I can't give a definitive answer but I remember reading quite recently that they were hill and dale.  I can't see Edison recording laterally because he was so into vertical cut and I can visuallize that a vertical cut system would be far more compact.

db
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On Wed, 5/6/15, Lou Judson <[log in to unmask]> wrote:

 Subject: [ARSCLIST] Talking dolls: hill and dale? - Re: [ARSCLIST] Playing Edison Diamond discs
 To: [log in to unmask]
 Date: Wednesday, May 6, 2015, 2:36 PM
 
 I wonder if the talking
 doll recordings were hill and dale or lateral grooves.
 Anyone know?
 
 I’m just
 curious.
 <L>
 Lou
 Judson
 Intuitive Audio
 415-883-2689
 
 On
 May 6, 2015, at 12:17 PM, Paul Stamler <[log in to unmask]>
 wrote:
 
 > This is a
 linguistic issue, more than anything else. In the last 20
 years, the word "phase" has come to be used where
 "polarity" would really be a more accurate
 description, and that'd hoe the word's being used in
 this context. A hill-and-dale (vertical) recording has the
 signal impressed on the groove vertically (duh), and when
 played back with a conventional stereo cartridge it will
 deliver signals from the two channels that are of opposite
 polarity. Combine the signals as-is and the desired material
 (music) will cancel, leaving only noise. Reverse the
 polarity of one channel, then combine them, and the desired
 signal will remain while the noise (ideally) cancels.
 > 
 > Peace,
 > Paul