4 W. Boivie — Relation of Isostasy to 



places within the area where the observations have been 

 made. It is not necessary for ns here to go into details 

 of the determination of the fignre of the earth for they 

 can be consulted in articles which are easily accessible. 

 Bnt let us see what we do at a single astronomic station. 



Let it be supposed that we have a mountain mass close 

 to the astronomic station, say mthin 100 miles. This 

 mountain mass mil have an attractive effect on a particle 

 at the astronomic station. As a result of this attraction 

 the plumb line to which all astronomic observations are 

 referred Avill be deflected towards the mountain. It is a 

 simple matter to compute this effect and apply it to the 

 observed latitude and longitude. We next compute the 

 effect of the isostatic compensation of the mountain mass 

 and apply this as a correction to the latitude and longi- 

 tude. We actually have mam^ mountain masses which 

 must be taken into consideration for each astronomic 

 station. What we use in our final data are the resultant 

 effects of all of the topographic features, whether land or 

 water, within 2564 miles of the station, together with their 

 isostatic compensation. 



Investigations of the effect of isostasy on the deflection of th& 



vertical. 



When Hayford had corrected all of his astronomic 

 stations, more than 500 in number, he made a mathema- 

 tical solution of the results from which he derived the 

 dimensions of the spheroid of revolution and the depth of 

 compensation. The most probable depth for the United 

 States from the data available was found to be 122 kilo- 

 meters. A depth obtained previously by Hayford from 

 fewer data was 113.7 kilometers. It is very interesting 

 to note that the depths differ about 8 kilometers, which 

 is quite a large per cent of the depth itself. 



Hayford found from his investigations that the result- 

 ant deflections of the vertical after the effect of topog- 

 raphy and isostatic compensation had been applied were, 

 on the average, about one-tenth of what they would have 

 been if the earth were rigid and there were no isostatic 

 compensation. 



Investigations of the effect of isostasy on the intensity of gravity. 



After Hayford had completed his investigations of the 

 figure of the earth and isostasy he began a second inves- 



