THE TEPHIGRAM 51 
logical sounding might be plotted so 
that one could trace the path of any 
chosen particle of air as it ascended 
or descended through the surround- 
ing medium, in this manner making 
it possible to see if work is being 
done by the rising air particle or if 
it is necessary to supply mechanical 
energy in order to make it rise. This 
diagram, which has long since found 
a niche in classical meteorology, 
forms the basis of modern attack on 
problems of the upper air through 
energy diagrams. The emagram and 
aerogram of Refsdal’ and the tephi- 
gram of Shaw** have superseded the 
Neuhoff diagram because of greater 
simplicity in usage and adaptation. 
Whatever the type of energy dia- 
gram used it is important to note at 
the start that in all of them it is 
assumed that one and only one ele- 
ment of air rises in some manner 
through the stationary environment. 
Thus the indications expressed in the 
diagram will depend in no small man- 
ner on the properties of the particular 
chosen particle. Actually the inte- 
grated effect of the large number of 
particles making up the air column 
should be considered. There is some 
doubt as to whether it is justifiable 
to neglect several other factors which 
may conceivably enter into the pro- 
cess. The ascent may be in the 
nature of lifting of an entire layer 
rather than the rising of a “bubble” 
of air, small compared with an air 
mass. Then there are the non-adia- 
batic effects of radiation. In spite 
of the complete neglect of such com- 
plicating factors, energy diagrams, 
based on the assumption that one 
relatively small mass of air rises 
through a more or less steady en- 
vironment, have been used success- 
fully. This fact per se indicates that 
the fundamental assumption is in 
the main justified. Furthermore, 
anyone who has had the opportunity 
to witness gliding activities can 
hardly doubt the existence of rela- 
tively small, rapidly rising up-cur- 
rents, called by the gliding enthu- 
siasts “thermals’’. 
The tephigram, with which we shall 
here be concerned, acquires its name 
from the thermodynamic quantities 
that are its coodrdinates: temperature 
(T) and entropy (4). The term 
entropy I shall not attempt to define 
here, for it is a concept which defies 
descriptive definition, and is a sort 
of mathematical adaptation. Its deri- 
vation may be found in any textbook 
cn thermodynamics. Generally, the 
synoptic meteorologist regards en- 
tropy as something which is propor- 
tional to potential temperature, for 
it may easily be shown that: 
j= C log @ + constant (1) 
where ¢ is the specific entropy of dry 
air, gi the specific heat of air at con- 
stant pressure, and @ the potential 
temperature. The choice of a value 
for the constant is entirely arbitrary, 
for, as with energy, it is not the abso- 
lute value of entropy that matters, 
but rather the changes. 
Entropy is used as the ordinate of 
the tephigram. Because of the re- 
lation (1) and the ease of obtaining @, 
the logarithm of the latter is often 
used as an ordinate in addition to 
entropy. The abscissa of the tephi- 
gram is temperature, usually ex- 
pressed in degrees C. In the diagram 
shown in Fig. 13 the temperature in- 
creases from right to left; in some 
types of the diagram this scale is re- 
versed (Fig. 15). The solid lines 
2A. Refsdal: Der feuchtlabile Niederschlag, 
Geofysiske Publikasjoner, Vol. 5, No. 12, 1930; 
Das Aerogram, Met. Zeit., Jan. 1935, pp. 1-5; 
Geofys. Publ., vol. 11, No. 13. 
3Sir Napier Shaw: Manual of Meteorology, 
Vol. JII, The Physical Processes of Weather, 
Chapt. 7, Cambridge, 1936. Cf. Woolard et 
al: Gruphical Thermodynamics of the Free Air, 
Mo. Wea. Rev., Nov., 1926, pp. 454-457. 
4C¢. M. Alvord and R. H. Smith: The Tephi- 
gram, M.I.T. Met. Course, Prof. Notes No. 
1, 1929 (out of print). Repr. Mo. Wea. Rev., 
Sept., 1929, pp. 361-369. 
