of Natural Philosophy. 135 
tion is lost in passing from one plane to another. The dem- 
onstration of the 38th is also inconclusive, because it has 
not been previously shown that the total loss of motion’ in 
passing through a set of planes becomes evanescent, 
the planes become indefinitely iene — their: suc- 
cessive inclinations indefinitely sm 
Prop. 47. The demonstration shee that we may. ‘ton a 
body by assembling particles round a given point, such’ that 
the body shall balance itself about this point; but it by no 
means Stes that when the body is given, a point about 
ps: it will balance itself can be found 5 7—much less that 
this point, as th or all 
tions of the same — PMT AIRE AT arsete wed 
Prop. 49. ‘The di pi | empl iene 
ly: intelligible. “There was the less reason for this inaceura- 
cy, as in Rutherforth, from whom the cote is copied it 
is drawn correctly. 
Prop. 51. The demonstration of this important thiotom 
is less general than the enunciation requires, by being con- 
- fined to the case in which the bodies move in the same 
. ~The statement with which the first corollary begins 
is true only under such pekeacte creme as ane tia can erie 
ly: be. “supposed able to apply. 
Prop. 56. In the great majority oki instances in \whichake 
screw is employed, the resisting force is: not bgcehanics.# 
through an inclined. plane, as the demonstration su 
it would be far more simple and satisfactory to infer the law 
of equilibrium directly from the relative velocities of the 
points of application of the power and resistance. 
Prop. 57. Schol. 1.. “In all compound m dined 
will be an. on when the sum of the powers are to. 
the weight, as the velocity | of the weight is to the sum of 
the velocities of the powers.” No interpretation can be put 
upon this statement which will render it true.” ‘The error 
arose, we presume, in some such manner as the followi 
_ Ttwas apparent: that i in compound mneebineys (or rather im 
3 eral resistances in 
souilibrie,) tha og sam of the oduets Hf ee each inte 
its velocity, was equal to ie sea of the 
weights each into its sabe. 
pearance of being capable of sesoletion into an analogy 
