SHAPE OF THE EARTH FROM A PENDULUM. 533 



above the level of the sea, would make its oscillation in a longer 

 time than when swinging at sea level. Therefore it is necessary 

 to know the elevation of the station in order to ascertain the force 

 of gravity in that latitude on the ideal earth. 



If the parallels were perfect circles and if observations were 

 absolutely correct, it would be necessary to swing a pendulum at 

 only two points on the earth's surface in order to determine its 

 shape. However, the results obtained by combining observations 

 two and two are not harmonious ; not only because the observa- 

 tions may be affected by errors, but the attraction of dense mat- 

 ter immediately beneath a station might seriously impair the 

 observations made there ; and as we never know the exact consti- 

 tution of the earth's crust at any point, it becomes necessary to 

 eliminate, as far as possible, this uncontrollable error by making 

 observations at many places. 



The ideal pendulum would consist of a ball of symmetrical form 

 suspended by a wire stiff and uniform. Like all ideal conditions, 

 these are never attained, but a close approximation is sought. In 

 seeking rigidity the pendulum rod must be so large in cross sec- 

 tion as to make the instrument cumbrous. This was a serious 

 feature when, in order to avoid slips in counting, it was not 

 thought feasible to use a pendulum that made an oscillation in 

 less than a second of time that is, a pendulum about thirty-nine 

 inches long. Again, as the pendulum was provided with sharp 

 knife-edges on opposite sides near its upper end, shaped like a 

 V, on which it swung, the greater the weight of the pendulum the 

 more wear there would be on these knife-edges. This becomes a 

 serious matter, as the length of the pendulum is estimated from 

 the line of support furnished by these same knife-edges. Then, 

 too, the swinging of a large and heavy pendulum was liable to 

 induce a swinging motion in its support, unless the latter were 

 exceedingly rigid, thereby vitiating the results. 



Several years ago it was realized that the resistance of the 

 atmosphere would vary with different conditions of moisture and 

 density, and hence retard the pendulum more at some times than 

 at others, more at some elevations than at others. Therefore it 

 seemed necessary, in the absence of any well-accepted correction 

 for these hurtful resistances, to swing the pendulum always under 

 the same atmospheric pressure and surrounded by similar condi- 

 tions as to moisture. This could be done only by inclosing the 

 entire pendulum in a chamber in which the air could be main- 

 tained at the same density and dryness. One can readily see how 

 difficult this would be with an apparatus more than four feet in 

 length and weighing many pounds. 



Although the shortcomings of the ordinary pendulum forced 

 themselves into recognition one by one, still the readiness with 



