THE NEW NATIONAL STAND AED OF LENGTH, AND ITS PEINCIPAL COPIES. 677 
Let X be the excess of Swedish B above Bronze 28 at the temperature 0°; y the rela- 
tive expansion for 1°. Then the first line gives the equation 
24 x^'r+983-33x:?/= + 17-0053, 
and so for the others. These equations, assumed to be of equal value, were treated by 
the method of least squares, and the result was 
+2-081441 
?/= -0-03350280. 
On substituting these values in the four equations, the residual errors are 
-0-0050, +0-0127, +0-0092, -0-0168, 
which prove that there are no important errors of observation or reduction. 
To find the excess of Swedish Iron B at temperature 62°, we must form x-\-yX^‘^. 
Its value is +0^-004267. 
And, as the relative expansion is — 0''-0335 or — 0‘“ -000120 : if to this we apply the 
absolute expansion of Bronze +0*°-000341 (as found above), the absolute expansion of 
Swedish Iron B for 1° of Faheexheit is +0'“ -000221. This applies to the length 
36 inches. 
In all the other instances, the range of temperature is almost exactly the same as for 
Swedish Iron B, but the number of observations is greater. For Cast Steel B the 
number is 148. 
The following is an Abstract of Eesults : — 
Name of Bar. 
Excess above Bronze 28 
at 62° Fahrenheit. 
Relative expansion of 
36 inches for 1“ Fahrenheit. 
Cast Steel B 
r. 
— 0-006565 
+ 0-005113 
+ 0-004267 
— 0-018638 
+ 0-082740 
+ 0-011634 
r. 
-0-03730370 
-0-03.356648 
— 0-03350280 
— 0-03979733 
+ 0-00072975 
— 0-00743411 
Low Moor B 
Swedish B 
Cast Iron C 
Brass 2 
Donkin’s Copper 
About 1853, October 26, Mr. Sheepshaxks introduced the use of the “block-and- 
sthrup ” moimting, and I beheve that after this time the system of floating the bars in 
quicksilver was rarely or never used. 
Between 1853, August 20, and December 24, Mr. Sheepshanks made numerous com- 
parisons of several bars, by the use of Baily’s Apparatus (the comparing apparatus of the 
Royal Astronomical Society), He was however much dissatisfied with the results, and 
never reduced them to the state of Abstracts. In a letter to myself, dated 1854, Jan. 2, 
Mr. Sheepshanks says, “ There is a clear difference in the comparisons depending on the 
position of the bars : the inside bar is always the longest. But this difference varies 
most lawlessly, from 3*^ to 10'’,” and then gives the means of comparisons on four days, 
each mean being derived from 18 observations, as follows: — 
d. 
d. 
d. 
d. 
Brass 2 farthest — Kew Bar nearest .... 
-1-93 
- 0-97 
-2-42 
-4-02 
Brass 2 nearest — Kew Bar farthest .... 
MDCCCLYII. 4 T 
+ 9-20 
+10*05 
+ 7-35 
+4-10 
