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Newton’s ‘Crucial Experiment’

Kirsten Walsh writes…

In his first optical paper, Newton claims that he has performed an Experimentum Crucis, which proves that refrangibility is an original property of the light, not an effect of the prism:

    …the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.

This experiment and its role in Newton’s theory of colours raises some questions that I’m not really sure how to answer.  I hope you can help me.

Firstly, let’s have a closer look at this Experimentum Crucis:

Newton's Experimentum Crucis

White light travels from the Sun (S), through the first aperture (F), through the first prism (ABC), where it is refracted for the first time, producing an image on the first board (DE).  A small amount of light passes through the second aperture (G), producing an image on the second board (de).  A small amount of light passes through the third aperture (g), through the prism (abc), where it is refracted for the second time, producing an image on the screen (MN).  Newton “took the first Prisme in [his] hand, and turned it to and fro slowly about its Axis”, so that different parts of the refracted image could pass through the apertures to the second prism.  He took careful note of where each image appeared on the board MN.

Newton finds that each time a particular ray passes through a prism it refracts to precisely the same degree.  For example, light that refracts to 50 degrees at the first prism refracts to 50 degrees at the second prism as well.  Newton argues that this shows that refrangibility is an original and constant property of light.

Newton’s Experimentum Crucis was heavily criticised by his contemporaries.  Hooke, for example, argued that this experiment is not a crucial experiment, because it does not prove that colour is an original property of light.  Hooke believes that light becomes coloured as it passes through the prism, and Newton’s experiment does not convince him otherwise.

While colour is conspicuously absent from Newton’s discussion of this experiment, this line of criticism is extremely common.  For example, Newton’s contemporaries, Hooke, Huygens and Pardies, and more recently, writers such as Sabra and Bechler have all made criticisms along these lines.  As I have previously discussed, Newton used mathematics and measurement in order to achieve absolute certainty.  So it is no accident that Newton only discusses refrangibility and not colour in this experiment.

Newton concludes that white light is composed of rays of every colour in equal amounts, but he argues for this in two steps:

1)      Light is a “Heterogeneous mixture of differently refrangible Rays”; and

2)      There is a one-to-one correspondence between refrangibility and colour.

So, while the Experimentum Crucis only supports step (1), it is often mistaken as an argument for Newton’s conclusion.  Newton takes a great deal of care to establish (1) experimentally, but he seems to take little care at all to establish (2), and hence, the conclusion.  In his first optical paper he simply asserts it as proposition 2; in his reply to Huygens he asserts it as a note to his definitions.

This raises two questions.  Why did Newton take so little care over step (2)?  How did Newton’s main opponents miss this lack of care?

3 thoughts on “Newton’s ‘Crucial Experiment’

  1. Hey Kirsten,
    interesting post! This whole project sounds great – I just stumbled across this page and am now certain to follow avidly. I’m a grad student just over in Sydney embarking on a project about Robert Hooke, so a couple of things interested about this post – have you had any more thoughts on it?

    First and quickly, it seemed to me reading Newton’s paper that he’s not completely cursory about your step (2). Like you say it’s asserted as his proposition 2, but it’s backed up by props. 3 & 4; “When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it”. And in the experiment he recommends to the RS at the end of his paper, he refers again to the impossibility of producing a different colour from a particularly refracted ray.

    Still, you’re right – he doesn’t take that much time to establish (2). But perhaps because it’s commonly accepted? Hooke, at least; Hooke’s quite happy with the one-to-one correspondence between refrangibility and colour. (It’s also part of his theory). In fact, Hooke seems quite happy to agree to most of what Newton says, if only Newton had framed his ‘theory’ as an ‘hypothesis’:

    “Nor would I be understood to have said all this against his theory, as it is an hypothesis; for I do most readily agree with them in every part thereof, and esteem it very subtil and ingenious, and capable of solving all the phænomena of colours: but I cannot think it to be the only hypothesis, nor so certain as mathematical demonstrations.”

    What he doesn’t like is your step (1). And he doesn’t like it because he takes the Experimentum Crucis to be consistent with his hypothesis as well as Newton’s. Newton’s is not unique in ‘solving the phenomena’, and we can’t be certain that it is true.
    (That does seem like a pretty exacting standard to use to completely dismiss a hypothesis. I’m sure part of his dislike of Newton’s paper is not only that Hooke thinks he does the job just as well, but also he published 6 years earlier, in the Micrographia. But is he also taking the piss? Newton’s the one well known for not fingo-ing hypotheses and for demanding, as you say, absolute certitude.)

    So! as Hooke goes (not sure about Huygens or Pardies!) I think your (2) just isn’t something Newton needs to prove.

  2. Interesting, I dropped by because of Giants Shoulders carnival. I think in regard to 2, no-one argued otherwise. If colors were NOT 1 to 1 with refrangibility than either a) two colors would have the same angle of refraction, in which case they would mix, and this is seen not to happen with a prism. or b) there is some angle of refraction no color uses, and for visible light this was not seen either (they hadn’t seen spectral lines yet).

  3. Thanks for your comments; you’ve both given me a lot to think about.

    I think you’re both correct in saying that (a) there were good reasons to believe that there is a one-to-one correspondence between refrangibility and colour and (b) this correspondence was commonly accepted. I think this answers my second question: how come none of Newton’s contemporaries criticised step (2)? But I’m not sure that this answers my first question.

    Newton aspired to mathematical certainty in his theory of colours: for example, in a letter to Hooke he asserts that the science of colours is “Mathematicall & as certain as any part of Optiques”. So step (2) is a really important step for Newton’s theory: he basically claims that everything that he has carefully and rigorously established with respect to refrangibility can now be applied to colour. But he does little more than to assert the one-to-one correspondence. I agree with Ian that Newton’s paper contains some evidence for this, but it is almost as though Newton is presupposing this one-to-one correspondence when he presents this evidence – but this is a strong claim, and I need to think about it some more. In any case, I think we agree that Newton isn’t being very rigorous here.

    I think the reason Newton isn’t very rigorous about this one-to-one correspondence is because he can’t be. It would have been impossible to give a mathematically precise proof of the one-to-one correspondence between colour and refrangibility. This would have involved assigning a precise hue to each angle of refraction. While it is possible to give a precise numerical value to every angle of refraction, it would not have been possible to do this for colour. One reason for this is that distinguishing between colours is subjective, so it is difficult to establish where the boundaries between different colours lie. Science of perception is now well-developed enough to have statistical and psychological measurement techniques that can make sense of subjective reports of similarity and difference of hue, but these techniques weren’t available to Newton. Another reason for this is that there were important questions about colour that needed to be resolved, such as, how many colours are there? Hooke and Huygens thought there were only two colours (although they disagreed about which two), but Newton thought the number of colours was indefinite.

    I have so much more to say about this! But I think I’ll leave it there for now.