ssh without password is not working correctly

[ShibuThomas]

HI all.

I want to do ssh login into two different mechines on by one.I tried the 
following squence.but it is not working correctly.
For Ex I have 3 mechines Host1,Host2,Host3.
I need to login into Host2,Host3 using SSH from Host1.
I tried the following:
step 1:
-logged into Host 1
-execute ssh localhost
-execute ssh-keygen -t dsa
-execute scp ~/.ssh/id_dsa.pub Host2:.ssh/authorized_keys2
-exectue ssh -l root Host2
not get the prompt for password.
Then I tried to connect to Host3
step 2:
-logged into Host 1
-execute ssh localhost
-execute ssh-keygen -t dsa
-execute scp ~/.ssh/id_dsa.pub Host3:.ssh/authorized_keys2
-execute ssh -l root Host3
not get the prompt for password.
But after this I tried to connect Host2 from Host1 using
-ssh -l root Host2
I got the prompt for enetring pasword.
Is anyone know how to rectify this.