The 4th case-affix is used after a crude-form which ends in an affix denoting 'condition' (abstract noun -- bhāvavacanāśca [[3.3.11]]) and having the force of the affix tum (or Infinitive or purpose).,
Ex. यागाय व्रजति 'he goes to offer a sacrifice' = यष्टुं व्रजति. So also त्यागाय व्रजति, भूतये व्रजति.
The word तुमर्थ means 'having the same significance as the affix तुम्.',