43 ^ Mr. Ivory on the astronomical refractions. 
to every constitution of the atmosphere. In proceeding far- 
ther, our reasoning must comprehend all the varieties of 
temperature and density that actually take place in nature 
from the surface of the earth to the utmost height at which 
the air possesses power to refract the rays of light. Even if 
we should succeed in this, it would be chimerical to expect 
that a formula can be found that would apply to single ob- 
servations without great occasional inequalities. This is not 
to be ascribed to any fault of the theory ; it arises from the 
nature of the observations themselves. If we examine a set 
of observed refractions, it will be easy to discover instances 
in which the true refraction has diminished when, according 
to the instruments employed, it ought to have increased ; and, 
the contrary. The refractions are therefore affected by cir- 
cumstances of which the observer has no intimation, and 
which cannot enter into any theory. The real causes of such 
anomalies is undoubtedly the irregular changes that take 
place in the remote parts of the atmosphere, which are not 
indicated by the barometer or the thermometer. We must 
conceive that the atmosphere is perpetually oscillating about 
a mean state, which it ought to be the aim of theory to dis- 
cover. The test of success in the research must be looked 
for, not in the perfect agreement of the theory with every 
single instance, but in the disappearance of the unavoidable 
errors in a sufficient number of observations made at different 
times. 
7. There is no ground in experience for attributing to the 
gradation of heat in the atmosphere any other law than that 
of an equable decrease as the altitude increases. This law 
prevails very nearly at least to the greatest heights to which 
