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What a quirky little book! The synopsis sounds ridiculous by today's standards; design a 900 foot cannon to shoot a huge ball to the moon using cotton impreganted with some highly flammable substance as 'fuel' (called Pyroxite)
And yet the book is laced with good sound science that one would expect to find in a modern hard SF book! The distance to the moon is known as is its orbital velocity and details such as the apogee and perigee of the moon are figured into the itineray. Its all jolly good fun with a mild poke at the Americans-even though the main characters are American and it reads as if written by an American, at times one detects the odd poke at the 'Yankees' as Verne's character refers to his colleagues.
A group called the Gun Club form with the intention of making bigger and better arms, but when peace is declared its members feel somehow deprived of an enemy to fight and so must look elsewhere. Then up pops the idea of a huge gun, bigger than anything they have seen before, and it will be used to fire a cannon at the moon to gain relations with the selenites up there (i.e. colonise!) and plant the American flag declaring the world theirs! But thats how people thought back in the day, and bear in mind this was written over 100 years before the 1969 moon landing!
All in all quite incredible and great fun!