APPENDIX A XLIX 
from their other properties and free from the complications of the 
interfermg causes which are always present in terrestrial investiga- 
tions. 
Astronomy still retains the advantage of dealing with matter under 
other conditions than on the earth, as well as under widely differing 
and extreme conditions. In the sun and the stars temperatures exist 
far more intense than we can produce in our laboratories. Matter is 
observed in various states of condensation, from the dense material of 
enormous sums to the seemingly rarified gases of the nebulæ, or the 
dust of the comets. Stars are seen in process of formation, or dissolved 
by intense heat into their constituent gases. 
The value of the study of properties under extreme conditions 
may be seen by considering the way in which experimental investiga- 
tions usually proceed. It is desired to ascertain how one of the cir- 
cumstances of a phenomenon varies with the variation of another 
circumstance. Thus suppose it is desired to ascertain the law of 
variation in length of a metal bar under differmg temperatures. 
The length of the bar is measured at different temperatures, and 
points are plotted on paper with the temperatures as abscissee, and the 
lengths are ordinates. A free-hand curve is drawn through these points, 
which on the principle of continuity is assumed to represent by its 
ordinates the lengths of the bar at all temperatures. 
The experimenter possibly does not actually plot his results in this 
way, but derives a mathematical formula analytically from the tabula- 
tion of his results; but that process is exactly equivalent to plotting 
the curve on paper. 
Now when the law is determined in this way and expressed either 
graphically, or by a mathematical formula, we may assume with 
confidence that it gives the length of the bar with an accuracy com- 
parable with that of the original observations, at temperatures between 
the limits of temperature of the observations. A certain amount of 
error of observation has to be reckoned with. Taking this into account 
a small portion of the curve is indistinguishable from a straight line. 
A rather longer portion may be considered to be a part of a cirele, or a 
parabola, or some other curve. It requires a considerable length of 
curve to show its real form. Hence, while we may assume our curve 
within the limits of observation to represent the operation of the law, 
we cannot with safety go beyond those limits. It is desirable, there- 
fore, to extend the observations over as wide a range of conditions as 
possible. 
At the present time astronomers are co-operating in collecting 
data relating to the structure of the sidereal universe, the directions 
and velocities of motion of the stars, and the variability of certain 
