FOR MEASURING THE EXPANSION OF SOLIDS. 
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detached from the part which is exposed to the fire, obviates one important 
objection which has always been made to other contrivances of the same 
nature, from the uncertain degree of heat and expansion to which they are 
liable ; while the simplicity of that part of the arrangement which alone is sub- 
jected to great heats, renders it little liable to injury; and together with the 
cheapness of the materials of which it is constructed, occasions but a very 
trifling expense for replacing it when injured. 
The calculation of the absolute expansion of the bar indicated by the scale 
may be performed as follows : — As radius to double the sine of half the arc 
read off, and found in a table of natural sines, so will the radius B be to the 
chord of the same arc ; and this divided by ten (the radius of B being ten 
times the length of the radius f h) will give the length required. Suppose the 
arc read off upon the scale to be 4°, 
Radius. Sine of 2°. Inches. Inch. 
then 1.0000000 : 0348995 X 2 : : 5 : .3489950 -r- 10 = .0348995. 
Now in working out this proportion it will be observed, that the multiplica- 
tion by 2 and by 5 being both constant may, in conjunction with the division 
by 1.0, be omitted; and leaving out also the final division by 10, the case 
resolves itself into seeking the sine of half the arc, read off upon the scale, in a 
table of natural sines, and reading it as the decimal of an inch. 
Moreover, the chords of small arcs are so nearly proportional to their arcs 
that, the number of degrees measured upon the scale never exceeding 10, they 
may be considered without sensible error as denoting equal increments of ex- 
pansion. The following short Table of the value of a degree, and minutes of 
a degree, may therefore be useful in practice. 
Table I. 
0 , Inch. 
1 o = .00872 
0 30 = .00436 
0 20 == .00290 
0 15 = .00218 
0 10 = .00145 
0 5 = .00072 
0 2 = .00029 
0 1 = .00014 
2 m 2 
