35 



8. As to the values to be expects 1 by theory at these stations, the formula which at, pi.-.-nt has most 

 claims to acceptance is that of VON HKI.MKKT, vix. : 



g = 978-000(1+0-00531 gin' 4) / 1 - M + 3* S _ 3// S-^ 1 



P ' I It 2RA 2K A '/ 

 where 



4> is the latitude (north or south), 



A the height above mean sea level, 



h' thickness of surface strata of low density, 



R Earth's mean radius, 



A density (5-6), 



s surface density (assumed 2 8), 



actual density of surface strata at the place, 



y an orographic correction, arising from mountain masses, &c. 



It is possible that at Winter Quarters, Mt, Erebus, Mt. Terror, Mt. Discovery, and other mountain 

 masses, and the proximity of McMurdo Sound with a considerable depth of water, might severally contribute 

 sensibly to the y term in (1), but without much more complete information than exists, no value derived 

 from this could make any claims to accuracy. 



The observed rock densities at Winter Quarters would seem to indicate that the mean surface densit v 

 did not differ much from 2 8. 



At sea level, at a station where the surface strata have a density of 2-8, and there are no causes (such 

 as high mountains or deep seas) in the neighbourhood for an orographic correction, 



g = 978 -000(1 + -00531 sin 2 <f>), 

 or, more conveniently, 



/ = 978-000 + 5- 193 sin- < 



= 980-5966-2-5966 cos 2<j> (2). 



The values of f/ calculated from (2) for the latitudes of Melbourne (37 49' 53"), Christchurch 

 (43 31' 50"), and Winter Harbour (77 50' 50"), are given in Table V. under the heading "Theoretical 

 sea-level values." The values under this heading, it should be noticed, are not the exact theoretical 

 equivalents of these observed values given in the table, because the latter have not l>een reduced to sea 

 level. The reduction to sea level is at best only an approximation, and different views may be entertained 

 regarding its application. If we suppose with VON HEI.MEUT 



3 = 2-8 = A/2 in (1), 

 we have 



2/t , 3/t 8 ,, /I1? 

 - R + 2RA = 



The corrections to the observed values answering to this would be 



At Christchurch, 25 feet above sea level, +0-001; 

 Winter Quarters, 30 +0-002. 



The height of the station at .Melbourne, in the cellars of the Observatory, was not exactly ascertained, 

 but was about 75 feet, so the correction required there would be about +0'005. 



These corrections are very trifling, considering the various sources of uncertainty. 



9. It will be noticed that the probable mean observed values are all slightly in excess of the theoretical, 

 especially at Christchurch. This same phenomenon, it may lie mentioned, appears, and to a greater 

 extent, in the results obtained by Austrian observers in Australasia, using half-second pendulums. 



F 2 



