How we cite our quotes: Citations follow this format: (Book.Chapter.Paragraph)
Quote #4
"Somebody put a drop [of Mr. Casaubon's blood] under a magnifying-glass, and it was all semicolons and parentheses." (1.8.32)
Here's another lens metaphor! Mrs. Cadwallader is making fun of Mr. Casaubon to Sir James Chettam. She thinks that he's too old and passionless to marry a pretty young girl like Dorothea, and Sir James agrees. And since the common belief in the early nineteenth century was that passion came from the blood (which is where we get the expression "hot-blooded" to mean "passionate"), Mrs. Cadwallader illustrates her point by suggesting that Mr. Casaubon doesn't have any blood at all – it's all punctuation marks because that's all he cares about.
Quote #5
He was ambitious of a wider effect: he was fired with the possibility that he might work out the proof of an anatomical conception and make a link in the chain of discovery. (2.15.6)
Mr. Lydgate's scientific ambitions extend beyond the Fever Hospital or his Middlemarch patients: he wants to discover something new about the basic unit of life that will make a "link in the chain of discovery." He wants to leave something behind him that will benefit the scientific community forever.
Quote #6
There was fascination in the hope that the two purposes would illuminate each other: the careful observation and inference which was his daily work, the use of the lens to further his judgment in special cases, would further his thought as an instrument of larger inquiry. (2.15.7)
Here's a reference to a "lens" that is literal, not metaphorical: Lydgate wants his scientific research (using the "lens" of his microscope) to parallel his "daily work" as a medical practitioner. He hopes that the general work he'll do as a researcher will benefit the particular cases he'll work on as a doctor, and vice versa. Eliot is suggesting that it can be beneficial to move back and forth between the particular and the general – which is exactly what she often does as a narrator.