I agree with many of the replays you have received. The Capacitor appears to be connected Phase to Phase as there is no neutral. This not clear due to the position of the image supplied, but it appears correct. There are also two lightning arresters connected from each phase conductor to an earth ground (likely).
Almost without exception distribution lines (35kV and lower to about 2.4 kV) are inductive in nature. All lines have both capacitive and inductive values but for Distribution lines, the capacitive value is usually 5 to 30 times less than the inductive value. This mostly because they are short, 7 miles or less, and the inductive values are enhanced by the load current flowing through the lines adding to mutual induction also.
An unloaded long transmission line may have enough capacitance to ground to cause voltage rise exceeding the insulation levels. This condition termed Ferranti Rise can be a problem and may require series inductors placed into the line during light or no load conditions.
For your picture the capacitor is considered "fixed" (in service all the time) and it serves two purposes. Power factor correction and voltage regulation. Adding capacitance both corrects for inductive loads and raises the line voltage. The size of the capacitor is usually limited to ensure there is no more than a 5 volt increase (on 120 volt base) if it is a switched capacitor. (Capacitor banks may be fixed or switched in and out of service as needed).
Hope this helps.