314 E. D. Preston — Deflection of the 



2500 and 1500 feet and the resulting deflection is only -J- of a 

 second. This value compared with the total deflection caused 

 by East Maui shows that the approximate data used for this 

 distant part of the island are quite accurate enough. For a 

 change of 10 miles in the distance or 10° in the .azimuth only 

 changes the deflection by a few hundredths of a second. A 

 difference of 500 feet in elevation has about an equal influence. 

 The distance of the center of West Maui from Kaupo is 35 

 miles and its mean azimuth 55°. 



That part of the island lying to the south of the prime ver- 

 tical is neglected. A computation of one of the compart- 

 ments giving only a deflection of /;, 002 ; besides whatever in- 

 fluence this land may have, is practically destroyed by the light 

 sea lying north of the prime vertical on the east, as the two 

 portions are nearly the same shape and size. 



The sea lying to the southward will have the same influence 

 as a volume of density equal to the difference of densities of 

 rock and sea water. Supposing the mountain to continue to 

 the bed of the ocean, with the same slope that it has from the 

 summit to Kaupo, gives a cone of density of rock minus water, 

 and volume equal to Haleakala, making up nearly all the disturb- 

 ing effect. Hence we multiply the deflection found for the 

 mountain by a factor depending on the relative densities of 

 rock and water. Increasing the total deflection found or 17"*8 

 by T 7 T of itself we get 29 /7 'l as the entire deviation of the 

 plumb line at Kaupo. The deflection found by triangulation was 

 29 ", This mode of computation is the same as that employed 

 by the Ordinance Survey in the treatment of deflections in 

 the south of England. A shorter way and one that can be 

 employed for an approximate value in some cases, is to con- 

 sider the mountain as a paraboloid of revolution. This was 

 done for Haleakala using the mean density furnished by the 

 pendulum, and a value for the mass of the earth, previously 

 employed in investigations of this kind. These data give for 

 the deflection at Kaupo, (Ka Lae o Ka Ilio) a station on the 

 south side of the mountain, 28 seconds, which is within one 

 second of what was found by Prof. Alexander who carried the 

 astronomical latitude of Haiku around the island, by triangula- 

 tion to Kaupo, and there compared it with the locally deter- 

 mined latitude. Of course this very close agreement is only 

 accidental because the data used are but approximate and the 

 mountain is not a perfect paraboloid of revolution. In fact 

 by this method the deflections cannot be known closer than a 

 few seconds : for an uncertainty of a quarter of a mile either 

 in fixing the radius of the mountain or in estimating the dis- 

 tance of the attracted point from the center of what would be 

 an equivalent paraboloid, will produce an uncertainty of at 



