The Tithe Applotment Composition Books (1823-1837) was a rural land-based taxation. The funds went for the support of the Church of Ireland clergy. All Protestants and Catholics were required to pay. However, be aware that you may not find your ancestor in the Tithe Applotment books. It’s the why I want to discuss.
The basic rule of thumb is that you should not expect everybody to be listed. The reason is that only those who were responsible for paying the tithe were listed by name. One person often collected for others in the townland. Another reason is some classes of occupiers, such as cottiers (occupiers who paid rent in labor) and farm servants, were not listed at all.
Another reason you may miss someone, is not because they were not listed, but the townland of residence threw you off. The place names of townlands in the Tithe will often differ from those in Griffith’s Primary Valuation (1847-1864). The Ordnance Survey in Dublin officially finished setting the boundaries and standardized the townland names during the 1830s after the Tithe Books had been compiled in many civil parishes. Place names and boundaries were somewhat fluid prior to the 1830s. So your ancestors may actually be listed, just not where you expected.
To sum this up, remember the following: 1) the Tithe was for rural Ireland only; 2) not everybody who paid was listed; and 3) townland boundaries and names were somewhat fluid during the Tithe era. Now you can approach this source in a new light.