SHAPE OF THE EARTH FROM A PENDULUM. 535 



certain the number of oscillations made by a pendulum within an 

 interval of several minutes without counting them. This at once 

 suggested that the danger of making a slip in counting the oscil- 

 lations, should they be as frequent as two in a second, might be 

 avoided, and thus a short or half-second's pendulum be employed. 

 This shortening resulted, of course, in a lightening, and each 

 ounce of diminution added to the safety of the knife-edge, thereby 

 contributing to the permanency of the pendulum. Nor was this 

 all : the parts now became of such wieldy size that the whole could 

 be incased in a chamber sufficiently air-tight to maintain a con- 

 stant atmospheric pressure either by exhausting a portion of the 

 air near sea level or forcing air in when stations at great altitudes 

 are occupied. 



With a pendulum so compact one can visit places heretofore 

 inaccessible with the larger forms, and require distant islands and 

 inhospitable climes to give a voice in determining the earth's 

 shape. Large land areas are needed for the measurement of arcs, 

 and hence less than one fourth of the earth only is available to de- 

 termine geodetically its shape. But now each party sent out on 

 a voyage of discovery or to observe astronomic phenomena can 

 take one of these compact pendulums along and make stations 

 within the bounds of the three fourths so that they may not be 

 encompassed by a figure dictated by the minority. 



Now that differential methods are used almost universally that 

 is, comparing the times of oscillation of the same pendulum at dif- 

 ferent places it is essential that the length may continue to be 

 what it was when swinging at the base station, or station where 

 absolute gravity had been determined. Supposing that due cor- 

 rection has been made for such changes in length as would be 

 occasioned by differences of temperature, the only possibility for 

 variation in length could come from disarrangement or wear of 

 the knife-edge. Any chipping of this knife-edge made of agate 

 could not be rectified, and dullness could not be removed with- 

 out making in so doing a new pendulum, thereby destroying its 

 differential value. In swinging, this agate V rests on a steel plane, 

 and as this plane, forming no part of the pendulum proper, is less 

 liable to injury or derangement, the idea occurred to the survey 

 officers to let these parts change places. So now we have a pendu- 

 lum with a slit in the upper end of its rod, having for its upper 

 surface a plane of hard steel. This plane rests on the agate knife- 

 edge which projects into the slit. If now the agate becomes dull 

 or injured it can be repaired or a new one substituted, and the 

 pendulum remain the same. 



As already stated, the usual procedure has been, when observ- 

 ing with a pendulum, to note the number of oscillations made in 

 a given interval of time ; then, by dividing this interval by the 



