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The text in my previous post doesn't seem to have wrapped correctly so here it is again with line breaks inserted

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Hanno,
        As promised I attach pdf files in which the cosine scales are 
printed high and low on the page. The programs that generated them differ 
by a single statement
/CosScaleStartPoint { 2.3 cm 11.5 cm } def
for the upper scale and
/CosScaleStartPoint { 2.3 cm 1.5 cm } def
for the lower. They can be printed together by passing the page twice but
as noted previously they will not then be precisely aligned.
 
I also attach a version of the flat Bygrave in which the cosine scale runs 
from -89°15' through zero to 89°15' with signs omitted on the negative angles.
This extended scale makes it fairly obvious why the dual zero pointers work. 
As I alluded to in an earlier post, with this scale multiplication is performed
by aligning a zero pointer with a number on the cotangent scale and reading left 
to right. Division is performed by aligning a zero pointer with a number on
the cotangent scale and reading right to left. The CosScaleTicksDown flag has
been set to true in this scale which allows calculations to be performed by
aligning the cosine and cotangent scales baseline to baseline which may enhance
visibility.
 
The code to generate the scales requires explicitly listing how each and every
scale tick is drawn and labeled. Inreasing the number of ticks just requires
expanding that list. Where do you think the additional ticks should be added?
 
Regards,
Robin
 
Note: in generating the last scale I found that not all signs were being omitted
from the lables of negative angles and also that the program would fail for
certain combinations parameters. These bugs have been fixed in the attached
Postscript file and I will post the new version of the code for other Bygrave
types in due course.