surfresearch.com.au  greenwood : tahiti and hawaii, 1863

Conversely, the illustration at the beginning of the chapter is titled "Surf Swimming off the Coast of Hawaii", detailed below.
 

Publication Details
In 1864, Beeton's issued a "Second series," that is a second voume, later titled  ?
A third edition, in two volumes. was published in 1865.
Another edition was published by John Camden Hotten in 1869.
It was subsequently published as
The Wild Man at Home: or, Pictures of Life in Savage Lands.
Ward, Lock, and Co.,Warwick House, Dorset Buildings, Salsbury Square, E.C. circa 1885.
 

Given the diverse references to , it appears the vast majority of this book is not based on  first person observations.
It is unlikely that Greenwood travelled to the South Seas, either Tahiti or Hawaii, in the 1800s.
The relevant chapter,
The report of surf-riding is credited to "Ellis", proably the noted polynesian commentator, the Rev.William Ellis.
Note that the report does not correspond to the 1830 account by the Rev.William Ellis : Surf-riding at Waimanu (Hawaii).
The specified location,

The account bears several similarities with that of James Morrison in1788, Surfriding in Tahiti.

The original source is possibly:
Ellis, Rev. William: Polynesian Researches, During a Residence of Nearly Eight Years in the Society and Sandwich Islands.
Volumes I to III.
Fisher, Son and Jackson, London, 1829. pages 223 or 305.
Noted in Dela Vega et al. (2004) page 18.

The commentary for the entry notes:
"Ellis describes surf riding in Tahiti and compares them to Hawaiians:
'Their surf-boards are inferior to those of the Sandwich islanders, and I do not think swlmming in the sea as an amusement, whatever it might have been formerly; is now practiced so much by the natives of the South, as by the North.'
Noted the Tahhltian surf God was named Huaourl.
Does not Include Hawaiian text." (Ellis, 1830 : Surf-riding at Waimanu)
The possible decline in Tahitian surfriding suggested here by Ellis may appear somewhat at odds with the account in Greenwood which records surfriders numbering "from fifty to a hundred persons of all ages."

Also see James Morrison,1788:Surfriding in Tahiti

Page 110

Faahee (1), or surf-swimming, is another favourite pastime with these people.
According to Ellis, "individuals of all ranks and ages and both sexes follow this sport with great avidity.
They usually selected the openings in the reefs or entrances of some of the bays, where the long heavy billows rolled in unbroken majesty upon the reef or the shore.
They used a small board, which they called papa faahee- swam from the beach to a considerable
distance, sometimes nearly a mile- watched the swell of the wave, and when it reached them, resting their bosoms on the short, flat-pointed board, they mounted on its summit, and amid the foam and spray rode on the crest of the wave to the shore; sometimes they halted among the coral rocks, over which the waves broke in splendid confusion.
When they approached the shore, they slid off the board, which they grasped with the hand, and either fell behind the wave or plunged towards the deep and allowed it to pass over their heads.
Sometimes they were thrown with violence upon the beach, or among the rocks on the edges of the reef.
So much at home, however:, do they feel in the water, that it is seldom any accident occurs.

" I have often seen along the border of the reef forming the boundary line to the harbour of Fare in Huahine, from fifty to a hundred persons of all ages, sporting like so many porpoises in the surf that has been rolling with foam and violence towards the land; sometimes mounted on the top of the wave, and almost enveloped in spray, at other times plunging beneath the mass of water that has swept like mountains over them, cheering and animating each other; and by the noise and shouting they made rendering the roar of the sea and the dashing of the surf comparatively imperceptible."

Surf Swimming off the Coast of Hawaii. Woodcut and design by Harden S. Melville. Engraved by Newsom Woods. Greenwood, James: Curiosities of Savage Life.   S.O. Beeton, London, 1863, page 96.

1. "Faahee"
This term is not found in any other account and may be an error in transcribing from the original text.

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