84 Dr. Young’s remarks on the reduction 
2. On the mean density of the earth. 
It has been observed by some philosophers, that the excess 
of the density of the central parts of the earth, above that of 
the superficial parts, is so great as to render it probable that 
the whole was once in a state of fluidity, since this is the only 
condition that would enable the heaviest substances to sink 
towards the centre. But before we admit this inference, we 
ought to inquire, how great would be the effect of pressure 
only in augmenting the mean density, as far as we can judge 
of the compressibility of the substances, which are the most 
likely to be abundant, throughout the internal parts of the 
structure. 
Supposing the density at the distance x from the centre 
to be expressed by y, the fluxion d y will be jointly propor- 
tional to the thickness of the elementary stratum, or to its 
fluxion — dx, to the actual density y, and to the attraction of the 
interior parts of the sphere, which varies as ^ yx ^ x ; since the 
increment of pressure, and consequently that of density, 
depends on the combination of these three magnitudes: we 
have therefore — n&y—y&x^—^^ an equation which will 
readily afford us the value of y in a series of the form 1 -J- 
ax 2 **|“ bx 4 “I - .... 
In order to determine the coefficients, we must first find 
' fyX xx* ^ T x + 5- ybx*- f- . . ., and multiplying this by 
(1 +^ 2 + bx 4 + •••) dx, we obtain 
— ny = ■ — n — nax 2 — - nbx 4 — ncx’ — .... 
