on some of the leading doctrines of caloric , &c. 349 
a + d", + — . 1=1 i .i=J . rf"', + 
— . 1=1 f.izl.'iii.r, + &c, 
234 
In the above series for steam, d'= 0.65, d” = 0.19, d!” = 
0.04, <f iv = 0.01, d v = 0 . a ~ 1.92. 
Example 1st. To determine the 8th term in the series, or 
the elastic force at 8 x 10, above 90°, (the first term ioo° 
being included) or at 170°. 
Here n=s 8 
a + »— 1 • d* = i»9 2 "h 4 ’55 ~ 
2 d" — 
— t w — 2 < »—■ 3 _ j/// „ 
2 3 4 
6.47 
4.08 
1.40 
o -35 
12.30 
Observation gives 12.05, forming a good accordance 
Example 2. Required the 10th term, or n = 10. For 190° F. 
a -f ~i . d ' = 7.77 
— ,!L=LZ.d"= 6.84 
n-i.-—.—J.d = 3.36 
rc-l.lZLf.IiZLl.lrii d*= 1 .26 
2 3 4 
I9.23 
At 190° experiment makes it 19.00, still coinciding nearly. 
By the same equation we find the 20th term or for 290° to 
be 124.28, while experiment gives 120.15, showing a differ- 
ence of 4.13 inches. At a higher point the error becomes 
greater. We here see that a geometrical series may coincide 
