By the time ex-Eaton House boys are in their thirties, the only Latin most of them will be able to quote will be the standard amo amas amat. However, there should be three bona fide legacies.
Firstly, because the Roman Empire cast such a long shadow in Western history a familiarity with ancient civilisation helps to understand classical allusions. For example, in European history the Russian and German titles for ‘king’, ‘Csar’ and ‘Kaiser’ respectively, refer to Caesar (the Germans pronouncing it correctly, incidentally) and fascism refers to the 'fasces', a symbol of Roman authority. In modern life, classical throwbacks still abound; in the architecture of our Victorian town halls and art galleries, the Renaissance pictures in those galleries, the names and founding of our cities (e.g. London and Manchester) and Latin terms like homo sapiens meaning wise man, et cetera (meaning "and the rest"). So, there is a rich cultural frame of reference to be gained from studying Latin.
Next, it should help second guess all Romance languages such as: French, Spanish, Portuguese, Italian and Romanian and help the boys to see where linguistic borrowings have taken place in English.
Lastly, Latin will help with English vocabulary. It is hard to overestimate the importance of this. Almost all of the words we learn for Common Entrance have English derivatives many of which are high-value words, e.g. fortuitous from the Latin, forte, by chance. After literacy and basic numeracy, the ability to express oneself articulately is probably the most useful and enduring skill an education can confer. It will increase your IQ – it is a critical part of it. If you are bright, it will help you to convey that. If you are not bright, it will help you to hide it!
Quod erat demonstrandum!