CHEMICAL AND PHYsICAL NOTES. 155 
Its weight on a spring balance is the measure of the power which it 
has to overcome a certain constant resistance, the resilience of the 
spring. The whole of this power is conferred on it by the force of 
gravity. By virtue of its mass alone it has no such power. Hence, 
in the case considered, when the density of the earth is supposed to 
be halved, the weight of the litre of water would be halved also, and 
it would be registered as 500 grammes on the scale of the spring- 
balance. The same would apply to the kilogramme of platinum. 
The spring-balance would give its weight as only 500 grammes, and 
it is evident that under the altered conditions of gravity they would 
still balance each other in the opposite pans of a pair of scales. 
Like the hypsometer, the aneroid barometer measures the pressure of 
the air, not the height of the barometer. It is a spring-balance, 
whilst the mercurial barometer is a pair of scales. 
The gravitation correction for the barometer, as supplied in me- 
teorological instructions, is based on the assumption of a homogeneous 
earth, and refers only to varying distance of the station from the 
centre of the earth. The force of gravity varies inversely with the 
square of this distance. It is obvious that there will be some differ- 
ence between the force of gravity at the level of the sea and that at 
the top of a high mountain in the neighbourhood. We have taken 
the mean radius of the sphere to be 6371 kilometres. At a height of 
1000 metres above the sea the force of gravity is less than it is at 
the level of the sea in the proportions 63727: 6371? = 0°99968. At 
a height of 5000 metres the relative reduction is 0°99843, and at 
10,000 metres it is 0° 99687. 
Owing to the spheroidal shape of the earth, places at the sea level 
are at different distances from the centre of the earth if they are 
situated in different latitudes. 
The most recent values of the dimensions of the earth’s spheroid 
are— 
Semi-axis major. . i : . 6378 kilometres. 
Semi-axis minor . ‘ » oo.» 66356 é, 
Difference 2, de. o> con oS 22 “ 
The greater radius is the equatorial and the smaller the polar, 
therefore the force of gravity at sea level is a maximum at the poles 
and a minimum at the equator, and the relation between them is 
0:99311. The difference between the equatorial and the polar radii 
is about three times the height of the highest mountain on the earth’s 
surface. 
