Shaykh Tusi writes in his book entitled Misbah ul Mutahajjid that 20th of the month of Safar is the day on which Jabir bin Abdullah Ansari a companion of the Holy Prophet came from Medina to Karbala to pay homage to the sacred grave of Imam Hussain and he was the first person who performed homage to the grave of the Imam.
Homage of Imam Hussain on that day is recommended and it is this very homage that is called Ziyuratul Arba'in. Shaykh Tusi appears to say that Jabir left Medina with the object of paying homage to the sacred grave of Imam Hussain and arrived at Karbala on the 20th day of Safar and not that he reached Karbala after forty days of the martyrdom of the Imam by chance.
It is not unlikely that it was so, because after the arrival of Ahlul Bayt in Kufa Ibn Ziyad immediately dispatched Abdul-Malik ibn al-Harith Salami from Iraq to the Hijaz so that he might arrive in Medina as early as possible and inform Amr bin Sa'id bin A-S Amavi, the Governor of Medina, about the martyrdom of the Imam and his companions and Abdul Malik proceeded to Medina at once, reached there after a few days, and formally conveyed the news of the martyrdom of the Imam to the governor.
In that case it is possible that on hearing about the tragedy of the martyrdom of the Imam and Bani Hashim and the companions of the Imam, Jabir bin Abdullah Ansari, who according to some narration had lost both of his eyes by that time, might have departed from Medina with the intention of paying homage to the graves of Imam Hussain and his devoted friends, who bravely met martyrdom, and might have arrived in Karbala on the 20th of safar i.e. that is exactly forty days after the martyrdom of the Imam and the tradition of the Ziyartal Arba'in of the Imam was commenced by him.