INTRODUCTION:
Imagine yourself at the opening of an art exhibit at a museum: a special showing that you need to have a ticket for.  You happen to find yourself in a group with art critics, tourists, and "normal" folks like yourself.  As is often the case, the paintings are hung along a corridor, and uniformed guards keep the flow of human traffic going "one-way". At the specified time, the velvet rope is dropped, and you and your fellow museum goers enter the corridor.

The tourists have less interest in the actual art than in being able to say they'd been to the museum when they get back home.  And you can hear mutterings of "My 5 year old can draw better" and "Let's go see the monuments next".  Unsurprisingly the tourists all arrive at the end of the exhibit quickly, in a tight little group.

Meanwhile, you and the rest of the general population are proceeding at a moderate pace, occasionally stopping to savor a particular oeuvre.  You arrive at the end of the exhibit decidedly later than the tourists (who are probably back on their bus).

The critics however are getting rowdy.  There is disagreement over the artist's brushstrokes, use of pigment, and career developement.  "He was a has-been by this period".  "Who are you calling a 'has-been', you hack?"  A fight breaks out.  More guards are summoned.  As you leave the building, you can still hear the rumpus.  Needless to say, the critics one by one straggle to the end of the exhibit last (doubtless greeted by a waiting police van.)
 

Yes, this is still the CHM 245 web site, and what you just read was an analogy for chromatography, a technique of separating components of a mixture based on their relative affinities for a solid medium.

The people represent a mixture containing three components.  Each component has a different affinity for the "stationary phase".  In my story above that would be the paintings on the "solid support" (the walls).  In liquid, or thin layer chromatography, the solid is silica or alumina (essentially sand or clay).  In gas/liquid chromatography, the stationary phase might be a wax or thick oil that coats the solids support, perhaps crushed brick.  All of that is packed into a coiled copper tube called "the column".
The security guards are the "mobile phase", keeping the flow of patrons going in one direction.  In gas chromatography, this is the flow of inert gas through the instrument.  In thin layer, or paper chromatography, it's capillary action, causing a liquid to rise up the stationary phase.  In column chromatography, gravity keeps the liquid flowing down the column.

The essence then of a chromatographic separation is the partitioning of a component between the mobile and stationary phases.  If the sample likes to stick to the solid phase, it will take a long time to reach the end of the column (or for PC and TLC, the "spot" won't move very far).  Hopefully, we have chosen our phases so that the components of the mixture have different affinities - i.e., they don't all stick at the same location and not move, nor do they all fly off to the end of the column at the same speed.
 

QUANTITATIVE ANALYSIS:

Gas chromatography offers a unique opportunity to determine the relative amounts of each mixture component, while keeping sample size down to microgram amounts.  Other techniques allow quantitation, but much more sample is required.
The output of the GC is typically a graphed series of peaks.  The relative areas of the peaks are proportional to the relative amounts of the compounds in the mixture.  The area can be obtained by:
1) Triangulation - the peak is approximated by a triangle.  The height and base are measured, and the area is calculated.
2) Cutting and weighing.  The original is photocopied several times, cut out with scissors, then weighed on a balance.  The relative weights are proportional to the areas.
3) Counting boxes.  If the output is on graph paper, the area can be obtained very accurately by counting the boxes under the curve.
4) An Integrating Recorder can be used.  This piece of equipment digitizes the voltage frome the GC, and calculates the relative areas of each peak, and prints the results.  Yes, we have one at Alexandria.

INTERPRETATION OF RESULTS:

TWO PEAKS IN THE GC:  The integrating recorder will give you percentages for each peak in your output.  Ideally, only two peaks will appear for your fractions, one for ethyl acetate and one for butyl acetate.  For now, let's assume that is the case.  Because the thermal conductivity detector response increases for compounds with larger molecular weights and/or increasing polarity, a correction factor must be applied (M_f in your Gilbert book).  Notice that the higher molecular weight butyl acetate has a lower correction factor than ethyl acetate.  After application of the correction factors though, the resulting percentages need to be renormalized to 100%

Example:  Let's assume that the recorder claims that the mixture is 50% ethyl and 50% butyl.  Apllication of the correction factors gives (50)(0.89) = 44.5% for ethyl, and (50)(0.74) = 37% for butyl.  Clearly a mixture of only ethyl and butyl acetates can't be 44.5% one and 37% the other.  What's the other 18.5 % ?!?
So we normalize the values to add to 100%:

44.5/(44.5 + 37) = 54.6% and 37/(44.5 + 37) = 45.4%

Notice that proper application of the correction factors should lead to a lowering of the percentage of butyl acetate.

EXTRA PEAKS IN THE GC:  Extra peaks might be due to air, acetone, water, or other impurities.  In this case, because the refractive index analysis assumes only two components in the mixture, we must identify and normalize the two peaks due to our acetates first, before applying the correction factors.  We have to normalize again after the correction factors too, just like before.
We need to do this because the percentages derived from refractometry must add up to 100%.  Impurities are not (and cannot be) considered.  For multiple peaks, no valid comparison can be made between refractometry and chromatography without the normalize-correct-normalize process.