The peculiar oscillations of water in steam boilers, as indicated by the steam gage, have been a subject of common remark. The causes for these oscillations are imperfectly understood by many in charge of such boilers, and in conversations with engineers of justly high reputation, we have found that certain causes of this fluctuation in hight are unrecognized. We may regard the following propositions as thoroughly established laws. First, the pressure of a homogeneous liquid is as its depth. Second, a liquid subjected to pressure from a supernatant fluid, obeys the same laws of pressure as though it were free from the pressure of the over-lying fluid, and the degree of pressure thus sustained upon its surface does not modify orcre- ate exceptions to this rule. Third, if the supernatant fluid be a gas, and the liquid upon which it rests be water, a certain amount of the gas, increasing with the pressure, will be dissolved in the water. Fourth, in the absence of nuclei, which serve by their adhesion to assist the escape of a gas from a liquid supersaturated by that gas, the escape will be irregqJar, unequal, and will partake of the nature of an explosion. Fifth, in the absence of nuclei, the boiling points of liquids are higher than when such nuclei are present. Sixth, when a liquid is agitated so as to render it of unequal depths in different parts, the pressure upon the bottom of the containing vessel and upon the sides against which the liquid rests will be unequal. A pressure gage, attached to any one point in the side of a vessel thus agitated, would show by its fluctuations the variations of pressure at that point, provided they did not succeed each other so rapidly as not to give time for this gage to act, in which case it would only show the mean pressure. A water gage is only a form of pressure gage, communicating at the top with the supernatant steam, and at the bottom with the water upon which the steam rests. The pressure of the column in the gage back toward the interior of the boiler is equal to the weight of a column of water having for its base the section of the aperture which connects the boiler and gage at the bottom, and of a hight equal to the hight of the water in the gage above that aperture, added to the pressure of steam upon the upper end of the column. The pressure outward toward the gage is equal to the weight of a column of water having the same base as before, and of a hight equal to the depth of the water in the boiler above the aperture connecting the boiler and gage at the bottom, added to the pressure of the steam upon the top of the water column as before. When both steam and water are at rest, the water, obeying the same laws of pressure as though there were no supernatant steam pressing upon its surface, seeks and finds a common level in both boiler and gage. In a boiler supplying steam to an engine, or blowing off steam, the state of internal affairs is never one of rest. To suppose the contrary would be to suppose a uniform pressure maintained, a constantly uniform heat applied to all parts of its heating surface, and the escape of steam from the water unattended by ebullition. That the pressure is never a constant quantity where steam is generated in a closed vessel, any one may see by watching a steam gage attached to such a vessel. The indication of fluctuations in pressure may also be detected in the variable sound of the steam when a boiler is blowing off. It is for this reason that in testing the evaporative power of boilers, it has been found necessary to eliminate the element of variable pressure, by allowing free escape to the steam, so that the pressure is constantly that of the atmosphere only. We do not, however, regard the constant short bubbling of water in boiling as of much effect in producing the fluctuations of water indicated by the water gage. There are two causes, however, which are sufficient to account for such oscillations.In the absence of nuclei the steam is generated under tension and escapes with a sort of explosive action ; this occuring at one end of a boiler would raise a wave on the surface, which wave would travel along the surface of the water precisely as it would in an open vessel, and when this wave reaches the end of the boiler where the water ga ge is attached, the water would rise in the gage and recede with the recession of the wave. Where a boiler is supplying steam to an engine performing variable work, the supply of steam will not be uniform, and the pressure in tbo boiler cannot be uuiform. Whenever the pressure is diminished suddenly the steam escapes from the surcharged water like the gas from so-called soda water, and the volume of mingled steam and water expands ; the water in the gage, obeying the same law as the water in the boiler, except in so flU as its temperature may be less. These causes would account for the oscillations of the water even admitting a uniform heat to be maintained in the furnace, a supposition which variations in draft, variable condition of the fire, and quality of the fuel, etc., forbid. Where two or more boilers supply steam through a common supply pipe, connected to the boilers by branch pipes, the elements of variation in pressure must be still more multiplied, a point upon which it is unnecessary to dwell. A consideration of the facts we have thus explained coupled with observation, will enable the intelligent reader to determine the causes of peculiar oscillations in individual boilers.