Sam-Nary

While I think the Romans would have the technology and tactics to conquer India, I don't they had the men or would have the opportunity. While Trajan would defeat and conquer the Parthans, he only occupied Armenia and the Tigris/Eurphretes river basin to the Gulf of Persia (don't ya just hate it when you get the wrong gulf?). This left much of the Parthan Empire unoccupied and allowed it to fall under the Sassanid dynasty in a fairly short period of time. Just to get to India, the Romans would need to finish conquering the Parthans/Sassanids and occupy it. To do this, Rome would need to massively increase the size of its army, just to maintain a firm stance in western Europe and along the Danube.

I'd expect that if Trajan continued to press east he might have been able to overpower the Parthans/Sassanids and secure their loyalty to the Empire, but would then need to stop and reorganize to integrate the Parthan/Sassanid military system into the Roman military system, which would take time. By the earliest possible time this could have been done, Trajan would have died and Hadrian would have taken the throne, and given Hadrian's politics, Rome would have abandoned all of Trajan's conquests in favor of a more defensable line.

Mosquito

Such operation would be impossible for political reasons. No emperor could leave empire for such expedition, it would take too much time and there was risk that when coming back someone else will take the power meantime.
And there would be no general to trust him enough to give such great army to command, he could have come back with it as belowed leader of such army and overthrone emperor.

emperor of seleucid

How about you cut your ignorance. Alexander after going to india. There are hypothesis that tropicals climate gave him diseases.

Mangekyou

Im not disagreeing with that. Im saying it may have been Malaria becasue it was rampant in Babylon at the time. It could have also been poison..Both options much discussed. However, considering he was badly wounded in India and he wa prone to the odd Bacchanalia, disease is a likelier option.

Delenda est Roma

In the OP the army is transported by sea.

Sam-Nary

Rome would still need to expand its army to undertake such a campaign. Moving by sea would bypass the Parthan/Sassanid Empire, but the Romans would still need to enlarge the army to maintain its other borders, which would raise taxes to both pay the soldiers and to pay for their being equipped and transported to India.

I don't think Rome could have done so easily. At least not during Trajan's lifetime.

Mangekyou

If the expedition went through land based route or if we are continuing from when he was alive and campaining, I would probably agree. Hadrian would certainly pull the borders back.

Guaporense

I should add that those 300,000 soldiers, each making 900 sestertii of silver per year, would have a total income of 270 million sestertii per year, which would be spend in India, that's about 300 tons of silver. Add the incomes of the centurions and other elite soldiers, which made 15 to 50 times the typical legionary salary and the expenditures increase to 350 tons.

The fleet of 200,000 tons to supply the invasion force will only be used in case the local supplies are not enough. Local food will be the main source of food if everything goes right. Food purchased with Roman silver coins.

Therefore, each year of the invasion will inject into India 350 tons of silver. Over the 5-6 years of the invasion, a total of 1,750 to 2,100 tons of silver would be injected into India. For comparison, China imported a total of 7,300 tons of silver during the whole 16th and 17th centuries. That was enough silver to actually change the monetary system of China to a silver based monetary system. And India's population in the 2nd century was a fraction of China's population in the 17th century. Hence, 2,000 tons of silver would be actually enough to turn India into a silver using economy and therefore will convert it into a cash cow province for Rome.

Mangekyou

If they inject too much it would debase the value.

Ancientgeezer

The Gulf of Mexico? That's really optmistic! The next thing will be the Legions deploying β XLVII Bombers!