cryptic/quick Crossword

[supersuezy24]

1a: Office of bishop of rome (6): ????s?
4a: Distressingly inadequate (8): ?a?????c
10a: Self propelled carriage (7): ????o?r
13a: Branch of knowledge (informal) (5): ????y
27a: To go off at this is feeble (4-4): h?l? - c?c?


2d: Female forename - lover of horses(8): ????i?p?
6d: Device to study the sun (9): ??l???t?a
17d: Poe's hair (anag) (8): ?i?o???e

[vegasmad]

27a. half cock

[JoolsTwo]

1a Papacy - is you s correct?

[Oldred]

13a ology ?

[mathsman]

4a pathetic
2d Philippa
6d bolometer??

[supersuezy24]

Thanks everyone :)
I was looking on google and found heliostat for 6d but 19a has me confused,

19a: put into fixed category(11): s?d???t???? (the d may be an s too)