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At the time of writing the analysis of the most recent pXRF data from New York and Massachusetts sites has not been completed. However, the results from the 165-year-old Smithsonian Castle, which is located on the National Mall in Washington, can serve as an example of the method for calculating growth rates.

Three locations around the Castle were measured by pXRF. In addition to the southwest corner (Fig. 1), a patch at the east entrance was measured, which historic photographs show was free of varnish as late as 1985. A third patch was measured on a gate post of the Enid Haupt Garden, built in 1987 adjacent to the Castle using the same Seneca sandstone. Ten points each were measured on the varnish patch and a bare stone area at the SW corner, and five points each at the other locations. The pXRF counts data were converted to Mn layer thickness using the Fe/Fe ratio method for the Mn patch and bare stone.

The results are presented in Table 2 along with estimated ages. The calculated growth rates for the east entrance and the gatepost are reasonably close, on the order of 90 nm/yr. This is significantly higher than the maximum rate of 40 nm/yr observed for desert varnish (Liu & Broecker, 2008). However, the growth rate for the southwest corner is only a third of this, if its estimated age is based on the assumption that the layer began to grow as soon as the stone was put in place. Although historic photographic documentation is mainly in black and white and insufficiently detailed for conclusive determination, it appears that growth actually started much later. Dividing the thickness of the layer, 4 microns, by the rate of 90 nm/yr gives an age of 45 years or a start date of 1970. This is consistent with the period of great population growth and associated increase in automobile traffic around the Washington urban area.

Table 2: Varnish growth rates on the Smithsonian Castle, based on Fe/Fe ratios measured on Mn patches and bare stone using pXRF.

Location	Thickness, µm	Time, years	Growth Rate, nm/yr
S.W. Corner	4.0 ± 0.57	155	26 ± 3.7
Gatepost	2.41 ± 0.06	29	83 ± 2.0
East Entrance	2.38 ± 0.06	25	95 ± 2.4