208 Trans. Acad, Sct. of St. Lows. 
The five horizontal strips when thus extended, may be con- 
sidered as one strip, having an area y° (y° — 2°), and the 
area of the vertical strips is 2° (y°—a*). The sum of the 
two resulting strips is 
ga = yf (yi—a®) +25 Gy — 2"). 
Equation (3) is readily reduced to this form. It is en- 
tirely similar to the well-known equation 
y —av=y(y—2)+2(y—Z2). 
As was suggested in the former paper, the two squares 
y’ and a may be changed by applying the multiplying 
factor to the horizontal sides of the two squares. The 
areas remaining as in former equations, and adopting the 
same unit, and the same values for y and 2, the area y™ 
would then be a rectangle, the vertical width of which 
would be y=5 inches, and the horizontal side would 
have a length y® = 1,593,125 inches or 30.8 miles. The 
rectangle x° would have a vertical dimension x = 4 inch, 
and the horizontal dimension would be 2° = 0.000,003,81 
inch, 
In order to adjust Eq. (5) to this change, it must be 
written, 
y* —a® = (y— x) + 2 (y’ — ya) 
~ x (y®a — y"x?) + x (y'x? yx) 
+a (y°a* — y*2*) +a (yrat ee y'x°) 
+ @ (y*a® — y®a®) + x (yPa® — y*a") 
+ aw (y?a' — ya*) + a (y®— 2°) 
The five horizontal strip areas of the diagram are noW 
replaced by one, the width of which is y— x = 4.79 
inches and the length y® = 1,593,125 inches or 30.8 miles. 
The remaining terms are represented by a series of rec- 
tangles having a common height a 1 inch, and filling 
the space x (y?— 4°) =¥, (1,593,125 — 0.000,003,81) 
square inches. 
