ALBERT

Notes: Abstract The application of the fast-Fourier-transform (FFT) algorithm to calculating one-dimensional and bi-dimensional (temporal and spatial), power and cross-power (coherence and phase) spectra is examined for solar photospheric fluctuations. Alternative methods for smoothing raw spectra, direct averaging (employing various weights) and indirect truncation of the correlation function, are compared, and indirect smoothing is compared with spectra calculated by mean-lagged-product (MLP) methods. Besides providing the raw spectrum, FFT techniques easily allow computing a series of spectra with varying amounts of smoothing. From these spectra a range of satisfactory compromise between resolution and stability can be determined which helps in the interpretation of spectral trends, and in identifying more clearly the existence and significance of spectral features. For bi-dimensional spectra presented as contour plots, this range of satisfactory smoothing can be restricted, particularly when spectral trends must be represented by small-scale contours. Equivalent spectra (i.e. comparable equivalent degrees of freedom) computed or smoothed by different methods have minor, but not negligible, differences. Examination of these differences favors computing of FFT spectra smoothed by averaging for photospheric fluctuations.

Notes: Abstract Fluctuations measured from a time sequence of high-resolution, high-dispersion Sacramento Peak Observatory spectrograms and previously analyzed by computing one-dimensional temporal and spatial spectra (Edmonds et al., 1965), are re-analyzed using bi-dimensional (temporal and spatial) power, coherence and phase spectra computed by fast-Fourier-transform techniques. The fluctuations measured are radial velocity for the FeI 5049.83, CrI 5051.91 and CI 5052.16 spectral lines, continuum brightness, and equivalent width and central intensity of the CI line. The bidimensional spectra, particularly those of coherence and phase, allow isolating different components of the fluctuations to a degree not possible in the one-dimensional analyses. Six components of the fluctuations have been isolated (Section 5 and Figure 11); the first three components are well-known but the nature of the remaining three is less certain: (1) Supergranulation which exists only in radial-velocity fluctuations and increases in power with depth. (2) Five-minute oscillations that dominate long-wavelength radial-velocity fluctuations, which may contribute of the order of one percent to continuum brightness and equivalent width fluctuations, and are waves which can propagate across the Sun's surface and possibly travel upwards at less than 70 km s−1. (3) A long-period, convective component which extends over all but very long wavelengths, is characterized by strong correlation between the radial velocity and photometric fluctuations, and involves low power levels for the radial velocity fluctuations. Seemingly, the radial velocity fluctuations lead those of continuum brightness by roughly 20 s. (4) Low and moderate wavenumber fluctuations which seemingly extend over frequencies ≲ 6 × 10−3 Hz and are characterized by low power levels for all types of fluctuations. It is difficult to deny the physical reality and distinctness from other components of these fluctuations, but whether they constitute a single component is uncertain. The radial velocity fluctuations seem to have the same phase relations with respect to each other as the five-minute oscillations. The continuum brightness fluctuations seem to lag the equivalent width fluctuations by roughly 17 s, lead the central intensity fluctuations by roughly 10 s, and lead the radial velocity fluctuations by roughly 15 to 20 s. (5) Possible line-formation (as distinct from continuum formation) brightness fluctuations at the center of the CI 5052.16 line, which seemingly are of low frequency and long wavelength and are poorly correlated with continuum brightness and radial velocity fluctuations. (6) A low-correlation, primarily photometric component restricted to long-periods and to wavelengths only slightly less than those of super-granulation. Its existence is suggested by a phase anomaly indicating that the radial velocity fluctuations lead the photometric fluctuations by roughly 4 min.

Notes: Abstract Successful subtraction of instrumental background variations has permitted spectral analyses of two-dimensional measurement arrays of granulation brightness fluctuations at the center of the disk, arrays obtained from Stratoscope I, 1959B-flight, high-resolution frames B1551 and B3241. (a) RMS's, uncorrected for instrumental blurring, are 0.0850 of mean intensity for B1551 and 0.0736 for B3241, somewhat higher than other determinations. These between-frame and between-investigation differences probably result from a combination of calibration errors, frame resolution differences, and, most likely, granulation pattern differences. (b) Significant variations over each array of mean intensities and RMS's, determined for sub-arrays with dimensions in the 2500–10000 km range, indicate spatial brightness and RMS variations larger than the ‘scale’ of the granulation pattern, supporting a turbulent interpretation of photospheric convection. (c) One-dimensional power-spectra shapes provide objective and discriminating criteria for determining granulation pattern differences and, possibly, frame resolution. (d) Two-dimensional power spectra show small, essentially random deviations from axial symmetry which lie almost entirely within the 50% confidence limits. (e) Spectral densities and fluctuation power spectra, computed from the two-dimensional power spectra and corrected for instrumental blurring, noise, and blemishes, have a useable radial wavenumber range nearly double that of earlier Stratoscope I analyses. (f) Corrected RMS's obtained from the corrected fluctuation power spectra, 0.145 ± 0.046 for B1551 and 0.136 ± 0.048 for B3241, depend critically on the accuracy of the correction. (g) The spectra's wavenumber range includes the granulation-fluctuation-producing domain but not the Kolmogoroff domain of turbulence spectra.

Notes: Abstract The fractional convective flux πF c (x c /πF) is computed for the effective level x c = logτ c = 0.125, using bi-dimensional co-spectra for relative continuum-brightness fluctuations ΔI and radial velocity fluctuations ΔV measured for the C i 5052.16 spectral line. A more uncertain flux for x Fe ≈ - 0.9 is obtained for the Fe i 5049.83 line. Since the results (Figure 1) incorporate current uncertainties in RMS ΔI , RMS ΔV and RMS ΔT (x), where ΔT are photospheric temperature fluctuations, they must be considered qualitative until these uncertainties are appreciably reduced. The requirement that the fractional convective flux 〈 1, places restrictions on these uncertainties which suggest that current RMS ΔT (x)'s are too large. The results confirm the importance of overshoot at the top of the solar hydrogen convection zone and suggest a non-negligible fractional convective flux throughout the lower photosphere. Qualitatively, they do not agree with the predictions of the generally-used, local, mixing-length theory or those of Parsons' (1969) modified mixing-length theory. However, qualitative agreement with the predictions of the non-local, generalized mixing-length theory of Spiegel (1963) and with the non-local theory of Ulrich (1970) cannot be considered as observational confirmation of these theories.

Notes: Abstract Synthetic one-dimensional scans of brightness fluctuations are generated from intergranulegranule profiles (IGP), which approximate observed scans of granulation fluctuations except that the local (i.e. IGP) mean intensity is kept constant. Comparing the power spectrum of such scans with the power spectrum of observed scans shows that nearly two thirds of the low-wavenumber (k 〈 0.0025 km-1) granulation power is due to this variable mean effect. This result favors the interpretation of granulation as turbulent thermal convection but cannot rule out the laminar convection interpretation.

Notes: Conclusions I have attempted to clarify some of the pathways in the development of Darwin's thinking. The foregoing examples of influence by no means include all that can be found by comparing Darwin's writings with Humboldt's. However, the above examples seem adequate to show the nature and extent of this influence. It now seems clear that Humboldt not only, as had been previously known, inspired Darwin to make a voyage of exploration, but also provided him with his basic orientation concerning how and what to observe and how to write about it. An important part of what Darwin assimilated from Humboldt was an appreciation of population analysis as a tool for assessing the state of societies and of the benefits and hardships which these societies can expect to receive from the living world around them. Darwin exhibited in his Journal of Researches a casual interest in the economic and political conditions of the countries he visited, but these considerations were much less important to him than to Humboldt. Instead, Darwin, with the assistance of Lyell's Principles of Geology, shifted from Humboldt's largely economic framework to a biological one built around the species question. This shift led Darwin away from a consideration of how the population biology of animals was related to man's economy to focus instead upon how population biology fitted into the economy of nature. Humboldt's Personal Narrative served very well as a model for Darwin's Journal of Researches, thereby helping Darwin gain scientific eminence. The Journal of Researches, like virtually all of Humboldt's writings, was a contribution to scientific orthodoxy. But Darwin had, along the way, acquired an urge to do more than just add his building blocks to the orthodox scientific edifice. He decided to rearrange those blocks of knowledge into a different structure, and for that task neither Humboldt's Personal Narrative nor any other of his works could serve as a model. Humboldt had lacked the confidence which Darwin needed that biogeography and the origin of species could be understood. Humboldt had not explored very far the possible connections between biology and geology. Nor had he provided a general synthetic account of population biology. Had he done so, he might have been more explicit about the extent of his endorsement of Malthus. But even if he had, Humboldt's strong orientation toward cooperation would probably have inhibited his recognition of the importance of competition in nature. Lyell, who had also benefited from reading Humboldt, gave Darwin insights that were lacking in Humboldt's Personal Narrative. Lyell admirably demonstrated how stratigraphy, paleontology, biogeography, and population biology could be interrelated, and his reasons for doing so were essentially the same as Darwin's. Lyell's understanding of biogeography and ecology came from the writings of Augustin-Pyramus de Candolle as much as from Humboldt's, and from the former Lyell derived an appreciation for the importance of competition and also a confidence that the mysteries of biogeography could be explained.117 Furthermore, Lyell's discussion of all these subjects and also of evolution in his Principles of Geology is a good synthetic argument that was the ideal model for Darwin's greatest book. Darwin, having become convinced that species change through time, was able to synthesize in his mind the contributions which he had derived from the writings of Humboldt and Lyell as they applied to the species question. When Darwin wrote his Journal of Researches there were two large gaps in his thinking about evolution that bothered him—the mechanism of evolution and the causes of extinction. It was only after reading Malthus in 1838 that he realized, as Lyell had more or less pointed out, how important was competition in nature. He now had the general outlines for his theory, and in the 1845 abridged edition of his Journal, now retitled The Voyage of the Beagle, he inserted a fuller discussion of competition in nature which showed his awareness of its importance as an ecological factor.118

Notes: Abstract The standard Lown-type capacitor discharge waveform was compared with a single half-cycle 60-Hz sinusoid for effectiveness of defibrillation. Both shock types were used in attempts to defibrillate a series of dogs over a range of intensities from that below the minimum required for defibrillation to values well above those which consistently were successful. An on-line computer was used to monitor energy, peak current, and peak voltage of each shock. The results were plotted as percent success vs each parameter and comparisons were made at the 80% level. The half-cycle sinusoid required 18% more energy but 20% less peak current and 15% less peak voltage for 80% probability of success at these intensity levels. These results indicate that the half-cycle 60-Hz sinusoid is a reasonable alternative as a defibrillating waveform for low-energy applications (open chest surgery, some pediatric cases, and small animal applications) where its advantages of waveform unaffected by load impedance, and simplicity of circuit, may be realized.