PROCEEDINGS. 
603 
physical conditions under which an unstrained stratum may 
exist in a cooling sphere, to define its position mathematically, 
and to indicate the bearing of the theory on geological phenomena. 
Mr. Artemas Martin read a paper written by Professor 
Florian Cajori, of Denver, Colorado, on the Difference Between 
Napier’s and Natural Logarithms. 
This paper is published in full in No. 1, vol. n, of The Mathe¬ 
matical Magazine, Washington, D. C., January, 1890. 
Mr. M. H. Doolittle presented a communication on Symbols 
of Non-Existence, of which the following is an abstract: 
[Abstract.] 
After a brief allusion to 0 as a symbol of non-existence, Mr. Doolittle 
dwelt chiefly on probability-equations as symbols of the non-existence 
of knowledge, either real or assumed. In tflte first edition of his Logic, 
Mill complained that mathematicians were attempting to coin ignorance 
into knowledge. In the last edition he acknowledged the injustice of 
this complaint. The mathematician merely analyzes an alloy of ignorance 
and knowledge and properly stamps it. In making this analysis prob¬ 
ability-equations are appropriate expressions for the ignorance involved. 
For example, the equation p — b when denoting the probability of an 
event, merely signifies the non-existence of knowledge (real or assumed) 
of any reason for expecting the occurrence rather than the non-occurrence 
of the event or the reverse. The equation requires no assumption and 
implies no existence of any knowledge whatever, unless it be (as Mr. Hill 
suggested) the mere knowledge that the event must either happen or fail 
to happen. If the mathematician has any knowledge or assumption of 
knowledge to express, there are appropriate symbols, and he should not 
confuse his analysis by attaching to probability-equations a meaning be¬ 
yond their proper scope. To illustrate more definitely, if the event be 
the random drawing of a white ball from a box containing balls of no 
other colors than black and white, the equation neither implies nor denies 
that the balls are equally divided in color; it is perfectly consistent with 
certain knowledge that they are all of the same color, if we do not know 
which; and it is amply justified by complete ignorance of the proportions 
in which the colors are mingled. 
