332 THE PRINCIPLES OF SCIENCE. [CHAP. 



infinitely numerous compounds. The properties of hardness, 

 elasticity, viscosity, expansion by heat, conducting powers 

 for heat and electricity, must also be determined in 

 immense detail. There are, however, certain of these 

 numbers which stand out prominently because they serve 

 as intermediate units or terms of comparison. Such are, 

 for instance, the absolute coefficients of expansion of air, 

 water and mercury, the temperature of the maximum 

 density of water, the latent heats of water and steam, 

 the boiling-point of water under standard pressure, the 

 melting and boiling-points of mercury, and so forth. 



Astronomical Constants. 



The third great class consists of numbers possessing far 

 less generality because they refer not to the properties of 

 matter, but to the special forms and distances in which 

 matter has been disposed in the part of the universe open 

 to our examination. We have, first of all, to define the 

 magnitude and form of the earth, its mean density, the 

 constant of aberration of light expressing the relation 

 between the earth's mean velocity in space and the 

 velocity of light. From the earth, as our observatory, we 

 then proceed to lay down the mean distances of the sun, 

 and of the planets from the same centre ; all the elements 

 of the planetary orbits, the magnitudes, densities, masses, 

 periods of axial rotation of the several planets are by 

 degrees determined with growing accuracy. The same 

 labours must be gone through for the satellites. Cata- 

 logues of comets with the elements of their orbits, as far 

 as ascertainable, must not be omitted. 



From the -earth's orbit as a new base of observations, 

 we next proceed to survey the heavens and lay down the 

 apparent positions, magnitudes, motions, distances, periods 

 of variation, &c. of the stars. All catalogues of stars from 

 those of Hipparchus and Tycho, are full of numbers ex- 

 pressing rudely the conformation of the visible universe. 

 But there is obviously no limit to the labours of astrono- 

 mers ; not only are millions of distant stars awaiting their 

 first measurements, but those already registered require 

 endless scrutiny as regards their movements in the three 

 dimensions of space, their periods of revolution, their 



