Plumb-line in the Hawaiian Islands. 311 



determination of periods, it is only necessary to deal with 

 differences instead of the whole interval. 



The determination of the relative forces of gravity at the 

 base and summit of a mountain gives sufficient data for the 

 computation of the ratio existing between the mean density of 

 the mountain and that of the earth. 



Whether we consider the matter lying between the summit 

 and the base, as a cone, a cylinder, or the segment of a sphere, 

 the mathematical expression for its attraction , on the upper 

 station is approximately the same, when the horizontal dimen- 

 sions of the figure are great compared with the vertical ones. 



In passing from the sea level to the top of Haleakala, the 

 time of oscillation was found to have increased by its -g-j^th 

 part, or since gravity varies inversely as the square of the time 

 of oscillation, the decrease of gravity in passing to the summit 

 is y-j^th part of itself. 



The two stations are not in the same latitude, nor is the 

 base station exactly at the sea level ; but corrections were first 

 applied to make them comparable as to latitude. The time of 

 oscillation at the base station was also reduced to what it would 

 have been at the level, of the sea. 



On account of distance alone we should expect the pendu- 

 lum to lose 41 seconds per day on being transported from the 

 sea to the summit. Asa matter of fact it was observed to lose 

 only 28 seconds. Hence the mass of the mountain accelerated 

 the pendulum by 18 seconds daily. 



Employing Young's rule we arrive at a value of 43 hun- 

 dredths for the ratio of the mean density of the mountain to 

 that of the earth. Assuming the earth's density to be 5*67 the 

 resulting density of the mountain becomes 2*4. 



This is not very far from the estimated density of the rocks 

 composing the mass, so that this determination does not indi- 

 cate any large cavern under the mountain, or any very great 

 attenuation of the matter composing it Mountains as a gen- 

 eral rule show a defect of gravity on their summits. But this 

 rule has been deduced from experiments made on continental 

 mountains, notably in Peru and India. If we admit that the 

 surface of the sea is elevated in the vicinity of continents by 

 the attraction of the land, mountains need not necessarily be 

 supposed light. The great plateau of India would raise the 

 apparent sea level immediately under it by nearly a thousand 

 feet. This would have a very perceptible effect on the deter- 

 mination of the mean density of the plateau. But in the case 

 of a mountain rising in the midst of a deep sea the surface 

 cannot be supposed to be influenced enough to materially affect 

 the determination of its density. In fact a plateau having an 

 extent equal to Haleakala and a height equal to its mean height 



