304 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1907. 
and leads to still more complex mathematical problems, whose solu- 
tion is absolutely necessary if we would understand the formation of 
clouds and rain. In this branch of study we have an instructive 
memoir by Brillouin, in which he is able to explain in a general way 
the formation of many types of clouds or layers of clouds as due to 
the mixture of masses of air having different degrees of temperature 
and moisture. The appearances of the clouds have been most care- 
fully observed and recorded for two centuries, but the ability to learn 
what they can teach us has only become possible within the past thirty 
years. . 
The first step in the application of thermodynamics to meteorology 
was undoubtedly taken by Espy in 1822, when he stated that the 
cooling due to the expansion of air ascending into regions of lower 
pressure caused the formation of clouds and the lower temperature of 
the air of the upper strata. However it was soon found that the cool- 
ing is not due to the expansion as such, but to the work done by ex- 
pansion against atmospheric pressure. This general explanation was 
accepted by French physicists in 1839, but was given greater precision 
by Sir William Thomson in 1864, and Peslin in 1869; it was satisfac- 
tory to American, English, and French students, but seems not to 
have been accepted in Germany until Professor Hann wrote an ex- 
planatory article in the Zeitschrift of the Austrian Meteorological 
Society for 1874, showing how the laws of thermodynamics apply to 
the atmosphere. This paper was followed by much more elaborate 
studies and a series of valuable publications by others, so that it is 
now easy to apply our knowledge of thermodynamics to the atmos- 
phere. A most helpful memoir along this line was that by Hertz, in 
which he gave a very simple diagram (known everywhere as the 
Hertzian diagram of adiabatics for the atmosphere) for determining 
what the condition of moist air must be on attaining a given height 
in the atmosphere. Assuming that it retains its original amount of 
heat during the whole time, his diagram shows very clearly the results 
of the ascent of ordinary clear air up to a level at which cloud forma- 
tion begins; then to the level at which the precipitation is in the shape 
of frozen water drops, or hail, and above that to the region in which 
precipitation must be in the shape of icy spicule, or snow. These 
four stages of cooling, viz, the dry stage, cloudy stage, ice stage, and 
snow stage, characterize nearly all the important phenomena of the 
weather. 
In his further applications of thermodynamics Professor von Be- 
zold has clarified our ideas by introducing a series of diagrams after 
the manner first taught by Clapeyron. Assuming that a unit mass of 
air mixed with a given quantity of moisture rises or falls adiabatic- 
ally, his diagrams then show its condition at any moment by means 
