On the Figure of the Earth. Ill 



If the earth were entirely formed of water, and if it be sup- 

 posed in conformity with the experiments of Canton, that the 

 density of water, at the temperature of ten degrees (50°. Fahr.) 

 and compressed by a column of water 10 metres (32.81925 ft.) 

 in height increases by 44 millionths, the flattening of the earth 

 would be X5^*» ^^ coefficient of the square of the sine of the la- 

 titude in the expression of the length of the second's pendulum 

 would be 59 ten-thousandths, and the mean density of the earth 

 would be nine times that of water. These results differ from ob- 

 servations by more than the errors to which they are liable. 



I have supposed the temperature uniform throughout the whole 

 extent of the terrestrial spheroid ; but it is very possible that the 

 heat is greater towards the centre, and that would be the case 

 if the earth, originally highly heated, were continually cooling. 

 The ignorance in which we are with respect to the internal con- 

 stitution of this planet, prevents us from calculating the law by 

 which the heat decreases, and the resulting diminution in the mean 

 temperature of climates ; but we can prove that this diminution 

 is insensible for the last 2,000 years. 



Suppose a space of a constant temperature, containing a sphere 

 having a rotatory motion ; and, suppose that after a long time 

 the temperature of the space diminishes one degree ; the sphere 

 will finally take this new temperature ; its mass will not 

 be at all altered, but its dimensions will diminish by a quan- 

 tity which I will suppose to be a hundred thousandth, a diminu- 

 tion which is nearly that of glass. In consequence of the prin- 

 ciple of areas, the sum of the areas which each molecule of the 

 sphere will describe round its axis of rotation will be the same 

 in a given time, as before. It is easy to conclude from this, that 

 the angular velocity of rotation will be augmented by a fifty 

 thousandth. So that, supposing the time of a rotation to be one 

 day, or a hundred thousand decimal seconds, it will be dimi- 

 nished two seconds by the diminution of a degree in the tem- 

 perature of the space. If we extend this consequence to the 

 earth, and also consider that the duration of the day has not 

 varied since the time of Hipparchus, by the hundredth of a se- 

 cond, as I have shewn by the comparison of observatioMS with the 



