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other considerations which have been neglected. All this is somewhat 
tentative, but the actual process is the only one by which, with our present 
mathematical resources, the results which have been obtained can be arrived 
at. And that is the reason why in the problems connected with the lunar 
theory it is necessary to assume in the first instance that the earth is at rest. 
Now I believe that a great many of the misconceptions — as I believe them 
to be — which Mr. Reddie has entered into, would be entirely removed if he 
could only satisfy his own mind of the fact, of which my own mind is 
perfectly satisfied, that in considering the motion of bodies, it is immaterial 
whether any other motion which they may have at the same time is taken 
into consideration or not. I can explain myself better by an instance. The 
motion of the moon round the earth would be the same whether the earth is 
supposed to be in motion or at rest ; and the action of gravitation takes 
place upon a body just in the same way whether that body is at rest or in 
motion. I could give experimental illustrations of this ad nauseam ; but I 
will confine myself to one simple illustration. Suppose I have two similar 
balls, and I project one forward horizontally, while at the same time I let the 
other drop ; it will be found that the action of gravitation upon these two 
balls is precisely the same : they will reach the floor precisely at the same 
instant. That simple experiment proves that the action of gravitation is the 
same in both cases 
Rev. Dr. Irons. — Will you explain whether you mean that this would be 
the result whatever amount of force was used to project the ball ? 
Mr. Brooke. — Whatever the amount of force — if it were projected a 
thousand miles. 
Mr. Reddie. — There is no issue between Mr. Brooke and me on that 
point, though I don’t admit that his reasoning from that fact is valid. 
Mr. Brooke. — I merely adduce that as evidence that the obedience of a 
body to the law of gravitation is not affected by its having any other motion 
at the same time. So in the same way the obedience of the moon to the 
law of gravitation, which brings it towards the earth, is not affected by the 
consideration whether the earth be in motion or at rest at the same time. 
But the necessity for simplifying the considerations of motion might be 
illustrated in a variety of different ways. For instance, suppose that we 
take the case of a steam-vessel. It may at the same time be going under 
steam in a certain direction, and it may have a wind, constant or variable, 
blowing upon it, which would tend to drive it in another direction. If we 
wished to investigate the circumstances in any particular part of the ma- 
chinery or point in circumference in the wheel or screw, how should we 
proceed ? We should not begin by taking into consideration the path in 
space in which this point we wish to consider is travelling in obedience to 
the propulsion of the vessel itself, and also in obedience to the wind, and in 
obedience to the impulse of the steam-engine ; but we should simplify our 
considerations by supposing the vessel to be at rest, and by considering 
simply the relation of the motion of the point in the wheel to the direction 
in which it is driven, and afterwards we might add the compound motions to 
