METEORS AS PROBES OF THE UPPER ATMOSPHERE 
work were analyzed by Olivier [64]. Unfortunately, the 
base line used (approx. 3.5 km) was inadequate for 
precision results, and in addition the original photo- 
graphs have been destroyed. Lindemann and Dobson 
[42] used this method to a limited extent. Whitney [94] 
experimented successfully with electronically synchro- 
nized shutters for paired meteor cameras, but obtained 
few observational results. Fedynsky and Stanjukovitsch 
[21] measured the deceleration of a meteor photo- 
graphically. 
In the Harvard two-station photography of meteors 
the base line has been 37.9 km, between the Cambridge 
and Oak Ridge stations in Massachusetts [88, 90]. The 
two Ross Xpress lenses of aperture 1.5 inches, focal 
ratio F/4, were occulted 20 times per second by single- 
bladed shutters powered with synchronous motors from 
commercial power lines. Meteor trails show 5 to 80 
breaks spaced uniformly in time. Exposure times were 
normally 1" or 24, the cameras being driven on polar 
axes to follow the stars. The camera settings were so 
chosen as to produce an overlap in areas at meteor 
altitudes. 
Analysis of the photographic meteor trails is sim- 
plified because the trails are amazingly straight [8, 22, 
78, 89], that is, great circles; a change in direction of 20’ 
along a trail is rare indeed, occurring probably in less 
than one per cent of the (1700) trails in the Harvard 
plate collection, except in a few cases, very near the end. 
Hence the measurement and reduction of two-station 
trails are straightforward though tedious. The general 
method has been described by the writer [88] although 
the detailed formulas have not been published. In the 
most common case the data consist of the trajectory 
referred to sea level, the velocity V and deceleration 
—V’ at a known altitude, and the light curve. Longer 
and brighter trails often provide deceleration measures 
at several points, although the deceleration is barely 
measurable in most cases. The precision of the trajectory 
is extremely high (within a few meters) when the instant 
of the meteor is observed; the velocity is determinate 
to better than one per cent on the average; the decelera- 
tion may be well or poorly determined, while the un- 
certainty in the brightness ranges perhaps from 20 to 
40 per cent. 
Because the available wide-angle lenses can photo- 
graph only very bright meteors (—1 to —2 visual 
magnitude or brighter) the rate of photography is slow, 
one meteor in perhaps 50 to 100 hours of total exposure 
[86]. Hence, in ten years of continuous photography 
during clear moonless nights, only about sixty meteors 
were doubly photographed in the Harvard program. 
However, a program sponsored by the U. 8. Naval 
Ordnance Department is under way to photograph 
fainter and more frequent meteors [91]. 
The Theory of Photographic Meteors. Theories of 
the meteoric process have been presented by Lindemann 
and Dobson [41], Hoffmeister [31, 32], Sparrow [81], 
Maris [50], Opik [67, 69], Hoppe [33], Levin [89, 40], 
and others. Of these investigators Opik has delved 
most deeply into the detailed physical processes in- 
volved, particularly that of the production of light. 
309 
The writer [88, 90] has used physical data and concepts 
based largely on Opik’s work but has combined them 
in a mathematical framework modeled on that of J. 
Hoppe. The present account will present a very ab- 
breviated version of this composite theory, influenced 
by the simplifications introduced by Jacchia [84] for the 
case where the meteor trail is completely observed. A 
criticism of the basic assumptions follows the formal 
presentation of the theory. 
In its passage through air of density p at a velocity 
V, a meteoroid of mass m and effective cross section 
Am?!? will, in time dé, encounter an air mass 
dma = Am?!® p Vadt. (1) 
We may assume from the kinetic viewpoint, at the 
high velocities involved, that in large measure the 
atmospheric molecules in the direct path of the 
meteoroid are trapped by the meteoroid or the gases 
escaping from its surface, momentarily carried along, 
and then swept backward at a relatively low velocity 
with respect to the meteoroid. It can be shown that for 
the photographic meteors the effective mean free paths 
of the air molecules (reduced, as shown by Lindemann 
and Dobson [41], by the ratio of the temperature 
velocity to the meteoric velocity) are generally smaller 
than the dimension of the meteoroid, except at ex- 
tremely high velocities or faint magnitudes. Hence, in 
most cases there is a concentration of air (and meteoric 
gas) in front of the meteoroid in excess of that which 
might be expected from the relatively slow escape 
velocity of the molecules. Some sort of shock wave 
must form, but the significance of the shock-wave 
concept has not yet been useful in the theory. 
The acceleration of the meteoroid may be written in 
the form: 
7 
i = — = ay ¥ te = —yAm~" pV, (2) 
where y is one-half the usual drag coefficient. Equation 
(2) expresses the conservation of momentum if y = 1 
and if the trapped air molecules are assumed to escape 
with negligible relative velocity. 
The rate of mass lost by the meteoroid is undoubtedly 
a complex function of p, V, m, A and the physical and 
chemical structure of the body. Opik [67] has shown 
that a meteoroid of pure iron would probably lose a 
considerable fraction of its mass as liquid because of 
its high thermal conductivity. On the other hand, the 
writer questions (as did Opik) that a large fraction of 
the photographic or visual meteors arise from iron 
meteoroids. More likely the mass is a heterogeneous or 
conglomerate solid of low physical strength. Hence its 
thermal conductivity is probably low. In this case the 
mass loss would be directly proportional to the heat 
transferred to the surface and inversely proportional to 
the latent heat of vaporization ¢ at approximately room 
temperature. fy 
We may expect that the heat available for vaporizing 
the meteoroid will be roughly proportional to the energy 
released by the trapped air mass, dima. If the efficiency 
