Cinders, you are talking about two different cartridges, the Pedersen cartridges ready for delivery in 1919 was called the Pedersen 30-18 (7,65x20),
and used a device inserted into a modified M1903 rifle with a magazine holding 40 rds. By the early 1930's all these Pedersen devices were scrapped
with the cartridges. The M1903 rifles were converted back to normal issue.
The 276 cartridge was developed by Mr Pedersen in the 1920's for his rifle design which used a breech mechanism somewhat like the GermanLuger
and required a special lubricant on the cartridge. John Garand's early design also used the 276 Pedersen on a ten round clip
Later it was decided to continue using the 30-06 and Garand's design was modified to use this cartridge but the Pedersen design could not be used.