Hi Bob,
1st Class: Infants under 12 months $10 US [2 pounds Stirling]; children - two children each under ten years, One Full Fare. Meals for Children are served in the Saloon at special hours, before the other passengers. Children are not entitled to seats at the regular sittings in the Saloon unless a full fare is paid.
2nd Class: Child one year and under 12, half fare each. Infants under 12 months $7.50 each. The right is reserved to charge full fare for one child occupying a whole berth, one fare being charged for two children under 12 occupying one berth. No westbound tickets issued for children under 16 unless accompanied by or coming to join parent or parents.
I have no rates for 3rd Class, but looking at the fares paid it would appear that for 3rd Class that children were charged a half fare; with a minimum charge for Infants.
With regard to the formula, infants were not taken into account. Cabin Passengers at Southampton are listed as 401 adults, 22 children and 4 infants = 427; equal to Adults computed by Part III M.S. Act 1984 [which I do not have] 412. That is 401+11. - The same for Steerage. 439 adults, 50 children and 6 infants = 495; equal to 464. That is 439+25. Overall for 3rd Class I have 709 passengers, of whom 630 were adults and 79 children/infants. A quick breakdown gives me 73 children and 6 infants = 666.5. - The Certificates of Clearance [which you have used for your figures] give 495+102+113 [for Queenstown]; of whom 632 were adults, 69, children and 9 infants; which also = 666.5. - 464+92+110.5. Does that extra half effect your 666 Great Beast Number?
I hope this helps,
Lester