GEODETICAL STANDARDS WITH THE ENGLISH STANDARD YARD. 
171 
blankets. The other bar is similarly mounted between tanks which are full of cold 
water ; but no current is required, as the observations are made in the cold weather ; this 
is also carefully covered with blankets. With respect to the interchange of the bars 
under the microscopes, this is effected with all desirable rapidity by a piece of mechanism 
whereby each bar (with its appendage of plank, tanks, and water) is simply rolled away 
from or up to the microscopes ; thus the observers do not have to encounter the weight 
of these masses. Thus arranged the comparisons of a hot and cold bar are effected with 
almost as much facility as the ordinary comparisons. 
The coefficients of expansion obtained from 6500 micrometer and thermometer 
readings for the four bars are — 
Baily’s metal I B . . . . 0-0000098277+0-0000000057. 
Steel I s ... . 0-0000063478+0-0000000056. 
Wrought-iron OI, ... . 0-0000064729+0-0000000031. 
Wrought-iron OI 2 .... 0'0000064773+0 - 0000000033. 
The Indian bars were heated up to very nearly, but not quite 100°. 
Probable Errors of Observation . — The quantities measured by the micrometers in the 
observations just specified are large, and require a very accurate knowledge of the values 
of the screws. The values for the two microscopes H and K are, expressed in millionths 
of a yard, 
H : one micrometer division .... 0-79566 + -00008 
K : „ „ .... 0-79867+-00009 
These were obtained from repeated measurements of a space of yoo °f an inch on F, 
the scale being readjusted to focus each measurement. There is no appearance of per- 
sonal error in the observations (of three observers) from whence these values are deduced. 
It appears that the probable error of a single measurement of a space of n thousand 
divisions, m bisections on each line being supposed, is 
for H . . . +\/^-^+0 072w 2 micrometer divisions, 
forK . . . ±\/^+0T16 n 2 „ 
The greatest space measured by either of the microscopes in the expansion experiments 
was 1100 divisions; and m being =2, the probable error of the measure would be 0-43 
or 0-49 of a micrometer division, according to the microscope used. The probable error 
of a single bisection by either of the observers is about +0 d, 316. 
The Standard Foot, and its subdivisions . — The length of this foot F in terms of Y 55 was 
determined as follows Four microscopes, H, I, J, K, were mounted on the stone piers 
at the distance of 12 inches apart, their axes being vertical and their outer foci in a hori- 
zontal straight line. The two bars lying side by side in their box, F was brought suc- 
cessively under the microscopes HI, I J, J K ; then Y 55 under the microscopes H K 
2 a 2 
