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of Edinburgh , Session 1867 - 68 . 
exact number of days in a sidereal year, nor anything else, and 
again, the very uncertain number, 5,672 (the earth’s density), 
— appears to me in the highest degree dangerous. How deceitful 
results thus obtained can be, I shall now, in conclusion of this dis- 
cussion, attempt to illustrate by a few examples ; and before doing 
this, I beg to state that, entertaining the highest respect for Pro- 
fessor Smyth, I have not the least intention of making light of his 
work, though this method of reasoning, being analogous to the 
reductio ad absurdum, will unavoidably at times have something of 
that appearance. 
“Ex. 1. It is a historical fact, that the present English weights 
and measures are not of any very great antiquity. At the time of 
the Norman conquest the yard was about 39-6 of the present Eng- 
lish inches, a little longer than the French metre ; and the foot, 
accordingly, 13- 2 modern inches, a little greater than the Paris 
foot. In the year 1101, King Henry I. determined the yard by 
the length of his own arm, and that is the determination which 
the present yard is intended to represent ; and that yard, more- 
over, has never been, even in modern times, defined by any fraction 
of any of the earth’s dimensions, but by its proportion to the length 
of the seconds’ pendulum at 51J° latitude, and of this yard the 
English foot is the third part. Now, a degree of the equator is 
just 365,260-524 ft. Divide a thousandth part of that number by 
the length of the sidereal year in solar days, 365-256358, and we 
have 1-0000114 ; that is to say, if we take a thousandth of a degree 
of the equator, and divide it by the number of days in a sidereal 
year, we have an English foot as nearly as a powerful microscope 
can determine it. And yet it is certain that this is purely accidental. 
“Ex. 2. If I take 10,000 times e, the base of the hyperbolic 
logarithms, and multiply it into the quantity, which in the lunar 
theory is called that is, the ratio of the difference between the 
moon’s and its ascending node’s mean motions to the moon’s mean 
motion, — and divide the earth’s polar radius by the product, the 
result is the length of the pyramid’s side. But are we to suppose 
that the Egyptians forty centuries ago were acquainted with the 
lunar theory, the earth’s compression, and the use of logarithms, 
and, moreover, took this clumsy method of perpetuating their know- 
ledge? Is it not far more probable that the architect simply deter- 
