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discontinuity) about a point ; and it is one of the earliest 

 geometrical facts, that angles are measured by their corre- 

 sponding circular arcs. A radius having first a given posi- 

 tion, and then revolving uniformly about the central point, 

 returns to its primitive position with every revolution, and 

 thus originates the idea of the measure of a periodical 

 function. A periodical function of this kind is furnished 

 by nature in the return of a particular star to the meridian 

 of a given place on the earth's surface ; and if at such place 

 a mechanism be contrived to give one revolution of a 

 radius in the same time with the return of the star, the 

 motion being uniform, then any point of the radius will 

 describe a part of the circumference of its corresponding 

 circle, exactly proportional to the time occupied by the star 

 during such movement of the radius, compared to the 

 period of its return to the meridian ; for example, if the 

 radius have moved uniformly through one right angle, the 

 star will have consumed one-fourth of its periodical time, 

 and thus we obtain a measure of time in terms of space. 

 As this measure is angular or circular only, a further 

 deduction is resorted to for a linear standard of reference, 

 by comparing together the rotary force expended on the 

 mass of the revolved radius regarded as concentrated in 

 the describing point of its circle, with the time of descrip- 

 tion ; for, the force being uniform, the greater the distance 

 of the massive point from the center, the smaller will be 

 the angle it can describe in an equal given time, because 

 the arc or distance to be described increases proportionally 

 to the increase of the radius. In our case, gravitation is 

 the given uniform force, which will cause a mathematical 

 pendulum to describe an arc in a time proportional to the 

 pendulum's length ; so that the length of the pendulum 

 that shall make one oscillation in the nth part of the time 

 occupied by the earth in its revolution on its axis may be 

 experimentally found, and this constitutes a natural stand- 



