intensity of the transition from the first excited state ($J=1$) to the ground state ($J=0)$ close to the Galactic plane ($b<5^\circ$), and additionally comprises a few CO clouds at higher Galactic latitude, as well as the Large Magellanic Cloud and the Andromeda galaxy M 31. Due to the composition of the map, the angular resolution is not uniform, but the best resolution of $\simeq 7\farcm5$ is reached for a large area around the Galactic plane.

From this map, it is possible to derive the line intensities of the higher harmonics, assuming thermal equilibrium: The frequency $\nu$ for a transition from a state of rotational quantum number $J$ to a state with quantum number $J+1$ of the CO molecule follows from elementary quantum mechanics: The rotational energy of a molecule with moment of inertia $\theta$ and angular momentum $\bmath{J}$ is $E_\mathrm{rot}=\bmath{J}^2/2\theta=\hbar^2\cdot J(J+1)/2\theta$. In the last step the quantum number $J$ was introduced. For the transition energy between two subsequent rotation levels, one obtains: $$\nu_{J\leftrightarrow J+1} = 2Qc\cdot(J+1) = 115\mbox{ GHz}\cdot(J+1)\mbox{,}$$ where $Q=h/8\pi^2 c\theta$ is a measure of the inverse moment of inertia of the molecule and $c$ denotes the speed of light. Thus, the spectrum consists of equidistant lines. The relative 