254 Temperature of Mercury in a Siphon Barometer. : 
DD’ =<(ét’ —t)p . wall 
dd’ =«(t/ —t)p’, ia 
and therefore DD’+dd’=<«(t’- t) (p+p’). 
We derive from the figure D’D” = OD” — OD —DD’ 
: d'd!=Od" — Od +dd’. 
Equating the second members of these last equations, according 
to (1), and denoting the upper reading OD” by (a,), and the low- 
er reading Od” by (6,), and substituting for DD’+dd’ its value 
expressed above ; we have a, - b,—(a—6)=«(t/—t)(p+p’), (2) 
which is of the form a,-—6,—(a—b)=A(t/ —2), (3) where A isa 
constant co-efficient, since (¢) is constant, and (p+p’) is constant 
for the same barometer. This equation exhibits the relation be- 
tween the elements of any two sets of observations, on the sup- 
position that the scale is not affected by a change of temperature. 
-'To correct this for the expansion of the scale, let D/EFP re- 
present the brass mounting which bears the scale D’0’ O"F'; 
and suppose the imaginary zero point O to have been assumed in 
the same horizontal line with the zero point O’ or O” of the brass 
seale at the temperature (t). Since the expansion of brass is 
more than twice that of glass, there can be but one point in the 
graduated line, at which the glass tube and mounting are invari- 
ably united. Let this point be V; and put OV=f. Let D”,d” 
be those points in the brass scale, which are conveyed to D”, d”’ 
respectively by the augmentation (ta t) of temperature. Deno- 
ting by (e’) the ratio of expansion of brass in length due to one 
centigrade degree, and by (a’), (b’) the distances O’D’”, O”d’” 
respectively, which are the actual readings at the temperature (); 
we have D’D” =e —t)(a’+f) . 
; da =e—1)(¥-f) 
and therefore D’D” — did!" =e'(t’ —t) (a -W 42h.) 
We have from the figure O'D’=0'’D”” 4+D’'D” ( 3’) 
O”d’=0"d'" +dd” (o"} 
Subtracting the latter of these last two equations from the for- 
mer, and employing the notation and the above value of Pr 
ad", we have a;— b,=a'—B/+e(t'— t) (a’— b/+2f.) 
Eliminating (a,—b,) between this equation and (2) there results 
a —¥—(a—~b)=e(¢' - 2) (p tp’) —o(e 0) (a —¥ 42h) 
Since the quantity (a’—b’) in cylindrical siphon barometers dif- 
fers from a constant by only about 4 millimétres for achange of 30 
centigrade degrees in the value of (i/—1’,) and since (#) is less 
