1 to continue

2 to proceed with

3 to go on with

1 derailment (railway accident)

2 to leave the rails

3 fig. to overstep bounds

4 fig. to have an extramarital affair

1 the right track

1 in succession

2 following closely

1 to continue

2 to follow after

3 to go on with

4 to succeed

5 to inherit

6 then

7 afterwards

1 one falls, the next follows (idiom); stepping into the breach to replace fallen comrades

2 advancing wave upon wave

1 to advance dauntlessly in wave upon wave (idiom)

1 night and day (idiom); continuous strenuous effort

1 to burn the midnight oil (idiom); to work continuously night and day

1 to follow the past and herald the future (idiom); part of a historical transition

2 forming a bridge between earlier and later stages