But it is not known whether this principle will remain true in the case of other physical laws. We can always proceed on the assumption that it does remain true. Thus it is always possible to construct physical laws in such a way that they retain their form when referred to moving coordinates. The ultimate ground for formulating physical laws in this way is merely a subjective conviction that the principle of relativity is universally true. There is no _a priori_ logical necessity that it should be so. Hence the Principle of Relativity (so far as it is applied to phenomena other than electromagnetic) must be regarded as a _postulate_, which we have assumed to be true, but for which we cannot adduce any definite proof, until after the generalisation is made and its consequences tested in the light of actual experience. [P. C. M.] Note 5. See “Electrodynamics of Moving Bodies,” p. 5-8. Note 6. Field Equations in Minkowski’s Form. Equations (_i_) and (_ii_) become when expanded into Cartesians:— ∂_m__{_z_}/∂_y_ - ∂_m__{_y_}/∂_z_ - ∂_e__{_x_}/∂τ = ρν_{_x_} } ∂_m__{_x_}/∂_z_ - ∂_m__{_z_}/∂_x_ - ∂_e__{_y_}/∂τ = ρν_{_y_} } ... (1·1) ∂_m__{_y_}/∂_x_ - ∂_m__{_x_}/∂_y_ - ∂_e__{_z_}/∂τ = ρν_{_z_} } and ∂_e__{_x_}/∂_x_ + ∂_e__{_y_}/∂_y_ + ∂_e__{_z_}/∂_z_ = ρ (2·1) Substituting _x₁_, _x₂_, _x₃_, _x₄_ and _x_, _y_, _z_, and _i_τ; and ρ₁, ρ₂, ρ₃, ρ₄ for ρν_{_x_}, ρν_{_y_}, ρν_{_z_}, _i_ρ, where _i_ = √(-1). We get, ∂_m__{_z_}/∂_x₂_ - ∂_m__{_y_}/∂_x₃_ - _i_(∂_e__{_x_}/∂_x₄_) = ρν_{_x_}{ = ρ₁ } - ∂_m__{_z_}/∂_x₁_ + ∂_m__{_x_}/∂_x₃_ - _i_(∂_e__{_y_}/∂_x₄_) = ρν_{_y_} = ρ₂ } ... (1·2) ∂_m__{_y_}/∂_x₁_ - ∂_m__{_x_}/∂_x₂_ - _i_(∂_e__{_z_}/∂_x₄_) = ρν_{_z_}{ = ρ₃ } and multiplying (2·1) by i we get ∂_ie__{_x_}/∂_x₁_ + ∂_ie__{_y_}/∂_x₂_ + ∂_ie__{_z_}/∂_x₃_ = _i_ρ = ρ₄ ... ... (2·2) Now substitute _m__{_x_} = _f₂₃_ = -_f₃₂_ and _ie__{_x_} = _f_₄₁ = -_f₁₄_ _m__{_y_} = _f₃₁_ = -_f₁₃_ _ie__{_y_} = _f_₄₂ = -_f₂₄_ _m__{_z_} = _f₁₂_ = -_f₂₁_ _ie__{_z_} = _f_₄₃ = -_f₃₄_ and we get finally:— ∂_f₁₂_/∂_x₂_ + ∂_f₁₃_/∂_x₃_ + ∂_f₁₄_/∂_x₄_ = ρ₁ } ∂_f₂₁_/∂_x₁_ + ∂_f₂₃_/∂_x₃_ + ∂_f₂₄_/∂_x₄_ = ρ₂ } ... (3) ∂_f₃₁_/∂_x₁_ + ∂_f₃₂_/∂_x₂_ + ∂_f₃₄_/∂_x₄_ = ρ₃ } ∂_f₄₁_/∂_x₁_ + ∂_f₄₂_/∂_x₂_ + ∂_f₄₃_/∂_x₃_ = ρ₄ } Note 9. On the Constancy of the Velocity of Light. Page 12—refer also to page 6, of Einstein’s paper. One of the two fundamental Postulates of the Principle of Relativity is that the velocity of light should remain constant whether the source is moving or stationary. It follows that even if a radiant source S move with a velocity _u_, it should always remain the centre of spherical waves expanding outwards with velocity _c_.