580 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
is unfortunate and does injustice to the luminous and unimpeachable 
character of Hamilton’s mathematical reasoning. It is equally a mistake 
to suppose that the quaternion calculus is merely an “ abridged notation.” 
It is a calculus sui generis, its novelty consisting, not in a notation, but in 
new ideas requiring a new notation for their expression. 
37th Meeting. February 8, 1888. 
The Chairman presided. 
Present, seventeen members. 
The minutes of the 36th meeting were read and approved. 
Mr. R. S. Woodward presented the principal features of a 
paper on The Variation of Terrestrial Density, Gravity, and 
Pressure, according to the Laplacian Law. 
Starting from the law assumed by Laplace, namely, that at any 
point within the earth’s surface the increment of pressure is 
proportional to the increment of the square of the density, the 
steps involved in the derivation of formulas expressing the den¬ 
sity, gravity, and pressure in terms of the distance of the point 
from the earth’s center were briefly indicated. A set of for¬ 
mulas adapted to the numerical computation of the density, 
gravity, and pressure was given, and a table of numerical values 
derived by means of these formulas was exhibited. Attention 
was called to the fact that, according to the law in question, 
gravity increases with the depth below the earth’s surface to a 
maximum which corresponds to a depth of about 610 miles, 
and then decreases to nothing at the earth’s center. 
Some examples of other laws connecting pressure and density 
but not applicable to the earth were briefly considered. 
An outline was given of a proposed extension of the Laplacian 
law, or rather of an investigation whose object is the discovery 
of all possible laws of arrangement of density applicable to the 
earth, provided those laws are continuous functions of distance 
from the earth’s center. 
Mr. Artemas Martin read a paper on Square Numbers whose 
Sum is a Square Number. 
