I am working on a design where I need to attach a stainless steel
surface to a sterling silver surface. I assume that pressing would
be the most likely means of fitting the two together as I obviously
cannot solder.

Can anyone direct me to technical to illustrate how to
do this.

Can anyone direct me to technical to illustrate how to
do this.

This is known as friction fit. The good thing in your case is that
harder metal is pressed into softer one. If you harden and temper
your steel, the task would be almost trivial. The most difficult
step is to get your steel to the right dimension, which should be
somewhat larger then corresponding opening. The proper way to
determine the size is to use Archimedes formula for determining
length of diagonal. It is square root of sum of squares of length
and depth of the footprint. Let’s say you want to press in square
piece of 1 mm thickness and 10 mm per side. The dimension of your
steel should be sqr( 10^2 + 1^2) = 10.0498 mm. Precision of 0.01 mm
is sufficient, so we simply use 10.04mm. Notice that I did not round
off, but truncate the result.

It would be easier this way. This needs to done in one direction
only, either length or width. The other direction should stay the
same.

Its no problem soldering stainless steel if you have the right flux.
wether you want to soft solder ie tin lead or hard solder ie silver
based brazing alloy.

Just do you research and the answer isout there.

Try Johnson matthey brazing products.

I soft solder stainless to copper and brass, and hard solder
stainless to stainless as well as copper and brass.

Janine- You can solder stainless to silver. Just ask any one who has
accidentally soldered their stainless tweezers to their work. Use
paste flux and silver solder.

The proper way to determine the size is to use Archimedes formula
for determining length of diagonal. It is square root of sum of
squares of length and depth of the footprint.

I am tempted to say that you are right, but my pedantic nature
compels me to provide explanation why I attributed method to
Archimedes.

Pythagoras was a geometer and his theorem was about equality of
areas formed by a square where hypotenuse was a side and two square
formed by catheti in the same manner. However, Pythagoras did not go
further than that in his thinking. Euclid, Heron of Alexandria,
Archimedes, and others were looking to expand usefulness of knowledge
of triangles. Nowadays, application of triangles involve use of
Trigonometry, which requires use of irrational functions. Ancient
greeks could not compute them and even if they could, it was too
labor intensive. So methods using quadrances ( squared distances )
and spreads ( squared sines of angles ) were developed. Archimedes
deserves a lot of credit for his insights into Pythagorean theorem
and it’s application. Also the theorem itself does not belong to
Pythagoras. It’s knowledge predates Greeks and could be traced to
Babylonian civilization. Pythagoras was the first who developed
proof of the theorem. So one would not be wrong in referring to
method as Pythagorean. On the other hand, could we credit the guy,
who invented the wheel, with invention of automobile?