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12. If y be the volume of the given mass of air at 0° and 760 mm. pressure : if the pressure increases to P, and the temperature to to, the volume will be given by the formula
V'=Vigo (1 + at) where a is the coefficient of expansion for air. But since this volume is to remain constant V=V',
.280 (1 + at) = 1 which is the relation required. In the example let V be the required volume.
V= 10 X 1 X = * = 14 cubic foot. 13. Steam at 100° C., in condensing to water, is said to give out 537 units of heat, or, in other words, 1 ounce of steam, in condensing to water at 100° C., gives out sufficient heat to raise 537 ounces of water through one degree centigrade.
1 lb. of steam at 100° gives out 537 pound-degree units.
t) units. The mercury gains 300 x .03 x t units, and the vessel gains 10 x ť units.
537 + 100 t = 10t + 9t.
20t = 637.
t = 311 % degrees. 14. Dew is aqueous vapour which has condensed on bodies during the night in minute globules. It is occasioned by the chilling which bodies near the surface of the earth experience in consequence of nocturnal radiation. Their temperature having then sunk several degrees below that of the air, it frequently happens, especially in hot seasons, that this temperature is below that at which the atmosphere is saturated. The layer of air which is immediately in contact with the chilled bodies, and has virtually the same temperature, then deposits a portion of the vapour which it contains.
If the bodies are chilled below zero, the dew is deposited in the solid form as hoar-frost; the flocculent of which form shows that the vapour is deposited in the solid form without passing through the intermediate liquid condition.
If two equal volumes of air at different temperatures are nearly saturated with moisture, and are then mixed, the resulting temperature is an arithmetic mean between the two, while the tension of aqueous vapour is a geometric mean between the original tensions : now the arithmetic mean between two quantities is greater than the geometric mean. Hence it happens that there may be in these cases too much moisture present to saturate the mixed volumes, and the excess is precipitated in the form of a cloud.
15. If a normal be drawn to the surface of the refracting medium at the point where the ray falls upon the surface, and if equal distances be measured along the incident and the refracted rays, and from the extremities perpendiculars be drawn to the normal, the ratio of the perpen
dicular from the incident ray to the perpendicular from the refracted ray is called the index of refraction between the media.
The formula for determining the position of the image F of the object Q, seen directly through the plate AB (A being downwards), may be expressed thus:
BF = AQ + AB • 1};
6 ; 1);
6 inches; which shows that the image will appear to the eye to be at A, just on the lower surface of the plate.
If now, at A, a small conical pencil be drawn similar and parallel to that at Q, the required drawing will consist (1) of the small cone at Q before it enters the plate, (2) of the small cone at A after it has left the plate, and (3) inside the plate, of the requisite connecting rays.
16. (i) A convex lens is formed by two spherical surfaces, so placed that the glass is thickest towards the centre, and thin at the edge. A concave lens has also two spherical faces, but the centre is the thinnest part, and the edges thick.
(ii) If a convex lens is so placed that the sun lies on its principal axis, an image of the sun will be formed on the other side of the lens at its principal focus. (iii) Size of image distance of image Size of object distance of object
1 1 But
If a small portion of the lens only is left uncovered at the centre, the aberration is less, and the image, though more distinct, and unaltered in size, is less illuminated.
** The next Guide (No. 6) will be published on the Wednesday following
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