APPLICATION OF MATHEMATICS IN METEOROLOGY. 217 
of air as the generating energy of the cyclonic vortices have 
been assumed, quite apart from the great excess of tempera¬ 
ture in the tropical zones which produces the general vortex 
covering a hemisphere. Ferrel assumed that the hemi¬ 
spherical vortex and the local vortex are similar in struc¬ 
ture, but quite independent of each other in the sources of 
their energy. He drew a bounding surface around a mass 
of air warm or cold at its center, as the case might be, and 
discussed the resulting vortex. The laboratory confirmed 
the derived circulation by placing water in a cylindrical 
vessel rotating as a whole about a vertical axis, the central 
portions being heated or cooled, or else having a vertical 
central current produced mechanically. There was no math¬ 
ematical objection to the Ferrel vortex itself, nor to the lab¬ 
oratory experiment, until it was attempted to match these 
results with the observed atmospheric facts. Meteorologists 
who were in anyways critical have found such difficulty in 
accounting for the local supply of central heat as to be quite 
doubtful about the value of Espy’s source of energy, and this 
was reluctantly adopted by Ferrel himself. The Weather 
Bureau Observations of 1896-97 traced out the stream lines 
of circulation with sufficient exactness to terminate this part 
of the discussion, by showing that in the local cyclones and 
anticyclones the air does not circulate as the Ferrel vortex 
requires. Hence, we conclude that FerreFs application of 
mathematical analysis to the explanation of cyclonic obser¬ 
vations is not satisfactory. This eliminates a long section 
from the literature of meteorology. 
(2) The German school of meteorologists began with an¬ 
other type of vortex motion, having also a beautiful mathe¬ 
matical analysis, depending upon a local overheated central 
column. Here, again, the objections are prohibitory, first as 
to the origin of the cyclonic heat for vertical convection, and, 
second, as to the nonconformity of the observed stream lines 
with the theoretical vortex. These two types of vortices are 
entirely distinct from each other: FerreFs has a cylindrical 
bounding surface, a zero velocity where the direction of gyra- 
