so that the total force can be divided into three components corresponding to the three brackets of expression (12); the first component has a vague analogy with the mechanical force due to the electric field, the other two with mechanical forces due to a magnetic field; to complete the analogy I can, under the first point, replace by in equations (11), so that X1, Y1, Z1 only depend linearly on the velocity ξ, η, ζ of the attracted body, since C has disappeared from the denominator of (11bis).
We pose then:
(13)
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it follows that C had disappeared from the denominator of (11a):
(14)
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and there will also:
(15)
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Then λ, μ, ν or is a kind of electric field, while λ', μ', ν' or rather is a kind of magnetic field.
3° The postulate of relativity would require us to adopt solution (11) or solution (14) or any solution that would inferred by using the first remark; but the first question that arises is whether they are compatible with astronomical observations; the discrepancy with Newton's law is of the order ξ², that is to say, 10000 times smaller when it were of order ξ, that is to say, if the propagation happens with the speed of light, ceteris non mutatis; it is permissible to hope that it will not be too great. But only a thorough discussion will be able to teach it to us.
- Paris, July 1905.