In Chapter 14, Bard kills Smaug by shooting him in the one spot on his belly that is not encrusted with protective gems. Tolkien uses imagery to emphasize Smaug's weak spot as an allusion that connects The Hobbit to the epic tale of the Trojan War:
The dragon swooped once more lower than ever, and as he turned and dived down his belly glittered white with sparkling fires of gems in the moon—but not in one place. The great bow twanged. The black arrow sped straight from the string, straight for the hollow by the left breast where the foreleg was flung wide. In it smote and vanished, barb, shaft and feather, so fierce was its flight. With a shriek that deafened men, felled trees and split stone, Smaug shot spouting into the air, turned over and crashed down from on high in ruin.
In The Iliad, the famous epic poem that tells the story of the Trojan War, a hero named Achilles is the most formidable warrior of the Greek army that invades Troy to reclaim their stolen queen, Helen. Achilles is such an impressive fighter not only because he is highly skilled, but also because of a blessing he received as a baby. Supposedly, his mother (a sea nymph) held him by his heel and dipped him in the River Styx. The water gave him a kind of everlasting magical armor, so that he could never be injured. The catch is that the heel his mother held onto during the ritual did not receive the same protection. Details about Achilles's death do not appear in The Iliad, but other sources complete the story: after Achilles kills the Trojan prince Hector, Hector's brother Paris shoots a fatal arrow through Achilles's vulnerable heel.
Like Achilles, Smaug is a seemingly invincible enemy, both because he can do a lot of damage and because he has the best armor imaginable. Smaug's armor is not explicitly magical, but it does have an air of mysticism and symbolism. The image of "sparkling fires of gems in the moon" underlines the way Smaug has stolen the glittering treasure in the mountain, fused it onto his skin, and turned it into a fiery coat of armor that is powerful enough to light up the night. In the Trojan War, the Greek army (for which Achilles fights) sneaks into Troy inside a great wooden horse to begin a 10-year military occupation. Likewise, Smaug has snuck into the Lonely Mountain for a long occupation. It is up to the mountain's inhabitants to, like Paris, find the conviction and means to fight this formidable enemy off.
The "deafening" imagery of Smaug's intense shriek further reinforces the epic scale of The Hobbit, even though it is essentially a children's story. The consequences of this battle—felled trees, split stone—are legendary. By alluding to Achilles's weak heel, Tolkien encourages the reader to see other parallels between this book and ancient Greek epics. For instance, Bilbo's constant teetering between adventurousness and homesickness makes him a lot like the hero Odysseus. Tolkien's use of songs emphasizes the novel's connection to the kind of oral storytelling that these ancient epics are based on. Tolkien thus hints at a rich mythology and history surrounding The Hobbit, even though it all takes place in a little world of his own invention.