In depreciation, the mid-month conventionmeans that an asset placed into service during a given month is assumed to have been placed into service in the middle of that month. For example, if you place a warehouse into service on October 6, you will assume it was placed into service in the middle of October and will record depreciation for HALF of the month of October. If a building is placed into service on October 23, you will assume it was placed into service in the middle of October and will record depreciation for half of the month of October.

The mid-month convention ALSO applies to the disposal of an asset. This means that an asset that is disposed of on October 25 will be assumed to have been disposed of in the middle of October. If an asset is disposed of on October 3, it is also assumed that the asset was disposed of in the middle of October. In either situation, depreciation will be recorded for half of the month of October.

The mid-month convention is pertinent for the income tax depreciation for certain property.  You can find more on this in the INTERNAL Revenue Service PUBLICATION 946.

Hope it helps..