Speaking quickly with the Neurologists here, between the lines is preferred (the standard). Being able to see changes in amplitude seems to be important for differentiating ET from other movement disorders such as PD.

The evaluation of tremor is done by tracing btw the lines. These spirals are used by mainly kinetik tremors. Intentional tremor is the tremor related with cerebellum anatomically. However we use this examination method for ET patients.

Tracing on the line has been previously described for Archimedes spirals and other pre-drawn spiral shapes. See for instance references 1-3 below. Perhaps tracing on the line is a bit easier for PD patients in off-state since the line-following could represent a kind of cueing. When we constructed our test battery [4] we were mainly inspired by the test described by Liu et al [1] where spiral tracing is done on the line. Our goal was to get a measure of a general level of drawing/handwriting impairment in advanced PD, not a tremor-specific one.

[1] Quantifying drug-induced dyskinesias in the arms using digitised spiral-drawing tasks.

Liu X, Carroll CB, Wang SY, Zajicek J, Bain PG.

J Neurosci Methods. 2005 May 15;144(1):47-52.

[2] Quantification of the drawing of an Archimedes spiral through the analysis of its digitized picture.

Miralles F, Tarongí S, Espino A.

J Neurosci Methods. 2006 Apr 15;152(1-2):18-31.

[3] A novel computer-based technique for the assessment of tremor in Parkinson's disease.

Aly NM, Playfer JR, Smith SL, Halliday DM.

Age Ageing. 2007 Jul;36(4):395-9.

[4] A new computer method for assessing drawing impairment in Parkinson's disease.

Westin J, Ghiamati S, Memedi M, Nyholm D, Johansson A, Dougherty M, Groth T.

J Neurosci Methods. 2010 Jun 30;190(1):143-8.