On the formulas for correcting reversing thermometers

The case often arises where a thermometer which has been inserted into a medium of temperature Tw is actually read in a place where the environment is at temperature t, ≠ Tw. Such a case is the soil thermometer , where the bulb is at Tw and the stem in the air at t; and such a case is the oceanographic reversing thermometer, brought up from a depth-of-reversal (Tw) to the ship laboratory (t). In each case the different cubical expansion coefficients of mercury and glass mean that the stem mercury capillary is taken from the true reading of Tw to a reading of T/ by the action of environmental change from Tw to T/.Sponsored by Grant NSF-GP 821 from the National Science Foundatio

Scaling Laws for Dark Matter Halos in Late-Type and Dwarf Spheroidal Galaxies

Maximum disk mass models fitted to galaxy rotation curves are used to show that dark matter (DM) halos in late-type and dwarf spheroidal (dSph) galaxies satisfy well defined scaling laws. Halos in less luminous galaxies have smaller core radii, higher central densities, and smaller central velocity dispersions. Implications: (1) A single, continuous physical sequence of increasing mass extends from the tiniest dSphs to the most luminous spirals. (2) The high DM densities in dSph galaxies are normal for such dwarf galaxies. Since virialized density depends on collapse redshift z, the smallest dwarfs formed about delta z = 7 earlier than the biggest spirals. (3) The high DM densities of dSphs implies that they are real galaxies formed from primordial density fluctuations. They are not tidal fragments. (4) Because dwarf galaxies become more numerous and more nearly dominated by DM as luminosity decreases, there may be a large population of objects that are completely dark. Such objects are a canonical prediction of cold DM theory. (5) The slopes of the DM parameter correlations provide a measure on galactic mass scales of the slope n of the power spectrum of primordial density fluctuations. Our results not yet corrected for baryonic compression of DM give n = -1.9 +- 0.2. This is consistent with cold DM theory.Comment: 19 pages, 5 Postscript figures; requires IAUS215.sty; to appear in "IAU Symposium 220, Dark Matter in Galaxies", ed. Ryder, Pisano, Walker, and Freeman, San Francisco: ASP, in pres

Commuting quantities and exceptional W-algebras

Sets of commuting charges constructed from the current of a U(1) Kac-Moody algebra are found. There exists a set S_n of such charges for each positive integer n > 1; the corresponding value of the central charge in the Feigin-Fuchs realization of the stress tensor is c = 13-6n-6/n. The charges in each series can be written in terms of the generators of an exceptional W-algebra.Comment: 27 pages, KCL-TH-92-