Newton's Two Falling Globes experiment

• Text of Of Gravity & Levity
• Comments on the Diagram
• McGuire and Tamny's Commentary
• Modern mathematical comments on the experiment

In 1664-5 Newton composed a series of essays and notes called Questiones Quædam Philosophicæ (Certain Philosophical Questions) This has been published by McGuire and Tamny with a detailed commentary. In Of Gravity and Levity Newton outlines a mechanism for gravitation based on the descent of streams of particles which drag bodies down by passing through their pores. He suggests some experiments which may be intended to test this theory by deflecting the streams or changing the body's structure. One of these involves two falling globes.

Transcribed in modern spelling: ``In the descent of a body there is to be considered the force which it receives every moment from its gravity (which must be least in a swiftest body) and the opposition it receives from the air (which increases in proportion to its swiftness). To make an experiment concerning this increase of motion, when the globe a has fallen from e to f, let the globe b begin to move at g so that both globes land together at h.

According to Galileo, an iron ball of 100 Florentine pounds (that is 78 lb at London in avoirdupois weight) descends 100 Florentine braces or cubits (or 49.01 ells, perhaps 66 yards) in 5 seconds.''

Newton presumably intended the experiment to demonstrate some aspect of falling bodies dependent on air resistance or his mechanism for gravity. (However, McGuire and Tamny, have suggested a different interpretation.)

Using modern (school) mathematics one could use the experiment to measure the acceleration due to gravity, g, and a constant associated with the decrease in acceleration as the body speeds up (due to air resistance or Newton's gravitational hypothesis.) This would be possible without a clock but would require the data supplied by Galileo's experiment. It would be necessary to perform the Two Falling Globes experiment with globes of the same mass and size as Galileo's. Since Newton carefully noted the mass and composition of the ball, which together define its size, this would not be a problem.

I am not suggesting that Newton thought this all out in detail, and certainly not that he worked out the necessary differential equations (which were beyond him at the time.) However, it is not unreasonable to assume that Newton, with his remarkable physical intuition, was able to grasp some part of it.

In particular, the simplest result is that in the absence of air resistance or other effects dependent on the speed of the globes, the distances ef, gh and eh obey

sqrt ( eh ) = sqrt ( ef ) + sqrt ( gh )

The distance fg is adjusted as Newton prescribes, so that a and b land together at h, and the three other distances are measured. If the measured distances do not satisfy the above equation, we have demonstrated the effect of air resistance (or whatever) and got some idea of its scale from the size of the disagreement.

Did Newton intend the experiment to show that, in the real world, the distances are not what you would expect for the ideal case (without air resistance or effects due to his mechanism for gravity), perhaps without being exactly sure what you would expect in the ideal case?

There are also more sophisticated uses for the experiment which are still plausible. For instance, we could make the approximation that a and b accelerate uniformly over the short ranges ef and gh which simplifies the analysis considerably. It would also be possible to repeat the experiment with globes made of a range of materials which might respond differently to the effects of air resistance and Newton's mechanism for gravity. Nevertheless, with the evidence available, we can only speculate about Newton's precise intention.

It is also interesting to note how practical it would be for Newton to carry out the experiment, since it would not require a clock, and could be done with buildings available to him at Trinity College. The similarity between the battlements at the top of the diagram and Great Court at Trinity underlines this. To study falling bodies with experiments involving clocks, requires accuracy better than a second or high towers - preferably both. It is tempting to say that Newton designed an experiment to avoid this.

Two Falling Globes seems to be more than a thought experiment since it is would be possible with the materials available, although there is no indication that Newton ever intended to perform any of the mechanical experiments in Questiones. As a test of the effects of air resistance and his mechanism for gravity it foreshadows the exhaustive pendulum experiments of his later life intended to disprove the aether. Above all it illustrates the nature of Newton's Questiones, in which he submits his own and others' theories to a barrage of proposed experiments. Newton's supreme genius in physics was his combination of abstract theoretician and skillful experimentalist with the ability to bridge the two with practical but decisive experiments.