Introduction:
William Jones was an 18th-century British philologist and scholar who made significant contributions to the study of languages and ancient Indian culture. His ideas were influential and supported by several notable individuals of his time. In this response, we will discuss the support for William Jones' ideas by Henry Thomas Colebrooke.

Henry Thomas Colebrooke:
Henry Thomas Colebrooke was a renowned Orientalist and Sanskrit scholar who lived during the same period as William Jones. He was one of the key proponents of Sanskrit and Indian studies, and his work greatly complemented the ideas put forward by Jones.

Support for William Jones' Ideas:
Henry Thomas Colebrooke supported the ideas of William Jones for several reasons. Let's explore some of these reasons in detail:

1. Sanskrit Studies:
Both Jones and Colebrooke shared a common interest in Sanskrit studies. They recognized the importance of Sanskrit as a key language for understanding ancient Indian culture, literature, and philosophy. Colebrooke contributed significantly to the field of Sanskrit grammar and translated numerous Sanskrit texts into English. His work further reinforced Jones' ideas regarding the richness and value of Sanskrit language and literature.

2. Promotion of Indian Knowledge:
Jones advocated for the recognition and promotion of Indian knowledge and culture. He believed that ancient Indian texts contained valuable knowledge that could benefit the world. Colebrooke shared this perspective and actively worked towards translating and preserving Indian texts. He translated important Sanskrit works on mathematics, astronomy, law, and philosophy, making them accessible to a wider audience. By doing so, Colebrooke supported Jones' ideas of acknowledging and disseminating Indian knowledge.

3. Collaboration and Influence:
Jones and Colebrooke had a close professional relationship and often collaborated on various projects. They exchanged ideas, reviewed each other's work, and provided mutual support. Colebrooke's endorsement of Jones' ideas carried significant weight due to his own expertise and reputation in the field of Sanskrit studies.

Conclusion:
Henry Thomas Colebrooke supported the ideas of William Jones due to their shared interest in Sanskrit studies, the promotion of Indian knowledge, and their collaborative relationship. Colebrooke's contributions further strengthened Jones' work and helped establish the significance of ancient Indian culture and languages in the academic world.

The ideas of William Jones were supported by:
- Henry Thomas Colebrooke: William Jones and Henry Thomas Colebrooke were both prominent Orientalists and Sanskrit scholars during the 18th and 19th centuries. They shared a deep interest in ancient Indian culture, language, and literature, and collaborated on various projects. Colebrooke was a strong supporter of Jones' ideas and contributed to the development of Indology.
Other options mentioned in the question are incorrect:
- James Mill: James Mill was a Scottish historian, philosopher, and economist who lived during the late 18th and early 19th centuries. While he was an influential figure in British intellectual circles, there is no evidence to suggest that he specifically supported the ideas of William Jones.
- Thomas Macaulay: Thomas Macaulay was a British historian and politician who lived in the 19th century. While he played a significant role in shaping British policies in India, there is no direct evidence to suggest that he supported the ideas of William Jones.
- Charles Wood: Charles Wood, also known as Viscount Halifax, was a British politician who served as the President of the Board of Control for India during the mid-19th century. While he was involved in Indian administrative affairs, there is no direct evidence to suggest that he supported the ideas of William Jones.
Therefore, the correct answer is D: Henry Thomas Colebrooke.