More than two streams in a row?

I can't get two streams in a row to work in node.js. See the following code:

var Stream = require('stream');

var stream1 = new Stream;
stream1.readable = true;

var stream2 = new Stream;
stream2.readable = stream2.writable = true;

var stream3 = new Stream;
stream3.readable = stream3.writeable = true;

var i = 0;

stream2.write = function(data){this.emit('data', data)};
stream3.write = function(data){this.emit('data', data)};

setInterval((function() {
stream1.emit('data', String(i++));
}), 100);

//works:
stream1.pipe(stream2).pipe(process.stdout);

//does not work - why???
//stream1.pipe(stream2).pipe(stream3).pipe(process.stdout);

How do I get the two streams in a row to work?