on the Elasticity of certain Metals. 861 
and brass wires are the ordinary wires of commerce wound on 
spools. 
To abbreviate the calculation, the times of vibration and the 
temperatures of each series of observations are united first in 
groups by taking the mean, and especial care was taken to 
allow about the same weight to all the several coefficients to be 
derived. The observed data corrected according to the rules 
of chapter 2, are contained in the following Table 4, in which 
the Roman characters denote nig chronological succession of 
the several series of observation 
TABLE 4. 
Tron. Brass. Copper. 
Temp. | vibration. Temp. | yipretion. Temp. | yipration. 
5 8. s S . 8. 
Tl 76:34 | 17-6154 JT; 69°01 20.9412 I; 74°06 12°4444 
56°87 17-5282 47°95 20.8067 47°96 12°3476 
28°85 20.7012 55°20 12-3696 
TI} 6°55 17-5950 40°80 12°3221 
55°75 17-5087 TI} 72°14 | 20.9105 24°04 | 12-2667 
42°42 17-4553 48°78 20.7600 
32°11 174150 TI) 62°60 12°3852 
21°91 |17°3679 | III) 70°28 | 20-8694 22°05 | 12-2465 
49°11 20°7368 
III} 78-73 17°5920 36°24 | 20-6669 | III} 77°27 12.4303 
59-72 17°5130 21°23 20°6193 66°16 | 12°3546 
20°97 17-3583 40°79 12°3028 
IV! 50°05 20°7333 23°37 12°2413 
49°57 17-4715 42°81 20°6915 
37°80 174279 34°59 =| 20°6425 
21°95 17-3627 
Vi 19°43 20°5428 
20°4737 
The following Table 5, in which the numbers are arranged 
according to the temperatures, is obtained by ee ee the 
values contained in Table 4 in the same manner as those of 
Table 2 of the example. 
The coefficients a and 6 are derived by — of least squares 
from the values contained in the third and fourth columns of 
‘Table 5, as in the example. Designating by «, ae modulus Al 
Pp. 
elasticity at 0°, the modulus for the temperature t is found to 
tor iron, e = &,(1 —0-0004477 — 0:000000127?) 
for copper, e = &, (1 — 0:0005202 — 0000000287?) 
for brass, =e,(1 — 0°0004287 — 07000001367?) 
The bers of ae next to the last column of Table 5 were 
calculated with these values. The probable error of each value 
of the brie of the coefficient of elasticity for 1° for a given 
temperature calculated from two groups of observations amounts 
aebondingly to + 0°000014. 
Am. Jour. Sct.—SzconD Serres, Vou. L, No. 150.—Nov., 1870. 
23 8 
