Australia nearly to Japan. From the Sea of Okhotsk there 
run three furrows: one south-westwards across Japan, the Malay Peninsula, and 
the Indian Ocean; a second south-eastwards across the Pacific; and the third 
northwards over the Arctic Ocean, continuing southwards by way of the Atlantic. 
Harmonics of the first and third degrees have in common the character of giving 
depression at the antipodes of elevation ; the harmonics of the second degree give 
depression at the antipodes of depression and elevation at the antipodes of eleva- 
tion, The maxima of the harmonics of the first and third degrees are found to 
Fig. 13. 
be rather greater than the maximum of the harmonic of the second degree. Of 
three quantities to be added together the two larger ones agree in giving depression 
at the antipodes of elevation; a result which is in accordance with the fact that 
most continents have oceanic antipodes. 
When we superpose the effects represented by all the various harmonics of 
the first, second, and third degrees, so as to make, as it were, a composite 
photograph of all the various elevations and depressions represented by them 
severally, each in its appropriate amount as determined by the harmonic analysis, 
we find the curve shown in fig. 14 as the theoretical curve of separation between 
regions of elevation and depression which are approximately equal in area, 
FF2 
