Tesla's small coil

I was re-reading Tesla's New York Academy of Sciences April 6 
lecture, and I could use a little help on one point.  When describing 
his small, high-potential coil, Tesla says that the secondary is 
constructed as "two flat spirally wound coils" (p. 49). But to me, S1 
and S2 in the diagram on p. 48 look more like regular multi-layer 
solenoidal coils rather than flat spiral coils (which I am assuming are 
"pancake" coils).  So what am I missing?  Any ideas or guesses as to 
how the windings go?

Steven Roys (sroys-at-radiology.ab.umd.edu)