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The Milanković astronomical theory of ice ages 1 posits that quasiperiodic expansions and contractions of Northern Hemisphere ice sheets are driven by variations in Earth's orbital geometry and axial inclination that influence the amount of summer insolation received at northern high latitudes. Astronomical periodicities of obliquity (41,000-year (41-kyr) cycles) and precession (23-and 19-kyr cycles) were found to be embedded in records of changing ice volume and climate 2 ; however, in addition to these cycles, climate variance in the Middle and Late Pleistocene was dominated by a 100-kyr cycle 2 , which was not predicted by the original theory. The development of improved chronologies 3 and advances in demarcating interglacial boundaries 4 have shown that the onset of interglacials over the past 600 kyr occurred near the maximum in boreal summer insolation, with perihelion (when Earth is nearest to the Sun) at the northern summer solstice. Mean daily insolation on 21 June at 65° N is often used as a predictor of glacial changes, because it represents maximum values at a sensitive time of the year at a critical latitude for ice-sheets. However, the data in Fig. 1 reveal that not all insolation maxima led to interglacials: some prominent insolation peaks are associated with incomplete deglaciations-that is, interstadials (for example, Marine Isotope sub-Stages (MIS) 6e and 9a)-and some prominent interglacials are associated with moderate insolation maxima, most notably MIS 11c (ref. 5). It is, in fact, difficult to decide which insolation maxima would lead to interglacials by using only this insolation curve. An additional complication is that deglaciations occurred approximately every 41 kyr (the so-called '41-kyr world') up until about one million years before present (1 Myr bp), but have been less frequent since then (the so-called '100-kyr world' , but see below). Therefore, any comprehensive explanation of how astronomical forcing translates into the sequence of Quaternary ice ages needs to account for the occurrence of interglacials at different frequencies.Several numerical models [6][7][8][9][10][11][12][13][14][15][16] have reproduced the pattern, and in some cases much of the timing, of glacial-interglacial cycles over part or all of the Quaternary. Although each of these has pointed at some of the ingredients involved in a comprehensive explanation, some include large numbers of tunable parameters, none is fully successful over the past million years, and few offer a consistent and simple rule that accounts for the whole Quaternary sequence. Here we ask whether the onset of interglacials over the course of the Quaternary can be predicted from simple combinations of astronomical parameters (that is, without any knowledge of atmospheric CO 2 concentration, dust or other climate data). We determine the parameters of such a model in a statistical way, which allows us to discuss whether a simple model can successfully accommodate the observed sequence and to assess how tightly the succession of ice ages is...

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Mueller's phenomenological theory of Rochelle salt, NaKC4H406. 4820, has been generalized, and the properties of the clamped crystal described. A local field theory of the clamped crystal has been developed on the basis of the structure analysis of Frazer, Danner, and Pepinsky. Special care has been taken to avoid any arbitrary assumptions in the theory. A chart is given which shows conditions for the occurrence of ferroelectricity, It has been shown that the difhculties of Mason and Devonshire's theories are the results of too simplified assumptions on the coeKcients of the local field. Various quantities which appear in the theory have been calculated using the fact that the reciprocal susceptibility of the clamped crystal has a single zero value. The calculated coe%cients which appear in the Taylor series expansion of Helmholtz free energy agree well with those predicted by the phenomenological theory. An explanation is given for the properties of the mixed crystal series, Na/K (NH4) i~PC4H40e 4HsO W.

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