Unless you are making a one-ball scarf or hat, there is going to come a point in your knitting (probably several, actually) when you will need to join a new ball of yarn. The absolute best way to do this is to join the new ball at the edge, as this avoids messy or gapped stitches. When you do this, you simply stop working with the old yarn at the end of one row and begin working with the new yarn as you begin working the next row.
However, there are sometimes that this just isn't possible. For instance, if you’re working in the round you obviously have no edge to join at. You also might be working on a project where you’re really concerned about running short of yarn and you want to use every inch possible. There are a couple of options for those times when you can't join at an edge:
The best thing to do, unless you are working with a very thick yarn, is work a couple of stitches while holding the old yarn and the new yarn together. Make sure to work these double-stranded stitches as single stitches on the next row--the double stranding won't show in the finished project. This particular method gives a nice stable join with no loosening of the stitches or possible gapping between them.
If you’re working with a particularly thick yarn (category 5 or higher), you’ll need to join as usual, meaning you’ll just stop working with the old yarn and start working with the new yarn, leaving a tail of 4-6” of each. You’ll probably need to snug up these stitches as you work the first couple of rows past the join, and may even want to temporarily tie a half hitch just to stabilize the area. Then when you're weaving in your ends, weave them across the join. In other words, weave the tail from the left over to the right and the tail from the right over to the left. This should keep that gap closed and give it the appearance of a normal stitch.
Editor's note: When joining yarn, you also have several options to splice your old yarn's end and new yarn's end together before continuing to knit or crochet. Use Google (Bing, Yahoo, etc.) to search for "Russian join," or for feltable yarns, search "felted join". You'll be able to find many written, illustrated, and video tutorials on these two popular yarn-splicing methods.
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