168 Wisconsin Academy of Sciences, Arts and Letters. 
established, the probability of sometimes posing such a clause 
as an objective total—the probability that what may be called 
collective syntax will occur—is comparatively small. More¬ 
over, broadly and figuratively speaking, it is much more prob¬ 
able that in thought-masonry individual blocks will at once be 
moved to their proper places than that, first of all, sub-struc¬ 
tures will be formed, which burdensome masses afterward, with 
an augmented effort quite unnecessary, must be moved to their 
required places. 
While suggesting mental operation different from my own, I may 
add that, given the expectation of an object, excited by “Astronomers 
declare”, a careless mind may lose it, if succeeding numerous details 
too much crowd upon attention—so far lose it, that, in spite of the 
plainly stated “Astronomers declare the sun to exceed the moon”, if I 
ask for a repetition of my statement, I may be told that “In the opinion 
of astronomers, the sun exceeds the moon.” That is, the expectation 
of an object has faded; from lateral, the infinitive phrase has changed 
to central; though not by me asserted as the main expressional pur¬ 
pose, it is sensed as what deserves assertion, which is formally given 
to it in the attempted repetition. 
Such mental operations merely show that, as often happens, the 
linguistic mechanism has failed to work as intended, the blame in the 
given illustration being fairly chargeable upon the listener’s careless¬ 
ness. They are of small importance to the student of linguistic thought 
or expression. 
II. A Preferred Interpretation. 
In presenting this I use a mathematical illustration, because 
of the mental and expressional precision to which we are 
trained in quantitative operations. Accordingly I note that 
the expression 3:2::12:11 is known as the statement qf an 
arithmetical proportion—a proportion being defined as the 
equality of two ratios. 
Now obviously equality, indicated by the foursquare lying 
dots, may also be indicated by the word ‘‘equals.” To com¬ 
plete the translation of mathematical symbols into usual lang¬ 
uage, “equals” must in grammatical parlance be provided 
with a subject and an object. These lie right at hand, the lat¬ 
ter being offered, as some might claim, by “12:11”, which may 
be rendered in words by “12 to be in relation with 11;” for 
