BAROMETRIC PRESSURES ON THE GREAT LAKES 11 



For the condition of equilibrium pi = p z and therefore from equation 

 (1) it is clear that 



(H i -H x }8 w +M l d m =(H z -H x )S w +M^ m (2) 



From equation (2) it follows, by cancellation and rearrangement of terms, 



that H 1 -H Z =-(M 1 -M (3) 



?>w 



Equation (3) expresses the fact that under conditions of equilibrium the 

 contour lines (lines of equal elevation) on the surface of the water must 

 coincide in shape with the isobars (lines of equal barometric pressure at the 

 surface of the water), that increasing elevations from contour to contour 

 must correspond to decreasing barometric pressures from isobar to isobar, 

 and that a unit interval between contours must correspond to an interval of 



between isobars. 

 8 W 



The elevation of the water surface on the Great Lakes is ordinarily ex- 

 pressed in feet above mean sea-level. Hi Hz is therefore most conveniently 

 expressed in feet. The barometric pressures are usually expressed by the 

 U. S. Weather Bureau in inches of mercury at 0C., and were so recorded on 

 the forecast maps used in this investigation. The density of mercury at 

 0C. = 13.6. The water concerned in equation (3) is the surface water of 

 the lakes, of which the temperature will seldom be outside the limits 32F. = 

 0C. and 80F. = 27C. Therefore the density of this water will seldom be 

 outside the extreme limits 1.000, at 39F.=4C. and 0.997, at80F.=27C. 

 With sufficient accuracy for the present purpose the density of the water 



may be assumed to be constant at 1.00, and may therefore be assumed 



&w 



to be constant at 13.6. 



For convenience, recognizing the units ordinarily used for elevations and 

 for barometric pressures, equation (3) may now be rewritten thus 



T 1 -ff 2 =-(M 1 -Af 2 )(13.6)(TV)= -(M!-Af 2 )(1.13) (4) 



Note that the division by 12 in the second member of the equation is to 

 take into account the fact that the M's are expressed in inches whereas the 

 H's are expressed in feet. 



The upper part of plate 1 shows the isobars over Lake Erie and vicinity a 

 obtained from the forecast map of the U. S. Weather Bureau as used at the 

 Chicago office of the Bureau for 8 p.m. on August 5, 1910. Note that the- 

 interval between isobars is 0.01 inch, that the isobars are nearly straight 

 across Lake Erie, and that the barometric gradient is downward to the 

 northeastward over Lake Erie. 



The middle part of plate 1 shows the contours of the surface of the water on 

 Lake Erie at 8 p.m. on August 5, 1910, in accordance with equation (4). 

 These contours would have existed if no wind had been blowing at that time 

 and if the water of Lake Erie had been in equilibrium at that time under the 



influence of gravity and barometric pressure. Note that an arbitrary zero 

 2 



