One obvious course of action when a project is behind schedule and you don’t want to cut scope is to expand the number of people on the project. The seldom works as expected.
Firstly, addition of new team members creates new work, the existing team members must spend time getting the new recruits up to speed, if the project has been running for a while, then this tacit knowledge transfer is not a trivial task.
Secondly, expanding the team size exponentially increases the number of channels of communication between people. In a team of 3 people there are three channels of communication A talks to B, B talks to C and C talks to A. By the channels of communication across a team have the relationship n(n-1)/2 where n is the number of team members. This means a team of 10 has 45, a team of 100 has 4,950.
Increasing team size may work, but it introduces its own complexity. Training new team members and the increase in channels of communication can make an increase in team size counter-productive.
This, and other concepts, primarily related to software development are explained in Brooks’ publication, The Mythical Man Month
Channels of Communication Relative to Number of Team Members
Strategic PPM 
I would like to comment on the quadratic law of the number of communication lines.
Statement of the quadratic dependence of the number of lines of communication among people is valid only for small compact groups, where there is a connection between all. With increasing numbers of people, each individual has connections only with its immediate vicinity or environment, which is one of the signs of rationality of large systems. For example, in the design teams with a hierarchical structure is almost no connection between the groups of lower level.
Studies show that this dependence is nearly linear, rather with an increase in the number of people asymptotically approaches the linear dependence.
Details you can find here:
Click to access Barseghyan-Team-Size.pdf
(Formulas (47) and (48) and Fig.8).
Pavel Barseghyan
Interesting point, I was modelling potential rather than actual connections, but your logic makes sense. However, your link doesn’t seem to work (I get a 404 error).
I don’t know what happened with PM World Today but link indeed doesn’t work.
The title of this paper is ’’Quantitative Analysis of Team Size and its Hierarchical Structure’’.
I can send it to you if you want. I just need an email address for that.
In 80s I had developed a mathematical theory for description of so-called Massively Interconnected systems for semiconductor chip design purposes.
In this paper I applied that theory (more precisely the connectivity differential equation) to the problems of quantitative project management, considering development teams as massively interconnected systems.
The article “Quantitative Analysis of Team Size and Its Hierarchical Structure” you can find here:
Other related publications and materials you can find here: http://www.scribd.com/pbarseghyan/info and
here: http://pavelbarseghyan.wordpress.com/.
Pavel Barseghyan