Please explain the significance of the following quote from Joseph Addison and Richard Steele's The Spectator: ". . .he pronounces Amen three or four times to the same prayer . . . to count the congregation, or to see if any of his tenants are missing."
The Spectator, a periodical issued from 1711-1714, gave Joseph Addison and Richard Steele the opportunity to satirize various aspects of English life--from literature and religion to politics and the economy. The created a fictitious group of men who formed a club to discuss events of the day, and one of the members--perhaps the most remembered member--was Sir Roger de Coverley, an old-fashioned, very conservative part of what is called the "landed gentry," men who owned a large amount of land and usually rented parts of that land to tenant farmers. Often, the relationship between the landed gentry and tenant farmers was that of parent and child, and the quote you mention in your question is an example of that relationship.
Although everyone who attends church is usually seen as equal in the eyes of God, in Sir Roger's view, he must act as a father does toward his children (the tenant farmers) by not only observing their behavior but correcting it:
. . . and sometimes stands up when everybody else is upon their knees, to count the congregation, or see if any of his tenants are missing.
In other words, Sir Roger is taking his paternal responsibilities very seriously by making sure that his tenants (figuratively, his children) are performing their religious duty by attending church. The problem, of course, is that Sir Roger should be concentrating on his own relationship with God, not worrying about whether his tenants are behaving appropriately in church.
The fact that Sir Roger "pronounces Amen three or four times to the same prayer" is part of Addison and Steele's gentle satire on the old-fashioned and slightly out-of-touch Sir Roger. In the Anglican Church, it is customary to say "Amen" only once and always at the conclusion of a prayer; Sir Roger, who is paying more attention to his tenant farmers than to the prayer, is completely unaware of his inappropriate responses. This is Addison and Steele's way of pointing out that some of the wealthiest citizens in the society are completely unaware of what is actually going on around them.