This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.
Figs. 27, 28, 29.
To find the Contents in Gallons of a Vessel, whose diameter is larger at one end than the other, such as a Bowl, Pail, Firkin, Tub, Coffee-pot, etc.
rule. - Multiply the larger diameter by the smaller, and to the product add one-third of the square of their difference, multiply by the height, and multiply that product by .0034 for Wine Gallons, and by .002785 for Beer.
1/3 of the square
3.4884 Wine Gallons, or nearly 3½ gallons.
1026 multiplied by .002785 equal 2.8574 Beer Gallons.