Burke's Barrage is a toss juggling

Toss juggling

Toss juggling is the form of juggling which is most recognisable as 'juggling'. Toss juggling is at once: a performing art, a sport, a form of exercise and meditation, a recreational pursuit and often is a hobby....

 pattern named after its inventor Ken Burke. It is quite popular among jugglers due to the impressive arm moves, but it's not so hard to master, compared to the Rubenstein's Revenge

Rubenstein's Revenge

Rubenstein's Revenge is a 3-ball toss juggling pattern named by George Gillson after its inventor, Rick Rubenstein. Along with Mills Mess and Burke's Barrage it is one of three well known named juggling patterns that involve complex carries and crossed arm throws...

 for example.

The pattern is based on the siteswap

Siteswap

Siteswap is a notation used to describe juggling patterns. It encodes the number of beats of each throw, which is related to their height, and the hand to which the throw is to be made...

 sequence 423. This sequence represents the height of the three basic throws in the pattern. The 3 represents a ball thrown at the typical height of a 3-ball cascade

Cascade (juggling)

In juggling, a cascade is the simplest pattern achievable with an odd number of props. The simplest cascade is the three-ball cascade. This is therefore the first pattern that most jugglers learn.-Three-ball cascade:...

. The 4 represents a ball thrown at the height of a four ball fountain

Fountain (juggling)

The fountain is a juggling pattern that is often used for juggling an even number of objects. In a fountain, each hand juggles separately, and the objects are not thrown between the hands. For example, in a four-ball fountain, each hand juggles two balls independently.A fountain can be synchronous...

. This ball stays on one side of the body while in the air and is thrown and caught by the same hand. Lastly, the 2 does not represent a throw, but circular motion of the hand carrying a ball through the pattern.

The idea is to throw the 4, then the 3, and when you catch the first ball you throw you make a big circle around the ball on the 3. Each 4 should be caught with a claw

Claw (juggling)

In toss juggling, a claw is a trick in which the hand throwing or catching a ball is turned upside down so that the palm of the hand faces the ground. The effect is that of the jugglers hand appearing to snatch the ball out of the air. A claw can be juggled as an isolated trick, or be...

 catch. In other words, each 4 throw is snatched with the palm facing down. The palm is turned to face up as the hand rotates around in its circle motion.

When Ken Burke himself juggles it, the circular carry passes between the 3 and the other 4, rather than around both of them.

It has nothing to do with Luke Burrage

Luke Burrage

Luke Burrage is a British juggler, musician, entertainer and author. He was born in Kent though lived most of his life in the North East of England...

, although he invented a juggling trick quite similar to Burke's Barrage, which he named Burke's Burrage. It is the same as a Burke's Barrage, but instead of making a big circle around the ball on the 3, you just put it apart on the side, which makes a more geometrical impression.