�y��vlog

The name cycloid is now restricted to the curve described when the tracing-point is on the circumference of the circle; if the point is either within or without the circle the curves are generally termed trochoids, but they are also known as the prolate and curtate cycloids respectively.

An annuity is usually held payable to the end of each year survived; but when, in addition, a proportion of the year's annuity is payable up to the day of death, the annuity is said to be Complete—the ordinary annuity being sometimes, for distinction, referred to as a Curtate annuity.

Dr. Wollaston had made a drawing of the orbit and its elements; but, having left it in town, he described the lines so accurately without naming them, that I remarked at once, "That is the curtate or perihelion distance," which pleased him greatly, as it showed how accurate his description was.

But if you mark a point B on the circumference of the flange of a locomotive-wheel, the curve will be a curtate cycloid, as in Fig.

A.--When the wheel of a coach rolls along the ground, any point of its periphery describes in the air a curve which is termed a cycloid; any point within the periphery traces a prolate or protracted cycloid, and any point exterior to the periphery traces a curtate or contracted cycloid--the prolate cycloid partaking more of the nature of a straight line, and the curtate cycloid more of the nature of a circle.