For the innermost stationary orbit, for which _n_ = 1, the ionizing work A₁ will accordingly be equal to the product of the constants _h_ and K of Planck and Balmer respectively; and for the orbits No. 2, No. 3, No. 4, etc., the values will be respectively ¼, ¹/₉, ¹/₁₆, etc., of this product. From the charges on the nucleus and the electron, which are both equal to the elementary quantum _e_ of electricity (see p. 90), and from the ionizing energy for a given orbit we can now find by the use of simple mechanical considerations the radius of the orbit. If we denote the radii of the orbits 1, 2, 3 ... by _a_₁, _a_₂, _a_₃ ..., we then obtain for the diameters 2_a_₁, 2_a_₂, 2_a_₃ ... the values 2_a_₁ = 1·056 × 10⁻⁸ cm. (or approximately 2_a_₁ = 10⁻⁸ cm.), 2_a_₂ = 4 × 10⁻⁸ cm., 2_a_₃ = 9 × 10⁻⁸ cm., etc. It is seen that the radii of the orbits are in the proportion 1, 4, 9 ..., or in other words the squares of the integers which determine the orbit numbers. It is in this proportion that the circles in Fig. 25 are drawn. We must remember, however, that we have here for the moment been thinking of the orbits as circles, while in reality they must in general be assumed to be ellipses. The foregoing considerations will, however, still hold with the single change that 2_a_ₙ will now mean, instead of the diameter of a circle, the major axis of an ellipse. Let us return to the formulæ Aₙ″ Aₙ′ ν = ----- - ---- _h_ _h_ K K and ν = ------ - ----- _n″_² _n′_² Here _n″_ denotes in the first formula the index number for the _inner_ of the two orbits between which the transition is supposed to take place, while in the second formula _n″_ denotes a definite series in the hydrogen spectrum. If _n″_ is 2 while _n′_ takes on the values 3, 4, 5 ... ∞ then in the Bohr model of the hydrogen atom this corresponds to a series of transitions _to_ the orbit No. 2 _from_ the orbits 3, 4, 5 ..., while in the hydrogen spectrum this corresponds to the lines in the Balmer series, namely, the red line (Hα) corresponding to the transition 3-2, the blue-green line (Hβ) to 4-2, the violet line (Hγ) to 5-2 and so on. If we now put _n″_ = 1 while _n′_ takes the values 2, 3, 4 ..., we get in the atom transitions to the orbit No. 1 from the orbits No. 2, 3, 4 ..., corresponding in the spectrum to what is called the Lyman series in the ultra-violet (named after the American physicist Lyman, who has carried on extensive researches in the ultra-violet region of the spectrum). Thus every line in the hydrogen spectrum is represented by a transition between two definite stationary states in the hydrogen atom, since this transition will give the frequency corresponding to the line in question.