The Senate may have legally and constitutionally given the powers to the Princeps but the Princeps still controlled the army, which was the true basis of it's power. The Empire needed an official loyal army that could protect it while not exhausting it with demands for men and funds. Octavian, now Augustus had such an army and could support it with a relatively light tax. That it's loyalty lay with the Princeps and not a republican Senate was irrelevant in the face of its efficiency. The power of the Princeps brought benefits to the 'Republic.'
The arrival of peace and stability brought prosperity. Prosperity meant that the Emperor had the funds to promote a building program that sanctioned the growing authority of himself as 'Princeps' and allowed him to transform Rome into the greatest city of the Empire.…
