Trust your eyes
What you measure and what you see isnt always the same. If a curve looks bottom-heavy to you, no matter what measurements say, it probably is. Allow for this in your design. Believe what you see.
Two identical shapes, next to each other, dont always look the same size. Heres an example. Look at the third numeral 8 from the left. To most people, the lower half looks smaller than the upper. They are the same size.
The numeral 8 on the left has a top that is bigger than the bottom. The proportions change, step by step, from left to right: the tops become smaller, the bottoms larger. At the end of the line, the size of the bottom is uncommonly big.
The third numeral 8 from the left, with top and bottom of equal size, doesnt look quite right. We are used to a slightly bigger lower part, such as the fourth and the fifth from the left.
Circles look smaller than rectangles
In this example, all the rectangles are the same size. The circles get bigger, little by little, from left to right. The second circle from the left looks smaller than the rectangles. It is the same height.
In most typefaces, the lower case letter o is higher than the lower case x. How much depends on the design. In Times Roman, the letter o is 4% higher than the letter x. The third circle from the left is 4% higher than the rectangles. The letter o in Courier and Helvetica is 7% higher the the letter x, as is the fourth circle from the left.
Verticals look thinner than horizontals
The stem of the letter E on the left is one-tenth thinner than the horizontals. The stems get bolder, step by step, from left to right.
The second letter from the left has stem and horizontals of equal thickness. The best proportion varies from one design to another. In Helvetica Bold, the stem is 20% wider than the horizontals, as in the letter E in the right.
Curved lines look thinner than straight lines
To make curves and straight lines look the same width, curves are usually thicker. In Times Roman, third from the right, the curve is 20% thicker than a vertical stem. Testing is a good way of deciding how much to add.
Relief for swollen joints
The letter r on the left has a large area of black where the stem meets the curve. This can ruin good texture. In each example from left to right, the curve is a little thinner. Second from the right is Adrian Frutigers solution for Univers Black.
On the left is a slanted stem. The outline next to it shows how two overlapping stems make the letter v. The result, on the right, doesnt look good. The lower half is too black. The white countershape isnt long enough. Stretching will help.
On the left is the letter v, assembled from two slanted stems. The counter of the second letter has been pulled down a little. In the third and fourth letters it has been pulled a bit more. How far is enough? It depends. A long counter is more useful in a small letter than it is in a big letter.
Beware of semicircles
Connecting curves and straight lines looks simpler than it is. A semicircle and a rectangle create what Peter Karow calls a "bone effect". (Digital Formats for Typefaces, URW Verlag, Hamburg 1987.) The straight edge of the black area between the two arrows can seem concave. On the right, the join has been softened.
Crossed lines can appear broken
A thin line that crosses a thicker line at an angle often seems broken. Here the thin lines have been shifted 2 pixels from one letter x to the next.
The row begins with an extreme example. The lower end of the thin part has been shifted 2 pixels in the wrong direction, to the right. The second from the left is the letter x in Times Roman, which doesnt compensate for this illusion. With each step to the right, the shift becomes more exaggerated.
Curves distort slant
The capitals shown here all have the same slant. But the slant of the letters f increases by 2.5° in each example from left to right.
The example on the left tilts 5° less than the rest of the italic. The difference is too great. The second is the letter f in Times Roman Bold Italic, 2.5° less than the italic. Its about right. The third leans as much as the rest of the italic, and seems about to fall over. The fourth appears to be in free-fall.
With each letter from left to right, the right baseline serif of the letter r is a little longer.
The serifs of the letters f and r are usually longer on the right side. Some say it prevents them from toppling over. People seem to like this at any rate. Second from the left is the letter r in Times Roman.
The three zeros are all the same weight. The percentage symbol of the left is too light. The middle one has the right weight, more or less. The rightmost is too bold.
Small versions of some characters assume additional duties: fractions are one example. Reducing them is not enough. They need extra weight, but not the full stem thickness.
Want more on optical illusion? Perception by Robert Sekuler and Randolph Blake is a good start.