18 Mr. D. D. Heath on Mr. Ferrel's 
whether he makes any claim to a discovery in this matter. 
When the mathematical investigation of the motions of a fluid 
surrounding the rotating earth is made to commence, as by 
Laplace and Airy, and by Mr. Ferrel in his paper of 1860, 
with the most general equations, it is at once evident to in- 
spection that the terms which suggest these "deflecting forces" 
really express the effect of passing from formulas adapted to 
a fixed to those adapted to a revolving observatory, as I will 
point out more clearly below. But 1 have to confess that this 
simple interpretation had not occurred to me till I had pon- 
dered for some time over Mr. Ferrel's papers. 
I wrote a paper in the Philosophical Magazine (March 
1867) on Deep-Sea Tides, based on Airy's "Tides and Waves"' 
in the Encycl. Jfetrop., but intended to be less abstruse and 
formidable. And I deduced these two terms in the way indi- 
cated by Airy (par. 87 and 88, where he also calls them the 
representatives of "forces"), making one term the expression 
of the alteration of relative motion by the mere passage north 
or south, as explained in the passage first quoted from Mr. 
Ferrel above, and the other the expression of the effect of the 
impressed east or west velocity by virtue of which the mass is 
carried outward or inward in the plane of the small circle of 
latitude (a so-called "centrifugal force"), and so throwing it 
southward or northward along the surface. And though I 
had to prove in the course of the investigation that "these 
forces counteract each other " as regards acceleration and 
retardation, I did so without further reflection or inference. 
I hope I have made it sufficiently plain that the two points 
Mr. Ferrel insists on in this communication — the positive one, 
that the principle of the conservation of areas requires an 
accelerated spiral motion in bodies impelled northwards, and 
the negative one, that an impulse given to a free body along 
the surface of the earth will not generally send it along a great 
circle — are utterly unfounded and erroneous. I now proceed 
to the paper of 1860 referred to by Dr. Haughton; and. still 
addressing myself mainly to the same class of readers, 1 will 
first notice some prominent points in the treatment and results, 
and then say a few words on the mathematical working*. 
1. His purpose is not to trace the course and effect of any 
accidental disturbance in the atmosphere or ocean, but the 
permanent and necessary motions, pressures, and shapes which 
must arise and subsist in virtue of the causes of motion which 
are permanently at work. In an ideally " perfect " fluid, and 
* It appears that the substance of this paper was distributed in pamphlet 
form by the Smithsonian Institute in Europe and America ; which I 
suppose has helped Mr. Fen-el's reputation. 
