The source is at sw1 and 2 wire cable runs from there to the fixtures. Run a length of two conductor wire from the existing fluorescent fixture to the new fixture.

Lighting Circuit Wiring Diagram Multiple Lights H1 Wiring
Wiring lighting circuit multiple lights. More current needed when additional light bulb added in the parallel circuit. Here 3 wire cable runs between l1 and l2 2 wire cable runs from the last light to sw1 and more 3 wire cable runs from sw1 to the 4 way switch and then to sw2. The break in the wire failure or removal of any single lamp will break the circuit and cause all of the others to stop working as there is only one single path of current to flow in the circuit. If three four or even more lights are required to be switched from a single source the new cable can be extended to as many lights as required. Battery runs out quicker for dc installation. Before you can wire multiple light fixtures to a switch you have to know how to do.
The basics of light switch wiring. Here the ceiling rose is shown with two cables both of which connect to line neutral and earth with no loop connection. Feed the ends of the wire through the cable clamps and tighten the screws until the wire is secure. The parallel wiring design is more complex as compare to series wiring. Wiring multiple lights to a single light switch is similar to the basic light switch configuration with the additional light bulbs attached to the first one as shown in the diagram. This video will show you how to wire a series of recessed light in your ceiling.
If more lamps are added in series lighting circuit they will all be reduced in brightness. If you wire lights in series. More size of cable and wire is used in parallel lighting wiring circuit. More lights can be added to this circuit by duplicating the wiring shown here for each additional fixture. I like to use the term daisy chain. Multiple light wiring diagram this diagram illustrates wiring for one switch to control 2 or more lights.
Loosen the screw on the side of the cable clamps on both fixtures. One cable connects to the previous light the other continues to the next light. Daisy chaining isnt the same as wiring lights in series. You can add as many lights in this fashion as need within the load limit of your wiringcircuit breaker. Because voltage are shared in series circuit. The hot and neutral terminals on each fixture are spliced with a pigtail to the circuit wires which then continue on to the next light.
How to wire multiple light fixtures to one switch.