Generally there wasn't a ratio to cavalry and infantry that I have found, the most important thing for Napoleon was artillery. Considering that he was on the cutting edge of the use of artillery (being a student of the Barons du Teil, two brothers that were supporters of Gribeauval, the legendary creator of the artillery system that would carry France into the Napoleonic Era). Gribeauval and the Barons du Teil would argue that artillery use should be concentrated and Napoleon would further this with the idea that all firepower should be concentrated on a critical point to unbalance the enemy (what he never said was how to determine the critical point, it has been argued that he meant the weakpoint, others say that he specifically meant the strong point (the strongest point would most unbalance the enemy if disrupted) but historians like David G. Chandler would argue that Napoleon was speaking generally and meant the focus point of the attack rather than some doctrinal ideal point.

Now, with this, Napoleon clearly had an idea of how he would use artillery and how much artillery he would need to achieve it. His idea was five guns to ever one thousand infantry. The idea is that artillery was meant to be used en mass rather than piecemeal (which many nations did before the Napoleonic era) and that they are supposed to support an attack and help create situations for the infantry to be able to successfully attack.

This ideal ratio isn't focused on artillery to support lesser skilled infantry, but rather the opposite. It has been argued by some that Napoleon's heavy use of artillery after the 1809 Campaign was meant to cover the lessening quality of his infantry but it was the opposite, the use of artillery was simply the continuation of the new ideas of the use of artillery.

At the time of the US civil war, the minimum crew manning an artillery field gun (12 pounder Napoleon cannon) was 6 men. More usually, the crew was 12 men, 8 serving the gun and 4 tending the horses.

The artillery was the King of Battle in the 19th century. Artillery was expensive, however, and never mobile enough to operate on its own or with cavalry support alone.

If artillery could keep up with cavalry, then cavalry would have been much more decisive against infantry than it ever was (as artillery could have broken up infantry squares and other mass infantry formations, allowing the cavalry to charge home).

Many armies tried to create horse drawn artillery which could keep up with the cavalry, deploy quickly, lay down powerful enough fire to disrupt infantry formations and allow the cavalry to charge home, break down and move fast enough to avoid being taken out by the heavier artillery deployed with infantry, or by an infantry advance.

This never really worked.

A 12 pounder Napoleon cannon weighed 3,865 lbs (including limber). Its caisson weighed 3,811 pounds (loaded with ammunition). A six man crew weighed 1,080 lbs (at 180 lbs/man). So the all up weight of a battlefield 12 pounder cannon deployment was 8,756 lbs. Note: 6 men are the minimum needed to serve the cannon. A more usual crew in the Civil war was 8 men to serve each gun plus up to 4 more to tend the horses.

A horse can pull a wheeled load of 700 lbs over fields or rough ground at a trot (1,100 lbs on dirt roads).

So to get a cannon to operate on the battlefield at cavalry speeds (or at least at a trot, which is near cavalry speed) would require 14 horses (12 pulling the caisson and gun, and 2 carrying 2 of the crew - There was only room for 4 crew on the limber and caisson. The crew could be mounted on the team horses (and in reality usually was – 12 pounder cannon in the civil war were usually served by 12 horses, not 14.) but this severely degrades the pulling power of the horse.)

Source: http://markerhunter.wordpress.com/2013/02/24/mobility-and-horse/

12 horse teams are not practical (it is hard to get all those horses pulling together and to control them).

It was usual to have a 6 horse team on the gun, and another 6 horse team on the caisson, but this makes rapid deployment and breakdown more difficult. Nevertheless, this was the usual deployment in the US civil war.

This deployment could travel faster, and was more mobile than infantry (allowing the guns to retreat (usually) if threatened by an overpowering infantry attack), but these cannon could not keep up with (or retreat away from) cavalry.

The other solution would be to use smaller cannon. In the Mexican American war, the cavalry used 6 pounder cannon. These threw half the weight of shot, but weighed much more than half as much as a 12 pounder gun. They were considered to have insufficient destructive power to really disrupt infantry formations.

Although, from the time of Gustavus Adolphus onward, cavalry tried to develop (and did deploy) horse drawn artillery in many armies, the power to weight ratio was always extremely marginal. Horse drawn artillery was never really fast enough or maneuverable enough (or cost effective enough) to allow heavy cavalry units, operating independently from infantry support, to defeat infantry formations.

What the cavalry really needed was a much lighter, powerful cannon. This was never technologically feasible.

So, armies had to use a combined arms approach. Artillery was important, but it needed to be protected against cavalry by infantry. Cavalry could not usually defeat infantry unless the infantry were disrupted by cannon, but cannon could not keep up with cavalry. Infantry could usually not be defeated by cavalry, but were vulnerable to artillery (and to superior infantry). Artillery could travel with infantry, and usually travel fast enough to retreat from dangerous infantry, but could not escape from cavalry.