10 EFFECTS OF WINDS AND OF 



(8) The relation of the research to four important outstanding problems 

 in science and engineering is briefly indicated. 



The table of contents at the beginning of this publication is intended to 

 give a good general view of the order of presentation in more detail than the 

 preceding statement; it will assist especially the reader who is referring 

 back to the publication to look up a particular topic. 



THEORETICAL BASIS FOR BAROMETRIC-OBSERVATION 



EQUATIONS. 



What is the shape of the surface of a lake when its water is in equilibrium 

 under the influence of gravity and barometric pressures? The wind is ig- 

 nored in this question. The answer is evidently the desired fundamental 

 theoretical basis for a study of barometric effects disturbances of elevation 

 of the water surface at a gage station produced by barometric pressures. 



If there is equilibrium at every part of the lake, under the conditions stated, 

 with no wind blowing, according to the fundamental principle of hydrostatics 

 the pressure at every point in the lake at a given elevation must be the same 

 as at every other point at that elevation. Also that pressure must be at 

 every point, x, 



p=(H a -H x -)8 w +M5 m (1) 



in which 



H s is the elevation of that part of the surface of the water which is 



directly above the point. 

 H x is the elevation of the point. 

 d w is the density of the water. 

 M is the length of the mercury column which measures the barometric 



pressure upon the surface of the water above the point. 

 d m is the density of mercury. 



H s H x is the distance from the surface of the water down to point X. 

 (H s H x )d w is the pressure at the point X due to the weight of the water 



above it. 



MS m is the pressure at the point X due to barometric pressure at the 

 surface above, which pressure is necessarily transmitted to 

 the point A' under the conditions stated. 



Note that M is the ordinary expression, incorrectly used, for the baromet- 

 ric pressure, namely, the length of mercury column which will balance the 

 barometric pressure, say 30 inches, under certain conditions. 



Consider the relations between the quantities H a and M for two points, 1 

 and 2, at the same elevation H x in the water of the lake, under the conditions 

 of equilibrium which have been stated. Let the elevation of the water sur- 

 face be called H i at point 1 and H* at point 2. Let the pressures at the two 

 points be called p\ and p 2 , respectively. Let the barometric pressures as 

 ordinarily expressed, in terms of M , at the water surface above the two points 

 be called M i and M 2 , respectively. 



