Definition of glance one's eye in US English:

glance one's eye

phrase

archaic
  • Look briefly.

    ‘he had glanced his eye over all the folios of my copy’
    • ‘Initially, I had glanced my eye over the weight-loss plan and dismissed it as a passing fad - and, more importantly, a grossly unhealthy one.’
    • ‘But the momentary apprehension was dispelled by hope and valour; and every man, says the marshal of Champagne, glanced his eye on the sword or lance which he must speedily use in the glorious conflict.’
    • ‘At first glance my eye goes up to that ball of flame on the right.’
    • ‘When I landed on the hard ground I murmured at the mean treatment of the sheep, and, glancing my eye upward, saw him looking at me from the roof of the house.’
    • ‘‘Indeed, your example is an unfortunate one for your argument,’ said Holmes, taking the paper and glancing his eye down it.’
    • ‘As he glanced his eye rapidly over the fatal list, he was much moved at finding there the names of more than one who had some claim to consideration in the army.’