By Bruce R. Doe

###### About The Product

Published through the yank Geophysical Union as a part of the *Field journey Guidebooks Series*.

This afternoon journey in downtown Washington, D.C., will let examine of pollutants, structural, and other forms of wear and tear to constructions with emphasis on these developed of excellent- to coarse-grained marble yet with representatives of limestone and pink sandstone. The journey will comprise so as of exam [date of labor initiated (i) and/or occupied (o.) and stone type]: the Renwick Museum (1859o., purple sandstone trim changed 1987), Corcoran Museum (1879c. enlarged 1927, coarse-grained marble), pink go structures (1915i.-1917o., 1927i., fine-grained marble), Memorial Continental corridor of the Daughters of the yankee Revolution, DAR (1904i.-1909o., fine-grained marble), Pan American Union construction (1908i.-1910o., coarse-grained marble), structure corridor (DAR) (1929o., limestone), Washington Monument (1885o., marble), Jefferson Memorial (1943o., external of fine-grained marble), and Lincoln Memorial (1922o., very fine-grained marble). Coarse-grained marble is in general extra proof against pollutants harm than fine-grained marble. Direct publicity to the weather hurries up degradation. the main critical toxins harm happens to balustrades and columns: runoff from bronze onto fine-grained marble may also reason severe degradation. Any type of overhang has a tendency to guard the underlying stone, yet exceptions may be visible on the Jefferson Memorial. typically, vertical partitions have much less pollutants harm than horizontal surfaces which may start to express roughening inside of years of set up. Limestone in universal use is strangely immune to degradation owing, no less than partly, to the porous nature of the stone that inhibits runoff. If one of many journeys is made to the Powell development of the U.S. Geological Survey in Reston, Virginia (1974o., concrete), it is going to be obvious that concrete behaves very similar to limestone and marble.

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0. 45) we ﬁnally have the equation for the pair correlation function in the following form: ∂fkl (X1 , X2 , t) ∂fkl (X1 , X2 , t) ∂fkl (X1 , X2 , t) + v1,α + v2,α + ∂t ∂ r1,α ∂ r2,α + F k,α (X1 , t) ∂fkl (X1 , X2 , t) F l,α (X2 , t) ∂fkl (X1 , X2 , t) + + mk ∂ v1,α ml ∂ v2,α + ∂fk (X1 , t) ∂ v1,α ∂fl (X2 , t) + ∂ v2,α ∂ =− ∂ v1,α ∂ − ∂ v2,α n 1 F kn,α (X1 , X3 ) fnl (X3 , X2 , t) dX3 + mk n n n X3 1 F ln,α (X2 , X3 ) fnk (X3 , X1 , t) dX3 = ml X3 1 F kn,α (X1 , X3 ) fkln (X1 , X2 , X3 , t) dX3 − mk X3 1 F ln,α (X2 , X3 ) fkln (X1 , X2 , X3 , t) dX3 .

1)), physical properties of gravitational systems diﬀer so much from properties of astrophysical plasma. 3 and many times in what follows. 6). 11). Answer. 22) depends on 2N constants Ci where i = 1, 2, ... 2N . If we assume that the distribution function is a function of these constants of the motion f = f ( C1 , ... Ci , ... 11) as Df = Dt 2N i=1 DCi Dt ∂f ∂Ci . 43) Because Ci are constants of the motion, DCi /Dt = 0. 42) satisﬁes the Liouville equation. This is the so-called Jeans theorem. 1).

0 ∂t ∂t ∂ r1,α ∂ r2,α ∂ (ϕˆk ϕˆl ) ∂ (ϕˆk ϕˆl ) ∂ (ϕˆk ϕˆl ) + v1,α + v2,α + ... = 0. 45) we ﬁnally have the equation for the pair correlation function in the following form: ∂fkl (X1 , X2 , t) ∂fkl (X1 , X2 , t) ∂fkl (X1 , X2 , t) + v1,α + v2,α + ∂t ∂ r1,α ∂ r2,α + F k,α (X1 , t) ∂fkl (X1 , X2 , t) F l,α (X2 , t) ∂fkl (X1 , X2 , t) + + mk ∂ v1,α ml ∂ v2,α + ∂fk (X1 , t) ∂ v1,α ∂fl (X2 , t) + ∂ v2,α ∂ =− ∂ v1,α ∂ − ∂ v2,α n 1 F kn,α (X1 , X3 ) fnl (X3 , X2 , t) dX3 + mk n n n X3 1 F ln,α (X2 , X3 ) fnk (X3 , X1 , t) dX3 = ml X3 1 F kn,α (X1 , X3 ) fkln (X1 , X2 , X3 , t) dX3 − mk X3 1 F ln,α (X2 , X3 ) fkln (X1 , X2 , X3 , t) dX3 .