of Natural Philosophy. : 137 
forces are not equal. But the - demonstration is such as 
would prove them no less equal, in all cases whatever.— 
We must confess ourselves ata loss to assign any consistent 
meaning to the term “ centrifugal force,” in relation to or- 
bits not circular. Is this force measured by the distance by 
which a revolving body would be more remote from the 
centre, in a given small time, if the centripetal force were 
suspended, than it actually is while the centripetal force’ 
acts? If so, the centripetal and centrifugal forces are al- 
ways equal, for the same point of an orbit, whatever be its 
figure. Or is it measured by the absolute increase of dis- 
tance from the centre, which would take place in a given 
sul peal body ci soo st be to its projectile 
orce? If so, in passing from the higher to the lower a 
is ic orbit, the een esa ites io 
quantity. : 
‘Lemma 4. The tnferente concerning ‘the in of on 
arc to the chord and tangent in their vanishing state, is in- 
conclusive when the tangent is less than the are, as it will be 
in certain positions of the subtense. The demonstration 
may be rendered complete in the following manner :—AB: 
AD+DB:: AC: AB+BC. But AB+BC is ultimately 
equal to AC ; hence AD+ DB is ultimately equal to AB, 
and more is the are AB-equal to the ¢ chord AB. | 
» The first Part of Book Ill. which treats of Hivdcminies: 
presents us with several instances of explicit or implied er- 
ror; particularly prop. 2, prop. 13, Schol. and propositions 
24, 26, 31, and 86. But we have no room to dwell upon 
them; and shall therefore a apis to the second Part, 
whieh i is devoted to Pneum : 
_ Prop. 51. The force with -sehich. vied strikes. a sail of 
: i - edition tion, 
The phrase a angle of incidence” ¥ 
sense as in optics: it is now same in the se sense 
of mechanics. But this correction goes but little way a 
wards freeing the proposition from exception. If the sai 
‘be supposed confined to move in the same direction w with 
the wind, which the demonstration seems to imply, a reso- 
lution of the force on a third ee of was ne- 
eessary, which — have wang accanil part of the force 
Vou. Ill.....No. 
