20 
transactions of the texas academy of science. 
continue to give their time to doing over again what had been already 
done. 
In his Field-Book, edition 1854, Henck says: “A prismoid is a solid 
having two parallel faces, and composed of prisms, wedges, and pyramids, 
whose common altitude is the perpendicular distance between the parallel 
faces.’’ This is ambiguous and stupid. It defines nothing. The old 
prismoid may be cut up into prisms, wedges, and pyramids, but this is 
not at all its essence, and, to me, does not even definitely suggest the 
more general solid for which in 1881 I introduced to English readers the 
word Prismatoid, now adopted by the Encyclopedia Britannica. 
The definition appearing in four successive editions of my Mensuration 
(Ginn & Co.) and four successive editions of my Elements of Geometry 
(Wiley & Sons), is as follows: 
A Prismatoid is a polyhedron tvhose bases are any two polygons in par¬ 
allel planes, and whose lateral faces are triangles determined by so joining 
the vertices of these bases that each lateral edge , with the preceding, forms a 
triangle with one side of either base. 
The prismatoid is identifiable with the pris¬ 
moid by considering a triangle as a trapezoid 
with one null side. The word is due to Witt- 
stein (1860). It is simply the German form of the 
word prismoid, and now having served its pur¬ 
pose to mark the importance of these triangular 
trapezoids, it is doubtful if it be worth retaining. 
The Newtonian formula, misnamed prismoidal, 
corresponded in range neither with the prismoid 
nor the prismatoid, nor their limiting form, the cylindroid. Maclaurin 
had indicated exactly its applicability. Yet, in 1857, fifteen years after 
Steiner, Gillespie reaped honor from merely showing that the formula is 
applicable to the space covered by the hyperbolic-paraboloid. 
In 1858 Chauncey Wright in the Mathematical Monthly (Cambridge, 
Mass.), in a special investigation devoted to the subject, obtained by the 
Differential Calculus (which was not at all necessary) the cubic equation 
of applicability, but missed Weddle’s beautiful rule. 
Prof. E. W. Hyde, in 1876, in an article entitled Limits of the Pris¬ 
moidal Formula, did not even get as far as his predecessors. 
In an extended memoir on the Prismoidal Formula, in Van Nostrand’s 
Magazine, 1879, J. W. Davis, again by the differential calculus, reaches 
this cubic. 
In Halsted’s Mensuration (1881) the applicability of the old or three-term 
prismoidal formula is exhaustively treated and without the calculus. For 
readers of the calculus the following may be given as a paraphrase of the 
method in Todhunter Int. Cal., p. 173, of showing that this formula ap- 
