Cartridge/arm matching

Rega RB 250 effective mass is 12g
and you know the compliance of your cartridge @ 100Hz (Japan standard)
make sure to multiply it on 1,5 or 2 to find out actual compliance at 10Hz

and then simpli check the diagram illustrates the relationship between cartridge compliance, tonearm mass and the resulting resonance frequency:

http://ortofon.com/hifi/support/cartridge-tonearm-resonance-frequency

you will see which cartridge (compliance @10Hz) will be the best match for your tonearm (effective mass) to stay in desired resonance range from 8 to 15 hz

The formula noted by Chakster is correct but it has a very limited purpose, viz., assuring that a particular cartridge/arm combination resonates somewhere around 8-15Hz. A resonance frequency in this range is presumed to avoid excitation by either musical signals cut in the grooves or typical record warps.

The Shelter/Rega combo falls inside this safe range, as do probably 90% of all cartridge/arm combinations. No need to fuss any further about the math, it won't tell you anything more and certainly won't predict the sonic behavior of any cartridge/tonearm combination. For that there is only one test, the ears of the listener.

As I originally posted and Stringreen repeated, what sonic issues (if any) are you trying to address?

>>The 103R is similar in compliance to the Shelter...

Actually, no. The compliance for the Shelter 501 MkII is 9 x 10-6 cm/dyne, while the compliance for the Denon DL-103 is 5 x 10-6 cm/dyne. That's quite a difference. There are very few if any, modern cartridges with lower compliance than the DL-103 family, which makes them a difficult challenge for use with most light, short tonearms (like the RB-250.

Resonance compliance is a complicated subject- it's not just about cartridge/tonearm weight or damping. Adding a heavier counterweight or mass to the headshell will not make a DL-103 sing on an RB-250 arm.

The Shelter should work with the RB-250, although as Stringreen mentioned you will need some method to adjust VTF, and you have few good options for azimuth adjustment, which is critical in order to achieve best sound with any MC cartridge.

Actually, yes. ;-)

The compliance Denon quotes for the DL-103 is based on a measurement at a 100Hz, which is not industry standard (or particularly useful). When measured at the industry standard (and more useful) 10Hz, the DL103's compliance works out to be approximately 11x10-6cm/dyne, which is actually a bit higher than the Shelter's.

Fully agree with the rest of your post.

Again, no. The adjusted compliance for the Denon DL-103 at 10Hx is often mistakenly quoted at 11x10-6cm/dyne. The fact is that no standard formula that works for converting compliance from all cartridges due to differences in construction and materials. Although Denon has always listed the compliance for the DL-103 at 11x10-6cm/dyne, the actual demonstrated compliance is a little less. The base rule of thumb for converting from 100Hz to 10Hz is to multiply by 1.5. Assuming that the actual compliance is 4.5, multiplied by 1.5 comes out to 6.75 calculated. I use 6 as a planning rule.

From 1973-1978 I worked for a Southern California audio dealer with several stores. We were also a distributor for Nippon Columbia, Denon's parent company. Among other brands we also carried Denon turntables and cartridges, but not the DL-103. One day in 1975 (as I recall), a technical engineer for Denon visited and made a training presentation for the sales teams. Shugita-san referred to the suspension and aluminum cantilever on the DL-103 as having the lowest compliance and being the most stiff and unbendable of any other cartridge on the market. He also stated that this cartridge was completely unsuited for any of the tonearms that we were carrying, including Denon, Luxman, Micro Seiki, Philips, Sansui and Thorens.

I have tried, many times, to get a DL-103 to work (aka sound good) mated with a medium compliance tonearm, always unsuccessfully. It simply does not sound the way the cartridge was designed to sound by the manufacturer.
I would not recommend that combination to my customers.