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basis of the laws governing stresses and strains, the study of optics, the 
propagation of impulses in homogeneous media, and a thousand practical 
things. As we rise higher and approach analysis we trace the lines along 
which stresses are propagated and materialize these in the beautiful iron 
bridge, with its parts nicely shaped and adjusted to the load it is to 
carry. Advancing further, our lines become in the strain diagram a veri- 
table graphical calculus, through which we discover the stress with which 
any load, fixed or moving, strains a structure, and therefore through it 
find a ready means of designing our creations to resist safely the stresses 
to which they will be subjected. 
But this brings us to the question of analysis—the other side of our 
subject. I shall not dwell upon algebra as we usually understand that 
term in high school and elementary college work. I need only speak of 
it as generalized arithmetic to recall to you how it gathers up the rules 
of the lower subject and condenses and generalizes them, and how, by 
introducing the result sought at the beginning of a series of operations, 
we easily carry to a conclusion logical sequences, otherwise exceedingly 
difficult to follow, and ascertain whether or not the problem proposed is 
capable of solution. 
It must be confessed, however, that algebra in the ordinary school 
sense is very largely a discipline, little used in the ordinary affairs of life 
and finding its principal utility in the studies which lie beyond. Yet to 
pursue these with ease and success, a knowledge of ordinary algebraic 
methods and facility in algebraic manipulation, including the analysis 
of the angle, is a prime requisite. I come now to speak of the higher 
analysis in the sense in which it is ordinarily applied—that is, the infini- 
tesimal calculus and its developments and allied subjects—the invention 
of which marks an epoch in human progress second, I believe, to no other 
scientific event. 
It is curious, when we think back over human advancement, that 
some of the things now most patent to our senses escaped recognition so 
long. The alchemist stumbled through centuries without learning the 
-hature of air and water. The most puerile ideas regarding the earth’s 
structure prevailed down to the American Reyolution and later. And so, 
while arithmetic, Euclid, Diophantine analysis and trigonometry are 
highly artificial, calculus brings us back to nature. Space and time were 
continually thrusting themselves upon the attention of man, motion in 
the former, rate in the latter, as exemplified by every moving thing and 
