14 Mr. D. D. Heath on Mr. Ferrel's 
If I were mainly writing for mathematicians, I should at 
once begin on his treatise of 1860, on which Mr. Ferrel's 
other papers and communications to ' Xature ' are founded; 
and my paper would not be long. But having rather in view 
readers who are not generally familiar with partial differential 
equations, and wishing to carry them along with me without 
impediment as far as I can, I will begin with a communica- 
tion to ' Nature ' (March 14th, 1872), which is in fact what 
was first brought to my notice and led me to further inquiry. 
It is headed " Ocean Currents," and forms part of a discus- 
cussion on the Gulf-stream and similar phenomena, in which 
Dr. Croll, Professor Everett, and a Dane, Professor Colding, 
are concerned. But it includes atmospheric motions in its 
scope. 
He begins with warnings against taking on trust " all the 
principles and theories based upon hjpotlietical forces which 
have come down to us from preceding generations, however 
plausible and however much sanctioned by authority they 
appear to be," with more in the same strain. But, after all, 
he adduces no example of such hypothetical assumptions of 
forces from older writers; and we shall see that it is he who 
is rather obnoxious to such a charge. 
He goes on to lament that Professor Colding has been 
" unsuspectingly led into error" by accepting from old text- 
books the statement that " if a particle of air at the equator, 
relatively at rest and therefore having a linear velocity in 
space of about 1000 miles an hour, is forced to move towards 
the pole, it will, on arriving at the parallel of latitude where the 
earth's surface has a velocity of only 900 miles, still have its 
velocity of 1000 miles in the case of no friction''' (which, here 
and elsewhere, I understand to include pressure of the sur- 
rounding air), " and consequently have a relative velocity of 
100 miles; and, on arriving at the parallel of 60°, will have a 
relative velocity of 500 miles." 
I should agree that a bare statement like this in a text-book 
would be objectionable as, at the least, misleading. Matter at 
the equator can no doubt be " forced " to move all the way to 
the pole. But the velocity and direction with and in which 
it arrives there will depend upon the means taken to force it. 
It would never get there by any natural impulse or pressure 
originating in the equatorial regions. For it is one of the 
plainest of fundamental facts in Dynamics (though we shall 
see that Mr. Ferrel denies it) that, taking gravity to be directed 
to the centre of the earth, as it is very nearly, a mass situated 
anywhere near the surface, but unconnected with it and un- 
resisted by the air, if put in motion, will begin to move infixed 
