Assiduity, n.; pl. Assiduities.
Etymology: [L. assiduitas: cf. F. assiduite. See Assiduous.]
1. Constant or close application or attention, particularly to some business or enterprise; diligence. I have, with much pains and assiduity, qualified myself for a nomenclator. Addison.
2. Studied and persevering attention to a person; -- usually in the plural.
Shades of meaning
Fernald has no entry of its own for assiduity; he lists it under industry.
Where he writes about it:
Assiduity (L. ad, to, and sedeo, sit), as the etymology suggests, sits down to a task until it is done. — from industry
Diligence (L. diligo, love, choose) invests more effort and exertion, with love of the work or deep interest in its accomplishment; application (L. ad, to, and plico, fold) bends to its work and concentrates all one's powers upon it with utmost intensity; hence, application can hardly be as unremitting as assiduity. — from industry
Labor and pains refer to the exertions of the worker and the tax upon him, while assiduity, perseverance, etc., refer to his continuance in the work. — from industry