16 Mr. D. D. Heath on Mr. Ferrel's 
principle of the conservation of areas must be satisfied; and 
consequently, when it arrives at the parallel of 60°, where the 
earth's surface has a velocity of 500 miles, it must have a 
velocity of 2000 miles." 
My first impression on reading this was that Mr. Ferrel 
could not mean to propound it as his own doctrine ; but must 
have intended some argumentum ad hominem against Professor 
Colding, though I could not see it. But it appears to be his 
serious belief, stated in his treatise of 1860 (parag. 22), and 
repeated and made the basis of calculation in a summary 
of his doctrine, by himself, in Silliman's Journal (2nd ser. 
vol. xxxi.). Now this " principle," as applicable to this case, 
is that, when a body is moving subject only to the action of a 
force directed to a fixed centre, the imaginary line which joins 
it with that centre sweeps out equal areas round it in equal 
times, however much the body may approach to or recede 
from it in the course of its orbit. Here, the centre of force is 
the centre of the earth; and the body moving over the surface 
is always very nearly at the same distance from it; and so, to 
preserve the equality of areas, it must preserve very nearly an 
equable velocity. Mr. Ferrel seems to imagine that the force 
shifts along the axis of the earth so as always to keep abreast 
of the moving body, and so to give it a corkscrew motion round 
the axis, but drawing it into continually narrower and nar- 
rower circles, and so giving it greater and greater velocities. 
What gravity really does is to keep the moving body, together 
with air and sea and all loose matter, from flying off into 
space, leaving the solid part to spin by itself. 
Mr. Ferrel goes on with his charge against Professor Col- 
ding : — " Adopting, thoughtlessly and very naturally, the 
erroneous principle which is usually taught " (that, namely, 
which he impugned above, that a body will keep the velocity 
and direction once given to it until interfered with) " he esti- 
mates the amount of deflecting force due to the earth's rotation; 
and the result is that his force is just one half of what it really 
is." I have not read Professor Colding's paper, and so can- 
not say whether he has made any mistake. And Mr. Ferrel 
seems to me to have confused himself about these " deflecting 
forces," and so not to be very intelligible to others. But I 
understand the charge to mean that the Professor has here 
estimated the relative eastward or westward motion as due to 
the earth's spinning under the moving body which keeps its 
original velocity, instead of doubling the effect by the imagi- 
nary " conservation of areas " principle. If so, he has cer- 
tainly so far done the right thing. 
But then he adds that the Professor has " entirely neglected 
