396 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1910. 



and Geodetic Survey is shown in plate 1.^ A set of invariable 

 pendulums is swung in an air-tight case in a partial vacuum, at a 

 uniform temperature. An electrical flash apparatus makes the half- 

 second beats of a chronometer visible and permits the observer to 

 note when the beat coincides with a swing of the pendulum. The 

 time of oscillation of the pendulum at the station where the intensity 

 of gravity is to be ascertained is compared with the time of oscilla- 

 tion under identical conditions at a station at which the intensity 

 is known. The desired value of gravity is then calculated. 



The value thus obtained for the intensity of gravity at any par- 

 ticular place can be compared with the intensity at other places only 

 by making all the conditions of attraction the same for both places. 

 Let it be supposed that any two results which are to be compared 

 have been obtained at stations that differ in latitude, in altitude 

 above sea, and in topographic surroundings. Then account must be 

 taken of all these conditions. 



Latitude and altitude both affect the distance from the earth's 

 center and gravity varies inversely as the square of that distance. 

 Hence observations are reduced to sea level and are then compared 

 with the normal value of gravity for the latitude of the observation 

 according to a formula constructed by the German geodesist, Helmert. 



Suppose, for instance, that an observation for gravity had been 

 made in a balloon over the sea. It would be necessary to correct 

 the result for the altitude of the balloon and compare with the 

 normal value given by Helmert's formula for that latitude. This is 

 what has been called the " free-air reduction." It is always made. 



The calculation of the influence of position and topographic sur- 

 roundings involves theoretical postulates which distinguish three 

 different methods. One may be described as the method of high 

 rigidity, since it rests upon the postulate of a rigid earth of uniform 

 density. The other two both develop from the assumption of iso- 

 static equilibrium, but they differ in that according to one the balance 

 is supposed to be complete, but according to the other it is partial. 

 An illustration may serve to make the distinctions clearer. 



Let us transfer the place of observation from the balloon over the 

 sea to the top of a lighthouse rising from sea level. The reduction 

 for elevation, the " free-air reduction," must be made as before, but 

 correction must also be applied for the mass of the lighthouse, which 

 is an excess of material, added to and rigidly upheld by the rocks 

 at sea level. It exerts an additional attraction, which must be de- 

 ducted from the observed value in order to obtain the true value of 

 gravity at sea level beneath the lighthouse. According to the pos- 

 tulate of high rigidity, all elevations on the earth's surface above 



1 Illustration kindly furnished by Mr. Geo. R. Putnam. 



