The crane worker has been transferred to a hospital in Swansea for further treatment, having originally been taken to the Royal United Hospital in Bath.
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A partial solar eclipse can pose more risk to eyesight than a full one, scientists have warned.
The power went out at around 12pm and reports suggest that up to 8,000 homes were affected.
The USA will have a total eclipse but the South West will be able to see part of the sun covered by the moon.