gives point contact, allowing for consistent measurements as the tip moves through its arc (via consistent offset distance from ball surface to center point, regardless of ball contact angle with the measured surface). Several spherical diameters are commercially offered; 1mm, 2mm, and 3mm are the standard sizes. Despite the advantage just mentioned (regarding contact angle irrelevance) of the ball (sphere) itself, the contact angle of the lever overall does matter. On most DTIs it must be parallel (0°, 180°) to the surface being measured in order for the measurement to be truly accurate, that is, for the magnitude of the dial reading to reflect the true tip movement distance without cosine error. In other words, the path of the tip's movement must coincide with the vector that is being measured; otherwise, only the cosine of the vector is being measured (yielding the error called cosine error). In such cases the indicator may still be useful, but an offset (multiplier or correction factor) must be applied to achieve a correct measurement (where the measurement is absolute rather than merely comparative). (This fact applies to the angle between the lever and the part, not to the angle between the lever and the DTI body, which is adjustable on most DTIs.) The same principle is also employed with CMM touch trigger probes (TTPs), where the machine (when used correctly) adjusts its ball-offset compensation to account for any difference between the approach vector and the surface vector. Some DTIs (such as the Interapid line and its competitors) are made with a built-in allowance such that a 12° tip angle (between the lever and the surface being measured) is the angle that corresponds to zero cosine error. This is a great convenience to the user because of the practicality of having the ball being clear of the indicator body such that the unit may pass over a surface. Changing the tip of a DTI is not as simple an affair as changing the tip of a drop indicator, because the tip, being a lever, has its length precisely matched to the clockwork inside the indicator, so that the length of the arc of its extremity's movement has a known ratio to the gears that drive the dial's needle. Thus to add a longer or shorter tip requires a correction factor to be multiplied with the dial reading in order to yield a true distance reading.