Jack Russell’s are intelligent and athletic small dogs bred to hunt and full of energy. They love to run and chase and most of all to dig. Doesn't sound like a good choice for an apartment dweller. However, these dogs do fairly well in an apartment setting. Urban dog owners tend to realize, maybe to feel a little guilty even, that their dogs require more active attention to their needs than some owners in the suburbs who assume their animals are getting enough exercise simply by having a small yard to spend time in.
Jack Russell’s do need company during the day, either their human or another dog to engage their interest. Because of the traits bred into the Jack Russell to create a dog able to keep up with mounted hunters all day and then burrow into the ground and catch and kill the quarry, they have a real need to expend huge amounts of energy. Adequate exercise is absolutely essential.
Crate training, the method of house training utilizing a crate, works well for Jacks in an apartment. If he's a puppy less than nine months old he isn't able to hold his bladder all day while you're at work. There are bound to be accidents but you're still better off not to confine him for nine hours or more to a crate as that will lead to separation anxiety issues that can easily escalate. Walking on a four hour schedule is much more comfortable for your dog. There are lots of neighborhood dog walkers who make a business of giving your dog not only a walk but a little company and recreation during the day while you're away. Most of these folks walk several dogs at a time which offers the added benefit of socialization for your dog.
A second option that's very attractive for owners of high energy dogs is dog day-care. These facilities are much like child day-care. The larger breeds are separated from the smaller dogs. They enjoy supervised play, snacks and in some cases hydro therapy, grooming and other services as well as the company of other dogs and experienced staff members.
With both of these services be sure you check references and let the providers know about any behavioral or aggression issues your dog has.
If neither of these options work for you the answer may be a second pet. I don't think a cat is a good idea with a Jack Russell. If he didn't actually do it harm it would have a life of intimidation and fear. If you get another dog don't simply put them together and let nature take its course. The result could be fatal. Introduce them in a careful and supervised way to be sure they're comfortable together before you leave them alone. Also, don't be tempted to get another Jack. They are particularly aggressive with others of their own breed.
If you do decide to leave your dog to his own devises during the day try to make it as interesting as possible for him. Being who he is, he's definitely going to let you know if he's not happy with the arrangement. Shredded furniture and bad toilet practices are likely to be the evidence of his displeasure. Be sure to leave plenty of toys and chew objects around. The puzzle toys that allow your dog to get treats when they perform a certain behavior are good. You should be sure he can see out of a window. You might allocate a chair or table for him to sit on as he watches the activities outside. Dogs like the soothing sound of a human voice so leaving the TV or radio on can be a comfort to him while you're out. I like to put the TV on the shopping channel as I know they can be counted on to continue talking no matter what.
Set aside enough time everyday to have 10 to 20 minutes of vigorous play like Frisbee fetch with a soft Frisbee in addition to a long walk of 15 to 30 minutes. This a good way for you both to wind down and strengthen your relationship at the end of the day. If you work with your Jack Russell, your Jack Russell Temperament will make for a happy home life.
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They love to run and chase and most of all to dig. Doesn't sound like a good choice for an apartment dweller. However, these dogs do fairly well in an apartment setting. Urban dog owners tend to realize, maybe to feel a little guilty even, that their dogs require more active attention to their needs than some owners in the suburbs who assume their animals are getting enough exercise simply by having a small yard to spend time in. 
