Suppose you cross male fly that is heterozygous for each trait (b+bvg+vg) with a female fly that is homozygous recessive for each trait (bbvgvg).
If these traits were on separate chromosomes they would assort independently:
Via Mr. Hammack's mad drawing skills
In this case (the traits are not linked), one would get a 1:1:1:1 ratio as shown below.
Via Mr. Hammack's mad drawing skills
In reality, these traits are located on the same chromosome, producing a 1:1 ratio as shown here:
Via Mr. Hammack's mad drawing skills
Linked traits do not exhibit Mendelian ratios.
Mendel must have noticed this, but didn't understand it—he got strange ratios he couldn't explain—so he ignored such traits.
The traits Mendel ended up studying were either on separate chromosomes or far apart on the same ones, so they were not linked.
Conclusion
If you have two sets of traits (like body color and wing length in Drosophila) and you are doing a test cross (homozygous recessive) with an individual that is heterozygous for both traits, there are two expected outcomes:
If you get a 1:1:1:1 ratio, then the traits are completely independent.
If you get a 1:1 ratio, then the traits are completely linked.
Crossing Over
Strange Ratios
Based on what we know about linkage, we would expect this cross to give a 1:1 ratio (gray–normal: black–vestigial).
But when T. H. Morgan (the fly guy at Columbia University) did these crosses and counted 2300 offspring, he got this strange data:
Homologous chromosomes exchange portions of their chromosomes (so that alleles can be recombined, i.e. move between chromosomes).
This event, called crossing over, occurs during prophase I of meiosis.
Remember the formation of chiasmata.
Crossing over is very frequent: every homologous chromosome undergoes at least one crossover event during prophase I of meiosis (generally it is more like 2 or 3).