Updated 17th November 2000

When you have removed the front cover the crossover is relatively neatly arranged at the bottom. You will have to remove some of the staples which hold the back cloth cover in place to completely expose the crossover.
Most of it is for the midrange treble, the bass parts are the large inductor (heavy gauge solid core wire would on cardboard spool) and 2 capacitors (cylindrical shaped components, white with black lettering) these are towards the bottom outside edge of the speaker. There are also three resistors (dark green) by the two capacitors with a red wire attached, these are only used when the speaker is actively driven with the DAX.
The crossovers for the left and right speakers a mirror images of each other so I have tried not to make any confusing references to left or right in this text.

It is probably advisable to make a simple drawing of the layout of the crossover, noting the wiring colours where appropriate. It will be useful as a reference should you need it.

Capacitors

Midrange/tweeter capacitors

There are the 7 x 10µF capacitors which are connected in parallel (see Note.3) below the bass panel. The connecting wire comes straight from the RED midrange/tweeter input to a tinned copper wire which connects the 7 capacitors in parallel. The other side of the caps are connected by a similar wire and connects to a 10µF capacitor and 0.5R resistor (dark green) in parallel, which are below the 7 caps.

Note.3 - Parallel connection means the ends of the components are joined together so they lie side by side, with capacitors this adds the values together, so 7 x 10µF = 70µF

The replacement cap I suggest you use is Reliable Capacitor - type Audiocap Metallized Polypropylene (PPMF) - 70µF/100V these are very good capacitors at a price that won't break the bank, they also easily fit in place of the originals.

Bass capacitors

The bass section capacitors are worth replacing also. These are situated towards the bottom outside edge of the speaker. There is a 10µF and a 5µF connected in parallel so you need a 15µF replacement. I suggest you use a Reliable Capacitor - type Multicap Metallized Polypropylene (PPMF) - 15µF/200V

Removing original capacitors

First de-solder the capacitors connecting wires. They are fixed down with silicone sealant so need prising off with a screwdriver or something similar. I strongly recommend you have the cardboard cover in place over the speaker panels to avoid an accident from flying debris!

Fitting new capacitors

As I suggested work on one speaker at a time so you have the other as a reference. The new capacitors are best fixed down with silicone sealant like the originals, alternatively PVA type glue could also be used. Avoid using hot glue guns as the heat could damage the components.
Try to make sure that the capacitors are the same orientation in both speakers, some don't have directional marking but use the writing on the labels as a guide, such that the input wire goes to the end the text starts from for both left and right speakers.
When you have set the new components set in place, simply re-solder the wires.

Inductors

Midrange/tweeter inductor

The midrange/tweeter inductor is the large coil of wire situated below and slightly to the side of the midrange/tweeter itself.
Note how both ends of the inductor connect to the middle section of the crossover which is the part of the circuit associated with the midrange/tweeter level switch.
The value of the inductor is 4.3mH, you may find a label stuck to it giving the exact value as these were hand made by Apogee.
The best replacement considering the available space is the Solo 14 AWG which is 1.25" high, as all the Apogees were hand made please check the available height to make sure they will actually fit.

Bass inductor

The bass inductor is wound on a round cardboard spool situated on the bottom outside slanted edge of the speaker. Both ends of the inductor are terminated in crimp type round eyelets. One goes to the Woofer red binding post, the other is screwed down to the back panel of the speaker where it connects with the inactive portion of the aluminium bass panel.
The value of the inductor is 2.3mH, this may well have a hand written exact value which will be pretty close to 2.3mH.
Again the best replacement considering the space available is the Solo 14 AWG.

Removing original inductors

The midrange inductor will probably be crimped and/or soldered to the copper connecting bars of the middle section of the crossover. If soldered you can simply de-solder it, where it is crimped it might be best to cut it leaving approximately ½" of wire which you can solder the new inductor to. The inductor wire is varnished so you would need to scrape the surface to remove this before trying to apply solder.
The inductor will probably be fixed down with silicone sealant, cable ties or a mixture of both (as Apogees were hand made there are some differences in construction techniques). As with the capacitors if the inductor is fixed down with silicone sealant you will have to work it loose with a screwdriver or something similar.
The bass inductor can simply be disconnected by undoing the connection to the red woofer terminal and unscrewing the connection to the inactive aluminium foil portion of the bass panel.

Be very careful not to accidentally damage the inactive part of the aluminium bass panel when removing this connection, also make sure you don't lose the washer which is necessary to stop damage to the aluminum foil when re-making the connection.

The inductor will probably be fixed down with staples and/or silicone sealant. First remove the staples you can see then work a screwdriver or chisel underneath it to free it from the wood back panel.
You may have to clean off the excess silicone sealant left behind by both inductors so you have a clean flat surface to fix the new ones to.

Fitting new inductors

The new inductors are probably best fixed in place with silicone sealant, you will probably find the connecting leads will not be long enough to reach to the connecting points. This will definitely be the case of the bass inductor where the input has to reach the woofer red binding post.
You will therefore need some wire, also some new crimp/solder eyelet connectors. The wire choice is up to you, I have used some Teflon insulated silver plated oxygen free copper wire from Audiocom (UK) which is excellent. The only important factor is it needs to be around 14-12 AW.
It is possible to "borrow" the spare unconnected active use wires for this purpose, especially for the bass inductor as the RED unused wire connects to resistors which are directly by where you want to made the connection.
For the midrange tweeter inductor you want the inner connection of the inductors to connect back to the positive (red) and the outer conductor to negative (black).
The inner connection for the woofers inductor goes to the red binding post, the outer connection to the speakers back panel.
Be careful not to over tighten the connection  to the aluminum bass panel. Hold the wire connection from the bass inductor and tighten gently, if you see the aluminum around the washer begin to wrinkle do not tighten any more.

Testing, testing

Make sure you are confident the wiring is correct before testing the speaker, and always start at a low volume level first. If the midrange/tweeter makes any violent movements at low volume levels, stop immediately and re-check the wiring.
As the capacitors are direct replacements for the originals, unless the ones you have been supplied with are faulty, you should be enjoying a clearer more musical sound straight away.
Capacitors like all new equipment need some hours of use for the sound to stabilize. This can be as little as 10 hours, or as much as 100 hours use depending on the make.
You may find the high frequencies seem too obvious immediately after you have replaced the midrange/tweeter caps, but the effect will lessen with time.
The inductors are supposed to burn in very quickly, but I am sure things have continued to improve over 100+ hours of use, I guess your normal listening level may well be a factor in this.