The phrase "and they were continually" is correct and usable in written English.
It can be used to describe an ongoing action or state that was happening repeatedly over a period of time.
Example: "The children were playing in the park, and they were continually laughing and running around."
Alternatives: "and they were constantly" or "and they were perpetually".
The boys skied blindly, shouting and calling to one another, and they were continually going off the trail and, c'mon, falling.
They appreciated the opportunity cost of their own time, and they were continually aware of their ever-present obligations mail to be answered, callers to attend to, and so on.
The surviving texts are the notes that Theophrastus used in teaching, and they were continually revised.
The curators see the project as open-ended and they are continually adding artists.
These are available in the literature, and given in the references, and they are continually and rapidly growing.
The correct coordinates of these fixed stations are known, and they are continually compared against the coordinates reported by GPS.
There are opportunities to gain related skills and knowledge in many areas of the curriculum and they're continually being developed".
The people behind search engines decide which sites get listed and in what order, and they are continually readjusting the code that determines those rankings.
And they are continually getting better at it.
"Compared to my old bank, it's really, really transparent, the fees are really fair, and they're continually working on bringing fees down and to make transfers more instantaneous.
"As an audience," said Christine Chariton, the senior director of marketing at GlobalSpec, "engineers and other technical professionals have many common traits: They are problem solvers, they like to be challenged, they enjoy tinkering with products and designs to make them better, and they are continually looking to be educated and build their knowledge base.
