312 E. D. Preston — Deflection of the 



would . only elevate the apparent sea level by about ten feet. 

 This quantity may well be neglected when we consider that 

 the mountain is 10,000 feet high and the mean density in any 

 case is not certain beyond two or three significant figures. 

 Therefore we should not exjDect to find in mountains in the 

 middle of the Pacific Ocean, a mean density differing very 

 much from that indicated by the rocks found on the surface. 



The value 2*4 which the pendulums both agree in showing, 

 certainly does not depart sufficiently from that furnished by 

 the rocks themselves, to allow us to assert that the mountain is 

 lighter than it should be, or that there is a defect of gravity on 

 its summit. On the contrary, the indication inclines slightly 

 to the other side, if we accept 2*3, which has been estimated 

 by geologists for the density of the rocks on Maui. Between 

 9500 and 10,000 feet there exist rocks of a comparatively 

 great density. This being the case at such an altitude, it is 

 most reasonable to suppose a density, great enough, to counter- 

 balance the beds of light lava and cinder, found on many parts 

 of the summit. 



In order to have a check on the whole work, as well as to 

 compare pendulum results with those from star observations 

 with the zenith telescope, the following plan was adopted : 

 Latitude stations were made on the north and south side of the 

 island, besides an intermediate station on the summit. All 

 these stations have been connected by triangulation, as a regu- 

 lar part of the Government Survey by Professor Alexander. 

 Comparing the astronomical deflections observed on either side 

 of the mountain, with those calculated from its volume and 

 density as furnished by the pendulum, we shall have a test of 

 methods as well as results and if it is found that these agree, 

 we should feel considerable confidence in our opinions concern- 

 ing the constitution of the crust. 



The attraction of a mountain may be calculated in several 

 ways. The best and most accurate, when sufficient data is at 

 hand is that due to Dr. Hutton and is briefly this : The coun- 

 try around the station is divided into compartments by concen- 

 tric rings and radial lines. The attraction of an element of 

 matter depends on its density and the square of its distance 

 from the attracted point ; and we have as a result a formula 

 which must be integrated with reference to three variables. 

 The first integration gives us a curve in the plane of the base 

 of the mountain : after the second we have a vertical curved 

 surface, and with the third results the volume and attraction of 

 one of our elementary compartments. Performing the inte- 

 gration then for azimuth, distance, and elevation, we have all 

 that is necessary to compute the attraction of the mountain in 

 the direction of the meridian of the station. Here the work 



