8 On the Construction of new forms of Thermo-Barometers. 
Again, let k=SP, the column of liquid in the tube at a given 
temperature ¢; e=SA; 0=Z EOQ, the inclination of the tube 
SP; h = the perpendicular column of liquid above the level of 
the liquid in the globe; @,= any other inclination of the tube 
corresponding to h, perpendicular column, the temperature bemg 
constant ; c = the distance of the level of the liquid in the globe 
from its centre ; r=OP ;—then we find 
h=ksin€—esin(9+45)+c, . . . - + + (8) 
a pea etn es 4o)— sin Sof ta ae 
sin @—sin 0, 
which gives the length of the liquid column so as to embrace a 
given range of pressure. For example, let h—A,=22°5 inches, 
which is equivalent to 3 inches of mercury ; 6=90°, the greatest 
angle at which the tube can be placed; 0,=15°, the least angle 
at which the tube can be conveniently placed; e=4; then we 
find k=30 inches nearly. 
When @=45°, equation (8) becomes h=ksin45—e+c. This 
quantity, substituted for 4 in equation (7), gives the formula for 
calculating approximately the range of the scaleer. For ex- 
ample, let 7 = 100" t = 62°, t, = 82, p=295, k=30, e=4, 
e='4; then we find g,=2°6, or the space of *13 of an inch to 
each degree of temperature. Supposing, therefore, the instru- 
ment to be made at mean temperature (62°), and mean pressure 
(29:5), the liquid may fill the tube (standing at an angle of 45°) 
to within 3 or 4 inches of the top. The globe may be about 24 
inches diameter; length of tube SQ about 34 inches; the dia- 
meter of the tube about °3 of an inch; and when the tube is held 
in a vertical position, the liquid should cover the bottom of the 
globe a little beyond the orifice of the tube leading from the 
lobe. 
i The temperature ¢ being constant, 7 and @ variable, the locus 
of the point P will be expressed by the polar equation 
r—k 
1l+cotd 
At the limiting angle 9=15°, we find OC=10 inches, and from 
the foregoing equation, we find the maximum value of OG=24 
inches. The dimensions of MN may therefore be taken as fol- 
lows: viz. ON about 12 inches, and O M about 26 inches. If 
the pin O be placed a little higher, then O N should be a little 
greater, and O M a little less. 
Hastings, November 20, 1859. 
—esin 45. 
