**Core Concept**
The appearance of the first epiphyseal centre is a significant milestone in the development and growth of long bones in children. This process is part of the endochondral ossification pathway, where cartilage templates are gradually replaced by bone tissue.

**Why the Correct Answer is Right**
The first epiphyseal centre typically appears around the age of 1-2 years in long bones, marking the beginning of the ossification process. This is a result of the differentiation of chondrocytes into hypertrophic chondrocytes, which eventually undergo apoptosis, allowing blood vessels to invade and initiate bone formation. The epiphyseal plate, a growth plate located at the ends of long bones, is responsible for the continuous growth and elongation of bones until skeletal maturity.

**Why Each Wrong Option is Incorrect**
**Option A:** The appearance of the first epiphyseal centre is not related to the appearance of the primary ossification centre, which occurs earlier in fetal development.

**Option B:** The first epiphyseal centre does not appear in the diaphysis, the shaft of long bones, but rather in the epiphysis, the end part of the bone.

**Option C:** The appearance of the first epiphyseal centre is not a result of the action of osteoclasts, which are involved in bone resorption, but rather the differentiation of chondrocytes and the invasion of blood vessels.

**Clinical Pearl / High-Yield Fact**
Remember that the appearance of the first epiphyseal centre is an important landmark in the growth and development of children, and its timing can be used to estimate the age of children in cases of forensic medicine or developmental paediatrics.

**Correct Answer:** C.