They ask for donations from wealthy donors, the general public, and appropriate research institutions (government or private). They employ professional fundraisers and so on.
Wealthy donors like to have their name on the new/refurbished building or a single project ("digitize these portraits"), but donate a lot of money for that purpose.
Research institutions will fund things necessary for the project, but it's difficult to get funding to make general improvements or maintenance. That's not their purpose. "Digitize the 19th century British portraits" sounds like a project, "migrate that data we digitized to CDs in 2000 to a new database system" generally doesn't.
The general public donate small amounts -- e.g. an extra £1 on their exhibition ticket, or £10 in the collection box when they leave, or an annual membership for paid-for exhibitions. This money can be spent fairly freely, so it's more likely to be spent on everything else -- maintaining buildings, rooms, curating collections, digitizing things that don't fall into a nice digitization project, and so on. In Britain, for the museums that have been free for a long time (including the British Museum), it can be difficult to increase these donations ("I already paid in taxes").
I can't see a by-collection breakdown in the annual financial report of the British Museum, or my former employer. Perhaps it would need an FOI request.
Wealthy donors like to have their name on the new/refurbished building or a single project ("digitize these portraits"), but donate a lot of money for that purpose.
Research institutions will fund things necessary for the project, but it's difficult to get funding to make general improvements or maintenance. That's not their purpose. "Digitize the 19th century British portraits" sounds like a project, "migrate that data we digitized to CDs in 2000 to a new database system" generally doesn't.
The general public donate small amounts -- e.g. an extra £1 on their exhibition ticket, or £10 in the collection box when they leave, or an annual membership for paid-for exhibitions. This money can be spent fairly freely, so it's more likely to be spent on everything else -- maintaining buildings, rooms, curating collections, digitizing things that don't fall into a nice digitization project, and so on. In Britain, for the museums that have been free for a long time (including the British Museum), it can be difficult to increase these donations ("I already paid in taxes").
I can't see a by-collection breakdown in the annual financial report of the British Museum, or my former employer. Perhaps it would need an FOI request.