It became increasingly clear that if further progress was to be made in high energy nuclear physics by experiments using artificially accelerated particles some new principle must be found that would cheapen the cost per GeV. It was lucky for CERN that just at the time a European machine was being considered this new principle was discovered. The problem was simple enough. A cheaper machine could be built if the amplitudes of the free and forced oscillations of the accelerating particles could be decreased in some way so that the vacuum chamber size and the cross-section of the magnet ring could be reduced. The simplest way to reduce the amplitude of the free oscillations is to increase the frequency by increasing the restoring force, and although this is easy to achieve in the vertical direction by increasing the magnetic field gradient, the condition for horizontal stability is violated if n exceeds unity. The new principle discovered by Christofilos and Courant, Livingston and Snyder increases the frequency of the betatron oscillations by alternating the sign of the gradient of the magnetic field. The structure of the magnet is no longer uniform round the ring with a constant gradient but is broken up into sectors whose gradient is alternatively positive and negative.