His fathers were traced back, in humble life, along a branch of the ancestral tree to the point where it joined the stem fourteen generations ago, and his heirship was thereby squarely established.

The tracing was done by means of the records of one of the great Hindoo shrines, where princes on pilgrimage record their names and the date of their visit.

This is to keep the prince's religious account straight, and his spiritual person safe; but the record has the added value of keeping the pedigree authentic, too.
When I think of Bombay now, at this distance of time, I seem to have a kaleidoscope at my eye; and I hear the clash of the glass bits as the splendid figures change, and fall apart, and flash into new forms, figure after figure, and with the birth of each new form I feel my skin crinkle and my nerve-web tingle with a new thrill of wonder and delight.

These remembered pictures float past me in a sequence of contracts; following the same order always, and always whirling by and disappearing with the swiftness of a dream, leaving me with the sense that the actuality was the experience of an hour, at most, whereas it really covered days, I think.
The series begins with the hiring of a "bearer"-- native man-servant--a person who should be selected with some care, because as long as he is in your employ he will be about as near to you as your clothes.
In India your day may be said to begin with the "bearer's" knock on the bedroom door, accompanied by a formula of, words--a formula which is intended to mean that the bath is ready.

It doesn't really seem to mean anything at all.