As I see it, she's basically weighing the value of science and religion. Religion is a "fine invention," and has it's uses and merits--perhaps to console or embolden, for example--but when you run into some of the many physical realities of life, no word or verse is going to cure a bacterial infection or mend a severed limb. I see one explicit image of "seeing," the seeing done by the Gentlemen, and two implicit images of seeing, that of the Microscope, and by contrast, that of Faith. To me, these elements imply man, science and religion respectively. It's an interesting question to reflect on now, far beyond Dickinson's time, how the domains of science and religion were previously antagonized, mutually exclusive entities, but that now the tools of science are slowly beginning to “see” parts of the religious domain, explaining some religious experiences in terms of brain chemistry and neuroscience. Religion however, as far as I am aware, has not made any new revelations in the scientific community. I don't really understand why she capitalized Emergency, unless for a sense of symmetry or to better direct attention. The emergency, as I understand it here, is any one of the literal emergencies I mentioned before. However I think one can quite naturally extend the idea to the practical realities of almost any situation, where the various phenomena of reality can not be explained or resolved by faith alone, relegating religion to a supporting role, if not entirely superseding it with science.

Emily Dickinson is playfully saying that it is easy to have faith when the proof is there for all to see, for example, you might believe something is true if you can see it with your own eyes. However, in the next 2 lines she is stating that mankind is skeptical by nature and having a tool like a microscope which helps one to see the "invisible" or less apparent proofs is sometimes very necessary. An example of this is bacteria. We are told that bacteria can kill us but we can't see bacteria with our eyesight. We have to believe that this is true and take proper steps to avoid contact with that bacteria. However, when this poem was written the idea that bacteria and germs kill people was still difficult for many people to believe and diseases like typhoid and cholera were hard to prevent because of people's ignorance. A microscope makes a believer (someone with faith) out of the nonbeliever (unfaithful).

The poem is gendered! The author is a woman, the sex mentioned is male. Males ("gentlemen") tell women to have faith (in what they say, based on what they see). But in case of an Emergency (a really great problem) the (female?) person speaking does away with this appeal to have faith and asks for the scientific rigor of the microscope. (As I happen to be a male, I think we males get a good kick in the ass here. 哈哈哈) (Capitalizing of nouns often occurred in the poetry of those times, to give a noun more weight. Here it may also contain some irony.)