Terminal Digits Research Articles

Jost Bürgi and the discovery of the logarithms

In the year 1620 the printing office of the University of Prague published a 58page table containing the values an = (1.0001) n for 0 ≤ n ≤ 23027, rounded to 9 decimal digits. This table had been devised and computed about 20 years earlier by the Swiss-born astronomer and watchmaker Jost Burgi in order to facilitate the multi-digit multiplications and divisions he needed for his astronomical computations. The “Progres Tabulen”, as Burgi called his tables, are considered to be one of the two independent appearances of the logarithms in the history of mathematics the other one, due to John Napier (1550-1617), appeared in 1614. There are only a few copies of the original printing extant: one of them is now in the Astronomisch-Physikalisches Kabinett in Munich. Based on a copy of this original, the terminal digits of all table entries were extracted and compared with the exact values of an, a matter of a split second on a modern computer. In this presentation we give a brief account of the mathematical environment at the end of the 16th century as well as a detailed description of Burgi’s Progres Tabulen and their application to numerical computations. We will also give a sketch of Burgi’s remarkable life and of his numerous achievements besides the discovery of the logarithms. Our main purpose, however, is to analyze the numerical errors in Burgi’s table. First of all, there are no systematic errors, e.g. the crux of the table, 1.0001 = 10, is correct with all digits given. 91.5% of the table entries are entirely correct, and 7.3% of the values show round-off errors between 0.5 and 1 unit of the least significant digit. The remaining 1.17% table errors are mainly errors of transcription and illegible digits. Statistics of the round-off errors leads to interesting conclusions concerning Burgi’s algorithms of generating his table and on his handling of the round-off errors, as well as on the computational effort involved.

Correlates of Digit Bias in Self-reporting of Cigarette per Day (CPD) Frequency: Results from Global Adult Tobacco Survey (GATS), India and its Implications

Cigarette per day (CPD) use is a key smoking behaviour indicator. It reflects smoking intensity which is directly proportional to the occurrence of tobacco induced cancers. Self reported CPD assessment in surveys may suffer from digit bias and under reporting. Estimates from such surveys could influence the policy decision for tobacco control efforts. In this context, this study aimed at identifying underlying factors of digit bias and its implications for Global Adult Tobacco Surveillance. MATERIALS OR METHODS: Daily manufactured cigarette users CPD frequencies from Global Adult Tobacco Survey (GATS)--India data were analyzed. Adapted Whipple Index was estimated to assess digit bias and data quality of reported CPD frequency. Digit bias was quantified by considering reporting of '0' or '5' as the terminal digits in the CPD frequency. The factors influencing it were identified by bivariate and logistic regression analysis. The mean and mode of CPD frequency was 6.7 and 10 respectively. Around 14.5%, 15.1% and 15.2% of daily smokers had reported their CPD frequency as 2, 5 and 10 respectively. Modified Whipple index was estimated to be 226.3 indicating poor data quality. Digit bias was observed in 38% of the daily smokers. Heavy smoking, urban residence, North, South, North- East region of India, less than primary, secondary or higher educated and fourth asset index quintile group were significantly associated with digit bias. The present study highlighted poor quality of CPD frequency data in the GATS-India survey and need for its improvement. Modeling of digit preference and smoothing of the CPD frequency data is required to improve quality of data. Marketing of 10 cigarette sticks per pack may influence CPD frequency reporting, but this needs further examination. Exploring alternative methods to reduce digit bias in cross sectional surveys should be given priority.

The advent of fair treatment allocation schedules in clinical trials during the 19th and early 20th centuries.

Methods to ensure that like will be compared with like in fair treatment comparisons were proposed at least as early as the 17th century. Reflecting a time-honoured device for ensuring fairness,13 Van Helmont14 and Starkey15 proposed casting lots to decide which patients should be assigned to orthodox physicians (to be bled and purged), and which to their own, alternative treatments. A century later, Anton Mesmer challenged his orthodox physician detractors to cast lots to decide which patients should be treated by them, and which by him, using ‘animal magnetizm’: In order to avoid any later argument and all the questions that could be raised about differences in age, in temperament, in diseases, in their symptoms etc. the assignment of the patients shall be made by the method of lots.16 [emphasis added] Casting lots is just one of several potentially unbiased methods that can be used to ensure that like will be compared with like in treatment comparisons. Alternation (or rotation) of successive patients to different treatments is an easily understood way of generating patient groups for fair treatment comparisons. As long as the underlying order of the patients' presentation has not been predetermined in some way that introduces bias, strict alternation ensures that no conscious or unconscious bias results in patients with better or worse prognoses being allocated to one of the treatment comparison groups. Other methods that have been used to ensure that like will be compared with like include patients' dates of birth, or the terminal digits of their case record numbers.

The use of mammographic tumour feature significantly improves outcome prediction of breast cancers smaller than 15 mm: a reproducibility study from two comprehensive breast centres

BACKGROUND: The efficacy and reproducibility of mammographic tumour feature use for predicting patient outcome were tested in consecutive in situ and 1–14 mm invasive breast cancer cases from two breast centres in two different health care systems. METHODS: All in situ and 1–14 mm invasive cancers detected in Falun from 1996–2006 (n = 971), in Roanoke from 2002–2007 (n = 555), and in women aged 40–69 (age limits for invitation to screening) in Falun from 1977–1995 (n = 844) were included; of these the mammograms, pathology slides and follow-up information were available in 95%, 97% and 91% of the cases, respectively. The cancers were classified according to their mammographic appearance: stellate or circular without associated calcifications, or malignant type calcifications with or without an associated tumour mass. The mammographic tumour features and the disease specific survival were correlated. Terminal digit preference of tumour size measurements was examined. RESULTS: Mammographic tumour features were similarly represented in both centres. A significant preference was observed for tumour size measurements divisible by 5 mm. Outcome was significantly poorer for cases having casting type calcifications on the mammogram and excellent for the remaining cases. CONCLUSIONS: Outcome prediction of patients with 1–14 mm invasive breast cancer is significantly improved by the addition of mammographic tumour features to the currently used prognostic factors. The integration of imaging morphology into the TNM classification of invasive breast cancers smaller than 15 mm facilitates specifically targeted therapy and may curtail overtreatment. The significant digit preference found in this study may justify using the terminal digits of "4" and/or "9" as upper size limits for tumour size categories.

Autoradiographic observations on developing and growing claws of reptiles

AbstractAlibardi, L. 2010. Autoradiographic observations on developing and growing claws of reptiles. —Acta Zoologica (Stockholm) 91: 233–241The present qualitative autoradiographic analysis aims to present the main features of morphogenesis and growth of claws in reptiles. Lizard embryos treated with tritiated thymidine reveal that epidermal cell proliferation in terminal digits is prevalent in the dorsal side and gives origin to the curved unguis of the claw. Less proliferation occurs in the ventral side of the digit tip where the concave sub‐unguis is derived. Adult claws of a turtle show that thymidine‐labelled cells are present along most of the epidermis of the claw, especially at the claw tip. Also, injection of tritiated histidine and proline, indicating active protein synthesis, confirm autoradiographic labelling along most of the epidermis of claws, in particular at the apical tip. The present study indicates that proximal matrix regions, as have been described in mammalian nails, are absent in reptiles. This pattern of claw growth probably derives from that of terminal digital scales. In fact reptilian (and avian) claws are formed from a modification of scales, a different condition from that present in mammals.

Age heaping and accuracy of age data collected during a community survey in the Yavatmal district, Maharashtra

Background:Age is an important variable in epidemiological studies and an invariable part of community-based study reports.Aims:The aim was to assess the accuracy of age data collected during community surveys.Settings and Design:A cross-sectional study was designed in rural areas of the Yavatmal district.Materials and Methods:Age data were collected by a house-to-house survey in six villages. An open-ended questionnaire was used for data collection.Statistical Analysis:Age heaping and digit preference were measured by calculating Whipple’s index and Myers’ blended index. Age Ratio Scores (ARS) and Age Accuracy Index (AAI) were also calculated.Results:Whipple’s index for the 10-year age range, i.e., those reporting age with terminal digit “0” was 386.71. Whipple’s index for the 5-year range, i.e., those reporting age with terminal digit ‘0’ or ‘5’ was 382.74. Myer’s blended index calculated for the study population was 41.99. AAI for the population studied was 14.71 with large differences between frequencies of males and females at certain ages.Conclusion:The age data collected in the survey were of very poor quality. There was age heaping at ages with terminal digits ‘0’ and ‘5’, indicating a preference in reporting such ages and 42% of the population reported ages with an incorrect final digit. Innovative methods in data collection along with measuring and minimizing errors using statistical techniques should be used to ensure the accuracy of age data which can be checked using various indices.

Effectiveness of a Polysubstance Dependence Detoxification Protocol for Patients With Co-occurring Disorders

Patients with polysubstance dependence and co-occurring psychiatric and substance use disorders represent a growing population. This study investigates the safety and effectiveness of a single-scale, symptom-triggered protocol for patients undergoing inpatient detoxification from alcohol, opioids, sedatives, or polysubstance dependence. Medical records staff generated a list of all charts containing a principal discharge diagnosis of alcohol, sedative, opioid, or polysubstance dependence between 2002 and 2004, when the Butler Instrument for Withdrawal Assessment protocol was administered. This list was arranged by terminal digits of the medical record numbers to randomize the selection, and staff pulled the first 100 charts for review. De-identified medical data were recorded from the charts to obtain information about medications, length of stay, and adverse events during hospitalization. The main outcome measures were adverse events and length of stay. The average length of stay was 4.2 days (SD = 2.3), rate of discharge against medical advice was 4% (exactly 4 patients out of 100), and no seizures or delirium tremens were reported. The results of this study suggest that a single-scale, symptom-triggered detoxification protocol can facilitate safe and rapid detoxification and stabilization, even for patients with polysubstance dependence and co-occurring psychiatric and substance use disorders.

Three patients in a Chinese family with hereditary sensory neuropathy mimicking leprosy

Hereditary sensory neuropathy (HSN) is a rare disorder of peripheral sensory neurons. It was also known as hereditary sensory and autonomic neuropathy. It is characterised by a chronic clinical evolution with ulcerations, loss of sensation and destruction of terminal digits of feet and hands. It usually begins in childhood. Symptoms start with inflamed fingers or toes especially around the nails. The loss of sensation in hands and feet often leads to neglect of the wounds and at last leading to amputation in extreme cases. Due to the genetic pattern of inheritance, children in a family are affected by the disease one by one in a cluster pattern. Sometimes, health workers can confuse it with leprosy in the field. We report three patients in one family with hereditary sensory neuropathy which mimicked leprosy.

(Errors in statistical tests)3

In 2004, Garcia-Berthou and Alcaraz published "Incongruence between test statistics and P values in medical papers," a critique of statistical errors that received a tremendous amount of attention. One of their observations was that the final reported digit of p-values in articles published in the journal Nature departed substantially from the uniform distribution that they suggested should be expected. In 2006, Jeng critiqued that critique, observing that the statistical analysis of those terminal digits had been based on comparing the actual distribution to a uniform continuous distribution, when digits obviously are discretely distributed. Jeng corrected the calculation and reported statistics that did not so clearly support the claim of a digit preference. However delightful it may be to read a critique of statistical errors in a critique of statistical errors, we nevertheless found several aspects of the whole exchange to be quite troubling, prompting our own meta-critique of the analysis.The previous discussion emphasized statistical significance testing. But there are various reasons to expect departure from the uniform distribution in terminal digits of p-values, so that simply rejecting the null hypothesis is not terribly informative. Much more importantly, Jeng found that the original p-value of 0.043 should have been 0.086, and suggested this represented an important difference because it was on the other side of 0.05. Among the most widely reiterated (though often ignored) tenets of modern quantitative research methods is that we should not treat statistical significance as a bright line test of whether we have observed a phenomenon. Moreover, it sends the wrong message about the role of statistics to suggest that a result should be dismissed because of limited statistical precision when it is so easy to gather more data.In response to these limitations, we gathered more data to improve the statistical precision, and analyzed the actual pattern of the departure from uniformity, not just its test statistics. We found variation in digit frequencies in the additional data and describe the distinctive pattern of these results. Furthermore, we found that the combined data diverge unambiguously from a uniform distribution. The explanation for this divergence seems unlikely to be that suggested by the previous authors: errors in calculations and transcription.

Variation in recorded blood pressure terminal digit bias in general practice

This study aims to identify the extent of terminal digit bias in routinely recorded blood pressures (BP) across a number of different general practices and report on changes in terminal digit bias over a 10-year period. It also explores the effect this may have had on the mean recorded BP in this population. BP records were taken from The Health Improvement Network database containing anonymized patient records from information entered by UK general practices in the financial years 1996-1997 to 2005-2006. The proportion of measurements ending in zero and the mean BP readings were calculated for each practice and for each year of data.Over this 10-year period the percentage of systolic BPs with zero terminal digits fell from 71.2 to 36.7% and mean recorded BP fell from 152.3 to 145.3 mm Hg. Correcting the BPs to remove terminal digit bias indicates a 2-3 mm Hg underestimation of the mean population systolic BP over this period. The between-practice variation in the percentage of zero terminal digit readings increased from 3.5 to 6.5 s.d. Although it is welcome to see a reduction in terminal digit bias, it is worrying to see the increase in variation between practices. There is evidence that terminal digit bias may lead to potential misclassification and inappropriate treatment of hypertensive patients. The increase in variation observed may therefore lead to an increased variation in the quality of care given to patients.

Error in statistical tests of error in statistical tests

BackgroundA recent paper found that terminal digits of statistical values in Nature deviated significantly from an equiprobable distribution, indicating errors or inconsistencies in rounding. This finding, as well as the discovery that a large percentage of p values were inconsistent with reported test statistics, led to a great deal of concern in the popular press and scientific community. The findings ultimately led to new guidelines for all Nature Research Journals.MethodsWe checked the statistical analysis behind the original paper's tests of equiprobability.ResultsThe original paper tested equiprobability with the Kolmogorov-Smirnov test outside its regime of validity. Correct tests find no statistically significant deviations from equiprobability for the statistical values in Nature.ConclusionStatistical tests should be used correctly.

Comparative Surface Morphology of Marine Coelomic Gregarines (Apicomplexa, Urosporidae): Pterospora floridiensis and Pterospora schizosoma

Two species in the aseptate gregarine genus Pterospora from the Pacific and Gulf coasts were analyzed by scanning electron microscopy, which revealed characteristics not reported in other gregarines. The gamonts of these species had branching trunks that ended in terminal digits, and both species moved by cytoplasmic streaming and peristalsis. Pterospora floridiensis had surface pits and tracts of parallel ridges that bended and connected with one another. Pterospora schizosoma had irregular-shaped surface swellings that were usually arranged in rosette patterns. These unique surface features have not been reported for other gregarines, and are strikingly different from the surface features of many septate and aseptate gregarines that inhabit the intestinal lumena of their hosts and move by gliding. The correlation of Pterospora's unique pellicular features to the habitat and cytoplasmic streaming characteristic of the genus may be significant, and may reflect an adaptation for development in coelomic environments.

Quality of age data in patients from developing countries.

Age misreporting is common in demographic studies but the prevalence and magnitude of age misreporting in clinical cohorts is unknown. We analysed single-year age distribution and terminal digit preference in cancer patients from developing countries. Age distribution was analysed by plotting a single-year age of 3874 cancer patients from 72 different countries, mainly from the Indian subcontinent and the Middle East, who resided in the UAE at the time of cancer diagnosis. Preference for age ending with digits '0' and '5' was evaluated using Whipple's index (WI), which has value 100 in cohorts without preference. Preference for all 10 terminal digits was expressed as the difference between the found and expected frequencies using Myers blended method and was graphed. Age data quality was low in cancer patients from the Indian subcontinent (WI = 177) and Middle Eastern countries (WI = 113-204). Females of all nationalities supplied better quality of age data (lower WI) than males. Preference for age ending with digits '0' and '5' was found in all populations except the UAE male citizens who did not show preference for terminal digit '0'. Age data quality in this cohort of patients from developing countries was low. Preference for age ending with numbers '0' and '5' is common. In studies conducted in developing countries, age data quality should be analysed as it may bias results and weaken the power of the study.

Terminal digit bias in a specialty hypertension faculty practice.

Traditional blood pressure (BP) methodology is subject to observer error such as terminal digit preference and single number preference leading to inaccuracies in measurement. A high percentage (60-90%) of terminal BP readings digit being zero has been reported from general medical- and hospital-based clinics. This study examined terminal digit preference in a hypertension specialty practice and assessed clinical factors that may be associated with zero preference in this setting. A retrospective chart review of patients presenting to the hypertension clinic at the University of Connecticut Health Center during the month of September 2001 was performed. Data were extracted on age, gender, height, weight, treatment status, and systolic and diastolic BP measurements taken by nursing staff and attending physicians. Terminal digit preference was apparent in BP readings taken by both nursing staff and physicians. Zero was the terminal systolic BP digit in 40% of readings taken by the nursing staff and 31% of readings taken by physicians. For diastolic BP readings, the percentages were 23 and 36%, respectively. Nurses also recorded 43% of diastolic BP readings with terminal digit 2. Age was significantly higher in those persons in whom the physician diastolic BP terminal digit was zero than in those with nonzero terminal digits (67+/-14 vs 59+/-18 years, P=0.008). Body mass index was lower in the patient group with diastolic terminal digit zero bias compared to those with nonzero terminal digits (28+/-5 vs 32+/-6 kg/m(2), P=0.02). In conclusion, although the frequency of zero digit preference did not reach the 60-80% levels found in previous studies, there was evidence of terminal digit preference in the systolic and diastolic measurements taken by nursing staff and attending physicians in a specialist hypertension clinic. We believe that the lower levels of terminal digit preference observed are an effect of increased training in proper BP measurement and technique. However, the observed bias in measurement even in a hypertension unit argues for regular monitoring and feedback to minimize such errors.

Terminal Digits and the Examination of Questioned Data

(2002). Terminal Digits and the Examination of Questioned Data. Accountability in Research: Vol. 9, No. 2, pp. 75-92.

Digit preference in year at menopause: Data from the study of women's health across the nation

PURPOSE: To assess possible digit preference in self-reported year at natural menopause, and to determine whether equal proportions is an appropriate reference distribution.METHODS: Data are from the cross-sectional telephone interview from the Study of Women's Health Across the Nation (SWAN), a multi-site, multi-ethnic study of women aged 40–55. Analyses included 2151 naturally menopausal respondents, who were asked the year their periods stopped. Using a chi-square test, we compared the distribution of the terminal digit for year of final menstrual period (FMP) to an equal proportions (EP) distribution assigning 10% probability of each of the 10 digits. Departures from EP, however, may be accurate and may reflect the observed age distribution of subjects rather than digit preference. Thus, we stratified by year of interview to determine if the distribution was the same across years—suggesting digit preference—or if it varied systematically. We then estimated an expected distribution of terminal digit for year of FMP, using prospectively collected data (not subject to digit preference or recall bias) from the Massachusetts Women's Health Study, applied to the SWAN age distribution. The SWAN terminal digit distribution was compared with this expected distribution.RESULTS: Terminal digit for year at FMP exhibited a strong departure from EP (χ2 = 841.60, p < 0.001), with highest frequencies for digits 4 and 5. Stratifying by year of interview, the distribution was shifted one digit in 1997 compared with 1996, consistent with unbiased reporting. Using the expected distribution as the reference reduced the chi-square statistic by a factor of 7 (χ2 = 119.51, p < 0.001).CONCLUSIONS: The distribution of terminal digits for reported year at FMP was far from uniform, but departures from EP were consistent with results expected from an independent prospective study. These results suggest that EP may not be an appropriate reference for studies of digit preference, particularly those with a restricted age range.

Mandibular reconstruction in a patient with pyknodysostosis

Pyknodysostosis is a rare skeletal disease considered to be a variant of osteopetrosis. Clinical features of pyknodysostosis include dysplasia of the skull with frontal and parietal bossing, dysplasia of the clavicles, and partial or total aplasia of the terminal phalanges. The tips of the fingers are unusually club shaped, with short, irregular terminal digits. Often the paranasal sinuses are hypoplastic or absent, and the fontanelles are patent and palpable. Pathologic fractures commonly occur in childhood because of the dense, fragile bones. Pectus excavatum, bowing of long bones, bilateral genu valgum, clavicular hypoplasia, as well as kyphosis and scoliosis, are additional orthopedic presentations of this disease. Morphologically, the skull appears disproportionately, large in comparison with the rest of the body, but the face is small because of the hypoplastic development of the facial bones. The eyes appear exophthalmic, and the nose has been described as a parrot's beak. Histologically, pyknodysostosis shows continuous endosteal bone formation without concomitant resorption and modeling. Although active endosteal bone formation usually produces a reduction in bone marrow volume, pyknodysostosis is not characterized by severe anemia. This suggests active medullary hematopoiesis. Prevalent oral features have been reported by Yamada et al. 3 , and include premature eruption of teeth, shortness of tooth roots, narrowing of pulp cavities, hypodontia, enamel hypoplasia, malocclusion and malposition of teeth, a double row of deciduous teeth in both the maxilla and the mandible, severe caries, macroglossia, a grooved palate, obtuse mandibular gonial angles, and generalized micrognathia 3 . Osteomyelitis of the jaws and recurrent fractures of long bones are characteristic complication of pyknodysostosis. 1,4,5 Green and Rowe 6 described a case of osteomyelitis occurring in a patient with pyknodysostosis after extraction of a mandibular first molar. Reconstruction was attempted using a titanium tray and an iliac crest bone graft. The reconstruction failed subsequent to infection. There has been no documented case of successful mandibular reconstruction in patients with pyknodysostosis. We report the management of osteomyelitis in a patient with pyknodysostosis and the early results of mandibular reconstruction.

Echoic Memory Interference and Comprehension in a Foreign Language*

Based on the hypothesis that students who are less able to comprehend speech in a foreign language suffer from greater echoic memory interference, faculty evaluated the listening comprehension of students in several introductory foreign language courses. The evaluations were used to assign students to weaker and stronger comprehension groups. Both groups were tested for echoic memory interference using the standard suffix procedure in which a list of digits is read with either a tone control, or a suffix recall, appended to the end of the list. Echoic interference is measured by comparing the recall performance in the suffix and nonsuffix (tone) conditions. Poorer recall of terminal digits in lists in the suffix condition, as compared to the nonsuffix condition, indicates echoic interference. The results were consistent with our hypothesis, suggesting that students with weaker listening comprehension depend more upon vulnerable sensory codes in echoic memory, while those with better comprehension rely on stable higher‐order codes.

The timing of granule cell differentiation and mossy fiber morphogenesis in the opossum.

The timing of developmental events may be important for the orderly formation of neuronal interconnections. In the present study, the timing of granule cell migration is compared with the arrival and maturation of mossy fiber projections. The opossum was chosen as the experimental animal because its protracted postnatal development enables the examination of developmental sequences not as easily recognized in other more commonly used mammalian species. It is shown that all areas that project to the cerebellum as mossy fibers in the adult opossum do so by postnatal day (PD) 30. Their major target, the granule cells begin inward migration from the external germinal layer (EGL) prior to PD 30, but do not form a distinct internal granular layer (IGL) until PD 35. Migrating granule cells penetrate into the IGL deep to granule cells that have begun dendritic differentiation. By PD 50, Golgi impregnations reveal that many granule cells have numerous immature processes, somal spines and dendritic growth cones. After this age these structures are rare and the vast majority of granule cells exhibit short dendrites with digiform endings. Dendritic differentiation subsequent to PD 54 involves an increase in the length of the shaft and the further maturation of terminal digits. Also from Golgi material, immature mossy fiber endings can be identified in the IGL by PD 35 and exhibit mature characteristics at PD 73. Thus, the formation and maturation of granule cell dendrites and their afferents (mossy fibers) occur over an extended period of time (PD 35-73). Moreover, granule cells exhibit a sequence of development similar to that of Purkinje cells: early arrival of their primary afferent projections in the cerebellar anlage; a period of exuberant dendritic growth; and a protracted and overlapping period for dendritic and synaptic maturation.

Localization of hexokinase in neural tissue: electron microscopic studies of rat cerebellar cortex.

The distribution of hexokinase (ATP:D-hexose 6-phosphotransferase, EC 2.7.1.1) in the rat cerebellar cortex has been studied at the electron microscopic level using the peroxidase-antiperoxidase procedure. Extensive staining of cytoplasmic regions, with some increased staining at mitochondrial profiles, was seen in the cell bodies of both neurons (basket, stellate, Lugaro, Golgi, and granule cells) and astrocytes. Oligodendrocytes showed little or no detectable staining. Purkinje cell perikarya were much less intensely stained than were the perikarya of other neurons. The initial portion of the Purkinje dendrite was, like the perikaryon from which it emerged, lightly stained. More intense staining was seen in the secondary and tertiary branches of the Purkinje dendrite, but the terminal branches were devoid of stain. Granule cell dendrites were well stained in their initial portions but devoid of stain in their terminal dendritic digits which form part of the cerebellar glomeruli. In contrast to the unstained granule cell dendritic digits, the central mossy fiber nerve terminal of the glomerulus exhibited intense staining of the mitochondrial profiles and of synaptic vesicles adjacent to the mitochondria. Axons of basket cells showed intense staining in the segments adjacent to the Purkinje cell soma, while terminal twigs of the basket axons in the pinceau surrounding the (unstained) initial segment of the Purkinje axon showed markedly decreased staining intensity. These results indicate that there may be substantial variation in hexokinase levels between the various regions of neuronal processes. Hexokinase was seen at both cytoplasmic and mitochondrial locations in a variety of cells. It does not appear likely that location of hexokinase can be directly correlated with cell type, i.e., with neurons versus glia.