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Asma gelişiminin olumsuz etkilenmemesi ve ürün kalitesinin devamı için yaprak miktarı ve alanının optimum düzeyde bulunması gerekmektedir. Çünkü omca için gerekli olan ve çoğunluğu meyve ve odun kısmında depolanan karbonhidratlar, fotosentez sonrası yapraklar aracılığı ile oluşmaktadır. Yaprak alanı ile ilgili bilgiler birçok alanda kullanılabilmektedir. Bunların başında fotosentez kapasitesi ve bitki büyüme oranı gelebilir. Yaprak alanı belirlemede çeşitli aletlerden ve yöntemlerden (planimetre, yaprak alanı ölçer, en-boy çarpımı, ağırlık-alan hesabı, görüntülü işleme programları vb) yararlanılmaktadır. Bu çalışmada materyal olarak 3 adet Amerikan asma anacı (5BB, 110 R, 1103 Paulsen ) ile 5 adet üzüm çeşidi (Alphonse Lavallée, Italıa, Mıchele Palıerı ve Narince, Yalova İncisi) kullanılmıştır. Anaç ve çeşitlere ait omcalardan 15-25 boğumlu 20 adet sürgün alınmış ve boğum sırasına göre yaprakların fotokopileri çekilmiştir. Yaprakların gerçek alan değerleri planimetre ile ölçülmüştür. Ayrıca yaprakların yaprak sapı ile ayanın genişlik ve uzunlukları da ölçülmüştür. Yaprak sapı, aya genişliği, aya uzunluğu (L1 damarı), aya genişlik x uzunluk değerleri ve gerçek alan arasında regresyon analizi yapılmıştır. Bir sürgün üzerinde en fazla yaprak alanı anaçlardan 5 BB (2484 cm2), çeşitlerden Narince‘de (2126 cm2) meydana gelmiştir. Her üç anaçta da 9.boğumda bulunan yaprak ortalama değeri vermiştir. Çeşitlere göre ortalama değer veren boğum numarası açısından Alphonse Lavallée, Mıchele Palıerı ve Yalova İncisi çeşitlerinde 11.boğum ön plana çıkmıştır. Narince çeşidinde 13., Italia çeşidinde ise 12.boğum ortalamaya en yakın değer vermiştir.

Although much has been written on the subject of polar planimeters, they still remain relatively obscure instruments. This is unfortunate: not only do they provide a remarkably quick and precise me...

Computer vision systems based on digital image processing have been proposed as alternative tools to traditional methods to estimate leaf area, replacing the most time-consuming steps and laboring manual measurements. However, many of the available applications are still based on manual determination of leaf dimensions or require excessive and laborious user interventions before providing results. USPLeaf was designed to process images containing single or multiple leaves, and automatically determine the leaf area without user intervention. The accuracy for leaf area measurements of the software was compared to the results obtained by the standard method, an electronic planimeter (LI-3100). The vegetal species, Mavuno grass (MAV, Urochloa hybrid) and Macrotyloma axillare (MAC), were chosen because they are characterized by different leaf shapes. A smartphone camera was used as image capture device. When using a standard black paper square of 9 cm², both LI-3100 and USPLeaf provided accurate and precise results, with an estimated average area of 8.90 and 9.00 cm² and a standard deviation of 0.17% and 0.00%, respectively. The relative error rate for the vegetal species varied from -6.37 to 2.25%. The regression analysis indicated that the software was a precise tool to estimate leaf area (R²=0.983 for MAV and 0.977 for MAC), but it also revealed that samples inferior to 25 cm² for grasses and 15 cm² for legume species should be avoided. The software can be used as an automated tool in image processing aiming to determine leaf area from digital images.

xperimental study was carried out at the Agricultural Engineering Department, Faculty of Agriculture, Omar El- Mokhtar University, Al-Beida, Libya. The objective of this study to develop apparatus for measuring plant leaf area based on the changes on resistance of air pressure as related to surface area of plant leaf.The results showed that, for predicting the change of leaf area at different air pressure, a series of simple regression analysis was employed. The analysis related the change in leaf area with air pressure. The regression analysis could relate the change in leaf area strongly with the air pressure as indicated by the high regression coefficients of the obtained equations. On the other hand, it can be seen power relationship between the leaf area (Y) (cm2) and air pressure(X) (m.bar), and this relationship submitted to the following equation: Y  9.8624X 0.6945 R2  0.9564 The accounting data of leave areas using the apparatus and a standardplanimeterwere recorded to obtain correction factor. The correction factor was 0.84, 0.85, 0.86, 0.87, 0.90, 0.92, 1.02, 1.05, 1.08 and 1.09 for leaves area; Olive, Lemon adalia, Marble, Bots, Almond, Garonaa, Grape, Roses, Peach and Plum, respectively. The average value of correction factor was found to be 0.96 of plant leaf area.

The development of software for automated image processing, with particular emphasis on agricultural monitoring applications, has increased in the last years. Leaf area measurements are important for several crops and pastures, once the leaf area index is related with growth and photosynthesis rates, being an essential parameter of process-based models of vegetation. The processing algorithms implemented in most software for leaf area measurements currently available require the determination of leaf dimensions. Hence, the automated processing of samples with multiple leaves is still limited, frequently requiring manual pre-processing of the images. In order to develop a new software system aimed at processing images of samples composed of multiple leaves without any requirements of manual pre-processing of the images, the USP-Leaf software was developed. The software’s performance was compared by using different devices for image acquisition: a semiprofessional digital camera (Sony, resolution of 12 megapixels); a mobile phone (Lenovo k5, resolution of 5 megapixels) and a desktop scanner (HP B20, 300 dpi corresponding to 3.508 × 2.480 pixels). The results were validated by comparing the values obtained with the standard method (electronic planimeter model Li-Cor 3100). The experiment was carried out at the Faculty of Animal Science and Food Engineering (FZEA), University of Sao Paulo, Pirassununga, SP, Brazil. The leaf samples were obtained from Brachiaria decumbens Stapf. cv. Basilisk pastures. A total of 20 samples comprising 15 leaves were collected, from which the images were acquired with each device. Edge detection, filtering and thresholding algorithms were applied to identify the leaf section of the image against the background. Considering the leaf area measured with the electronic planimeter, the relative error rate of the software’s estimates was lower than 7%, being highest when the scanner was used and lower with the digital camera. Pearson’s correlation coefficients were higher than 95%, regardless of the device used for image capturing, indicating that the software was able to provide accurate estimates of leaf area. The linear regression equation associated with the estimated leaf area using the mobile phone showed the highest values for the intercept and the higher standard error associated with this parameter (2.9 ± 5.69), despite showing a slope close to 1 (1.0 ± 0.07). The leaf area estimates were close to the standard method, showing that the software’s performance was not affected by the device used for image acquisition.

Drawing on a didactic gap detected between the elementary concept of area and the infinitesimal approach to it within the Italian secondary school curriculum, the notion of swept area is introduced in grades 10–11. The idea of swept area is introduced through the mediation of an artifact, the Polar Planimeter, both as a concrete physical-tool and as a virtual-object. It triggers and supports the semiotic productions of the students so that they can grasp the new concept. The notion of didactic cycle is used for designing students’ learning sequences. The activities in such sequences are of two types: sensory-motor and symbolic. The mediation of the artifact allows intertwining the two types so that the one can constantly be built on the other. Indeed, the practices mentioned above show a deep intertwining between their cultural and cognitive components.

This study evaluated the correlation between measurements of rib-eye areas of sheep carcasses by traditional methods and those obtained by scanned images. Thirty pictures of the longissimus dorsi muscle of sheep carcasses were drawn on tracing paper and analyzed for muscle area (rib-eye) using four methods: scanned images, which utilizes the software DDA -Determinador Digital de Áreas (Digital Area Determiner); measurements "A" and "B" applied to the equation: (A/2 × B/2) × π; Planimeter method and rib-eye grid method. All rib-eye area figures were measured five times by each method, setting up a completely randomized experiment with four treatments and five replicates. Data were submitted to analysis of variance and means were compared by the Tukey test, Pearson correlation and linear regression by the SAS software. Easiness and difficulties perceived by the evaluators in the performance of each method were also recorded. The method of scanned images analyzed by the software DDA showed high correlation with the methods traditionally used, and can be considered feasible to determine carcass rib-eye area, with the advantage of being easy to operate, flexible, and economical.

Precise calculation of total body surface area (TBSA) or premarked surface areas (P-MSAs) is of great importance in many biomedical applications. The aim of the paper was to present a simple procedure of measurement of P-MSAs in small animals and to determine a more accurate Meeh's constant ( k), for a commonly used weight range of laboratory rats. A series of 30 Wistar rats, weighing 195–240 g, were anaesthetized and weighted. The TBSA of each animal was measured using a clear pocket and a planimeter. The data obtained were entered into the Meeh's formula (TBSA = kW2/3), the most commonly used for small experimental animals, so that a k value for each animal as well as a mean k value (9.83) were obtained. The TBSA of the animals was also calculated using the aforementioned mean k value and compared with that obtained using k values reported in previous studies. According to our findings, the new mean k value, determined with the use of our procedure of surface area measurement, ensured greater accuracy in the determination of the TBSA of experimental rats of a specific weight range. We also suggest a new procedure of surface area measurement which is easy, accurate and does not require animal sacrifice.

This paper compares two different approaches to calculate the average cross-sectional area of breakup fragments. The first one is described in the NASA standard breakup model 1998 revision. This approach visually classifies fragments into several shapes, and then applies formulae developed for each shape to calculate the average cross-sectional area. The second approach was developed jointly by the Kyushu University and the NASA Orbital Debris Program Office. This new approach automatically classifies fragments into plate- or irregular-shapes based on their aspect ratio and thickness, and then applies formulae developed for each shape to calculate the average cross-sectional area. The comparison between the two approaches is demonstrated in the area-to-mass ratio ( A/m ) distribution of fragments from two microsatellite impact experiments completed in early 2008. A major difference between the two approaches comes from the calculation of the average cross-sectional area of plates. In order to determine which of the two approaches provides a better description of the actual A/m distribution of breakup fragments, a theoretical analysis in the calculation of the average cross-sectional area of an ideal plate is conducted. This paper also investigates the average cross-sectional area of multi-layer insulation fragments. The average cross-sectional area of 214 multi-layer insulation fragments was measured by a planimeter, and then the data were used to benchmark the average cross-sectional areas estimated by the two approaches. The uncertainty in the calculation of the average cross-sectional area with the two approaches is also discussed in terms of size and thickness.

The goal of the authors was to evaluate the repeatability and accuracy of real-time ultrasound technique under Hungarian conditions. Ribeye area was measured at first time on live animals, before the day of slaughtering with Falco 100 ultrasound equipment in Charolais fattening bulls. Ultrasound pictures were traced at two times by the same operator. After slaughtering, ribeye area (REA) was measured on the carcass by planimeter at the same anatomical point like ultrasound measurements. Statistical analysis was carried out to examine the relationship between carcass and ultrasound REA. After it, repeatabilty was established by comparing the ultrasound pictures twice.

The camera lucida drawing method with planimetric area measurements was compared with direct microscopy and systematic point count in a quantitative study of glomeruli, the study including differential counts of nuclei and determination of the total and mesangial areas. Good reproducibility was found using both methods, but the camera lucida drawing method was found to be at least three times more time-consuming than direct microscopy for total and differential counts of nuclei and systematic point count for mesangial area determination. Measurement of total glomerular area was done planimetrically, by point counting and by determination of the area as an ellipse or a circle. The results obtained planimetrically and by point counting did not differ significantly, whereas the difference between the results of the planimeter measurements and the results obtained by applying the formula of an ellipse or a circle on glomerular sections was found to be statistically significant. If central sections were compared with random sections of glomeruli, deviation of results was found to be greater in the random sections, and it was calculated that 10 central and about 30 random sections have approximately the same value in quantitative examination of a renal tissue specimen. Thus, it appears advisable to use direct microscopy for total and differential counts of nuclei, systematic point count for mesangial area determination, planimetric measurement or point counting for total glomerular area determination and to apply this method on central sections of glomeruli.

Introduction. Leaf area measurements are used commonly in the study of growth and development of fruit trees. These measurements can be made destructively by using a variety of sen- sitive instruments and/or non-destructively by using models of leaf area estimation. For models of leaf area estimation, some leaf parameters such as the length and width of leaves are usually used in the measurements. Construction of a model of leaf area estimation. Computer programs such as Excel, SAS and SPSS may be used in this process. In brief, after a leaf has been placed on a sheet of paper and photocopied, a digital planimeter or suitable tool may be used to measure the actual leaf area. The leaf width (W) and length (L) of the leaves sampled can be measured by a simple ruler. After this, regression analysis of the data may be performed separately for each genotype, species or cultivar. The analysis can be conducted with various subsets of the independent variables; for ins- tance, leaf length (L), leaf width (W), L 2 , W 2 and (L 2 /W 2 ) to develop the best model for predicting leaf area. Regression analyses should be carried out until the deviation sum of squares is minimized. Models of leaf area estimation for specific crops. In our study, prediction models of leaf area were developed by referring to the relevant current literature that studied such fruits as avocado, banana, blackberry, cacao, cherry, chestnut, grape, guava, kiwifruit, lotus plum, peach, pistachio, rabbiteye blueberry, red currant, red raspberry, sour orange, strawberry, pecan and white mulberry. Advan- tages and disadvantage of the models of leaf area estimation. Some advantages and a disad- vantage of models of leaf area estimation are presented. Conclusion. Our mini-review has shown that the models which have been formulated and which will develop in the future for some fruit spe- cies can be reliably used. Turkey / fruit-growing / models / forecasting / leaf area / methods / measurement / evaluation

Introduction . Simple, accurate and non-destructive models determining leaf area of plants are important in many experimental comparisons. Determining the individual leaf area (La) of A. deliciosa (A. Chev.) vines involves the measurements of leaf parameters such as leaf length (Ll) and width (Lw), or some combinations of these parameters. Materials and methods . A 2-year investigation was carried out in Italy during 2005 (calibration experiments) and 2006 (validation experiment) under open field conditions. It aimed at comparing existing predictive leaf area models for A. deliciosa leaves using non-destructive measurements, and assessing the accuracy of the optimum model selected using an independent dataset. Results and discussion . Regression analyses of (La) vs. (Ll) and (Lw) revealed several models that could be used for estimating the area of individual A. deliciosa leaves. A linear model with (Ll × Lw) as the independent variable [La = 0.82 (Ll × Lw) – 0.28] provided the most accurate estimate (R 2 = 0.985, mean standard error = 25) of A. deliciosa leaf area. Validation of the model with (Ll) and (Lw) measured on leaves from other orchards grown in different locations showed that the correlation between calculated and measured areas was very high. Conclusions . With the model selected, agronomists and physiologists can estimate accurately and reliably the leaf area of A. deliciosa plants without the use of expensive instruments, e.g. , a leaf area planimeter or digital camera with image measurement software.

(2007). As the Planimeter's Wheel Turns: Planimeter Proofs for Calculus Class. The College Mathematics Journal: Vol. 38, No. 1, pp. 24-31.

The aim of this study was to evaluate the accuracy of a number of methodologies, i.e. PLANIMETER, GEOMETRIC, GRID, UNESP-GRID, UFSM, ZEISS and DELTA-T, in determining ribeye area (REA) of 65 Saanen goats of varying body condition. Goats were grouped according to body weight at slaughter (5.3, 11.2, 12.9, 16.4, 21.0, 22.1, 27.7, 28.6 and 35.2 kg). Tracing based on transverse section between the 13th thoracic and 1st lumbar vertebrae was used to determinate REA. There was no significant interaction between methodologies and body weight at slaughter. PLANIMETER, UNESP-GRID, GEOMETRIC and UFSM methods were similar in average values to the standard DELTA-T method. The REA was overestimated by the GRID and underestimated by the ZEISS method. The UNESP-GRID, GEOMETRIC and UFSM methods have coincident curves comparable to DELTA-T, when used to estimate goat REA. The UNESP-GRID and GEOMETRIC were the methods of choice based on accuracy, practicality and feasibility.

2. E. Cartan, Groupes simples clos et ouverts et g?om?trie riemannienne, J. Math. Pures Appl. 8, (1929), 1-33. 3. R. Courant, Differential and Integral Calculus, II. Originally published in 1934 as Vorlesungen ?ber Differentialund Integralrechnung. Translated by E. J. McShane. Wiley Interscience, New York, 1988. 4. R. Courant and F. John, Introduction to Calculus and Analysis, II, Wiley Interscience, New York, 1974. 5. W. T. England and T. L. Miller, Volumes and cross-sectional areas, this MAGAZINE 74:4 (2001), 288-295. 6. R. L. Foote, Planimeters and isoperimetric inequalities on constant curvature surfaces, preprint. 7. R. L. Foote, Geometry of the Prytz planimeter, Reports on Mathematical Physics 42, no. 1,(1998), 249-271. 8. R. L. Foote, Planimeters, http://persweb.wabash.edu/facstaff/footer/ Planimeter/Planimeter.htm. 9. G. A. Galperin, A concept of the mass center of a system of material points in the constant curvature spaces, Comm. Math. Phys. 154, (1993), 63-84. 10. A. V. Shchepetilov, Two-body problem on two-point homogeneous spaces, invariant differential operators and the mass center concept, Journal of Geometry and Physics 48, (2003), 245-274. U.M. Spivak, Calculus on Manifolds, W. A. Benjamin, New York, 1965.

In this research, leaf area prediction models were developed for some leaf-used medicinal plants namely Calamintha nepeta, Datura stromonium, Melissa officinalis, Mentha piperita, Nerium oleander, Origanum onites and Urtica dioica growing wild in Black Sea region of Turkey. Lamina width, length and leaf area were measured non-de - structively to develop the models. The actual leaf areas of the plants were measured by PLACOM Digital Planimeter, and multiple regression analysis with Excel 7.0 computer package program was performed for the plants separately. The produced leaf area prediction models in the present study were formulized as LA = (a) + (b 1 × L) + ((b 2 × (L × W)) + (b 3 × L 2 ) + (b 4 × W 2 ) + (b 5 × (L × W 2 )) + (b 6 × (L 2 × W)) + (b 7 × (L 2 × W 2 )) where LA is leaf area, W is leaf width, L is leaf length and a, b 1 , b 2 , b 3 , b 4 , b 5 , b 6 , and b 7 are coefficients. R 2 values for medicinal plants tested varied with species from 0.82 in Origanum onites to 0.98 in Urtica dioica. All R² values and standard errors were found to be significant at the P < 0.001 level.

Dois métodos de quantificação de biofilme da dentadura (contagem de pontos e planímetro) foram testados e comparados com o método de pesagem de papel e Índice de Higiene de Prótese. Superfícies internas de 62 próteses foram coradas, fotografadas e as áreas total e do biofilme foram projetadas em papel e contornadas com grafite. O método de contagem de pontos (experimental 1) foi aplicado com uma grade de pontos. Para o método do planímetro (experimental 2), as áreas foram medidas com um planímetro digital e para o método de pesagem (controle 1) foram recortadas e pesadas em balança de precisão. No Índice de Higiene de Prótese (controle 2), utilizou-se a atribuição de escores. Os resultados mostraram uma porcentagem de concordância entre os métodos experimentais e controle 1 de 82% (contagem de pontos) e 95% (planímetro), bem como alto grau de correlação (r = 0,98; r = 0,99) entre os valores obtidos. Quando comparados com o controle 2, houve concordância em 55% (contagem de pontos) e 37% (planímetro) dos casos. Os métodos experimentais podem ser úteis em estudos clínicos para avaliação da eficácia de agentes de higienização. Two methods of quantification of the biofilm (point-counting and planimetric) were tested and compared with the paper-weighing method and with the Prosthesis Hygiene Index. The internal surfaces of 62 complete dentures were stained and photographed. The slides were projected on a paper sheet. The total area and the area covered with biofilm were contoured using a black pencil. The point-counting method (experimental 1) was carried out on a mesh of equidistant points. For the planimetric method (experimental 2), the areas of interest were measured by means of a digital planimeter. In the paper-weighing method (control 1) the areas of interest were cut and weighed on a precision scale. In the determination of the Prosthesis Hygiene Index (control 2), the accumulation of biofilm was estimated by means of a scoring method. The results revealed an agreement rate of 82% between the paper-weighing method and the point-counting method, and an agreement rate of 95% between the former and the planimetric method, which was confirmed by high coefficients of correlation (0.98 and 0.99, respectively). The comparison with the Prosthesis Hygiene Index resulted in 55% of agreement with the point-counting method and in 37% of agreement with the planimetric method. The experimental methods can be useful in clinical studies involving the evaluation of the performance of denture cleansers.

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T19:00:48Z No. of bitstreams: 0 Made available in DSpace on 2013-08-22T19:00:48Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-05-01 Made available in DSpace on 2013-09-30T19:59:49Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-05-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T13:19:58Z No. of bitstreams: 0 Made available in DSpace on 2014-05-20T13:19:58Z (GMT). No. of bitstreams: 0 Previous issue date: 1998-05-01 Este trabalho teve por objetivo verificar a viabilidade do uso de digitalizador de imagens manual, acoplado a um microcomputador, para a avaliação do consumo de folhas de soja, por lagartas de 5o instar de Anticarsia gemmatalis Hübner (Lep.: Noctuidae), em comparação com o método de pesagem e do planímetro, baseando-se na eficiência dos métodos e no tempo gasto para a avaliação. Os testes foram realizados utilizando-se folhas de soja `IAC 8' e lagartas criadas em dieta artificial. Foram realizados 2 tipos de teste: 1o) oferecimento de folíolos inteiros de soja às lagartas e, 2o) oferecimento de disco de folhas de área conhecida. No 1o teste comparou-se o método de pesagem com o digitalizador de imagens (scanner); no 2o experimento foram comparados o método do planímetro com o digitalizador de imagens que emprega o programa PCXAREA. Os resultados obtidos demonstraram que não existem diferenças nas medições de folíolos e discos de soja consumidos por A. gemmatalis quando comparados os métodos tradicionais (planímetro e pesagem) e o de digitalização de imagens. A medição com o digitalizador reduziu o tempo de avaliação em 88,5% e 87%, em relação ao planímetro e método de pesagem, respectivamente, sendo plenamente viável a sua utilização. The viability of the use of an image analyzer (scanner), was compared with the use of leaf weight and planimeter techniques, to measure leaf area consumption by insects. The tests were conducted with 5th instar Anticarsia gemmatalis Hübner (Lep.: Noctuidae) larvae reared on artificial diet. Soybean leaves (cultivar IAC - 8) were offered to velvetbean caterpilars held in Petri dishes. Two experiments were conducted in a completely randomized design: (1) with whole soybean leaves, and (2) with leaf disks. The image analyzer use was compared with the leaf weight method in the first experiment and with the planimeter. The image data was analyzed with PCXAREA software. There were no significant differences between the image analyzer and the standard techniques. The evaluation time with image analyzer reduced by 88.5 and 87% the time consumed with planimeter and leaf weight methods, respectively. Based on the results, it is concluded that the use of a scanner is viable for measuring leaf area consumption by insects. UNESP USP UNESP

We have developed a system that measures the volume of air cells in the temporal bone through computerized digital processing of high-resolution CT images. By using this method, the volume of pneumatization was measured, and the results were compared with the measured area of pneumatization obtained from two conventionally used simple ear X-ray methods (the planimeter and rectangular dimensional methods). A total of 57 ears, from 34 subjects, confirmed as normal by CT were examined. The average volume of pneumatization measured on CT images was 5.97 +/- 4.15ml, and the average areas of pneumatization measured by the planimeter and rectangular methods were 9.08 +/- 5.64 and 17.39 +/- 9.77 cm2, respectively. Graphically, when the volume of pneumatization was plotted on the Y axis and the planimeter-measured area of pneumatization on the X axis, a regression formula of Y = 0.651X + 0.054 was obtained, with a correlation coefficient of 0.89. With the volume of pneumatization plotted on the Y axis and the rectangular-dimensional-measured area of pneumatization on the X axis, the regression formula was Y = 0.375X - 0.559, with a correlation coefficient of 0.88. Both these correlation coefficients were considered high. Furthermore, 3D models of the air cells in the temporal bone were created and compared for patients with high and low correlations. In order to capture the morphological characteristics of these 3D models, they were examined from four different angles (lateral, upper lateral, anterior lateral and upper medial). The results showed that regardless of whether air-cell growth was present in the direction of the apex partise petrosae in patients with a low correlation coefficient, such growth played a major role in the degree of the correlatiton. Future studies will be required to clarify this point, though it can already be said that 3D models are indispensable for studying the air cells in the temporal bone. When we compared the volume and area of pneumatization in the temporal bone at different CT cross-sections, we found correlation coefficients in the vicinity of the canalis semicircularis lateralis of about 0.9 or higher. A statistical comparison of correlation coefficients for the CT, planimeter, and rectangular dimensional methods, made by using the CT cross-section with the highest coefficient, found a significant difference between the CT method and the other two methods (p < 0.05). In other words, the volume of pneumatization can be estimated more accurately with CT images than with simple ear X-rays.

In studies involving the carcass characteristics conducted at the Department of Animal Science of the Federal University of Piaui, the linear measurements of rib eye area (REA) and subcutaneous fat area (SFA) have been carried out by the plastic grid method, in which readings are made by counting in cm². In order to test this widely used approach, this study aimed at conducting a comparison among three other more or less precise procedures in order to verify the traditional method accuracy. To estimate the effect of both genetic patterns and the four determination methods (Feedback, AutoCAD, Planimeter, and Weighing) on REA and SFA, analysis of variance (ANOVA) was used in 2 x 4 factorial arrangement. There was no difference among the four methodologies and the feedback method shows easier implementation, more practicality and reliability to be used in researches. KEYWORDS: Measurement; rib eye area; subcutaneous fat.

WOS: 000281700000038 A leaf area (LA) estimation model developed in a temperate climate for sweet cherry (Prunus avium L.) was tested for validation on 'Regina' trees on two rootstocks of varying vigor, 'Gisela 5' (Gi5) and 'Gisela 6' (Gi6), in a cool temperate climate (the Great Lakes region of North America). To determine the degree of accuracy of the model, actual LA values measured by digital planimeter were plotted against predicted LAs calculated by the model. The relationships (r(2) values) were very high and varied little between rootstocks (r(2) = 0.9886 for Regina/Gi6 and r(2) = 0.9849 for Regina/Gi5). This study demonstrates that the model is valid for use by cherry researchers in different growing regions and for rootstocks that impart different levels of vigor scion, such as 'Regina'. Scientific and Technological Research Council of TurkeyTurkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [BIDEB-2219] We thank Dr. N. Suzanne Lang for editing this paper. This study was supported by The Scientific and Technological Research Council of Turkey (BIDEB-2219).

Drawings from a random sample of 32 registry certificates were used to evaluate procedures for measuring the percentage of white coat color of Holstein cows. Measurements were obtained using a planimeter and by visual evaluations of two inspectors. Mean white percentage of the total cow, excluding face, was 27.8%. With the planimeter, correlations between white percentages on the drawing of the total cow and on the upper and lower body sections were .99 and .92; correlation between right and left sides of the same drawing of the total cow was .96. Percentage of white exhibited greatest variability relative to the mean when measured in the upper body (CV = 122). From upper body, white percentage was correlated >.97 between inspectors and planimeter and >.98 between inspectors. If errors were distributed normally, confidence limits of correlations would be narrow; e.g., 95% limits of correlation .96 are .92 to .98. However, percentage of white appears to be a nonnormal variable skewed to the right. Attempts to transform data to avoid a departure from normality were not successful; additional attempts using other transforms seem warranted. Visual appraisal appears to be an efficient procedure for evaluating percentage of white coat based on registry certificates.

Lang, A.R.G. and McMurtrie, R.E., 1992. Total leaf areas of single trees of Eucalyptus grandis estimated from transmittances of the sun's beam. Agric. For. Meteorol., 58: 79-92. Total leaf areas of isolated plants can be estimated from the transmittance of the direct beam of the sun. Leaf area is obtained by integrating the logarithm of transmittances over an area which encompasses the shadow of a plant. Details of the theory and procedures are given. A central assumption of the method is that projections of the foliage are arranged randomly on an area about 10 times the area of leaves. Experiments with small trees grown in the field and in pots showed that total leaf areas for E. grandis trees estimated from transmittances were linearly correlated with measurements from a planimeter, over a range of leaf areas from 0.06-1.6 m 2 per tree, and were, on average, 14% lower. The lower values were probably caused by departures from the random distribution which was assumed theoretically. Because of its operational simplicity, acceptable accuracy and theoretical basis, the procedure is believed to be useful for studies of developing trees in plantations in the early stages of growth, for ecological studies in sparsely vegetated communities, and for estimates of surface area when examining spray retention and rainfall interception by isolated plants.

Three leaf area measuring techniques were compared. Although statistical considerations received priority, practical issues such as economy of time, labour and finance, were also evaluated. The electronic light interception planimeter and the squared grid method (SGM) are already in common use, while computer‐aided image analysis (CAIA) is relatively unknown for grasses. Results indicated that the planimeter is significantly (P≤0.01) less precise and accurate than the other techniques, between which no significant (P>0.05) differences were detected. Individual SGM operators, although highly consistent within themselves, differed significantly (P≤0.01) in their respective abilities to measure absolute leaf area. It was concluded that, on a practical basis, the planimeter and CAIA were likely to be the most efficient in the long term, with CAIA being more reliable. Under situations of limited finance and equipment, the SGM would seem to be a viable alternative.

The aim was to introduce a new method, the DAZ method (drainage area zonation), to quantify environmental parameters, such as bedrocks, soil type, and land use in drainage areas. The work was carried out within the framework of the Swedish project “Liming—mercury.” Two important points in the project are that there are quantifiable relationships between the character of the drainage area and the lake and that several limnological and morphometric parameters may have an impact on the Hg content in fish. The DAZ method accounts for the fact that, for example, a certain soil type does not have an even distribution in the whole drainage area. To get a simple yet relevant measure of the influence of, for example, soil type on the lake character, the drainage areas were divided into zones using a special transparent paper placed on the map. The method gives normalized values depending on: (1) distance between the object and the given lake, (2) the main direction of water flow in the drainage area, and (3) the area of the environmental parameter (for example, area of bedrock). In the DAZ method, dot counting is used for determination of area. The dot-counting method has been compared with other methods for area determination (planimeter and square counting). Dot counting is the fastest and the counting of squares the most time consuming. The statistical reliabilities of the dot method and the planimeter method were compared. The planimeter is best for large homogeneous objects. Dot counting, on the other hand, is very well suited for heterogeneous objects. The statistical certainty of area determination depends on size, heterogeneity, and form of the objects, as well as the time dedicated to the determination. A nomogram is also given, which illustrates the relationship between the number of counts, that is, the number of times the transparent dotted paper is put on the map and the dots counted, the error in the area determination, and the statistical reliability.

Conventional techniques for leaf area measurement, although non-destructive and capable of handling large samples, often produce values widely different from true leaf areas. Parameter values estimated by conventional methods can be corrected with a high degree of accuracy by using correction factors. The present investigation evaluates the significance of factors derived for two common conventional methods and ten apple cultivars. The studies were carried out between 1983 and 1989 at three locations in District Tehri Garhawl, India, on mature fruiting trees of ten commercial apple cultivars. Leaf samples were selected randomly and leaf areas determined by eight methods. The estimated parameter values were assessed statistically and compared with the true leaf area, as measured by planimeter, to test their reliability. The estimated leaf area corrected by derived constant factors in two conventional methods (leaf area determination by L x W and fresh weight) showed a high degree of accuracy and both const...

This study compared the application and reliability of 4 methods for biofilm quantification (computerized, paper-weighing, point-counting, and planimetric) in complete dentures, verifying the correlation between them. The internal surfaces of 62 complete dentures were stained (5% erythrosine) and photographed. The slides were projected on paper, and the areas (total and biofilm-covered) were outlined with a pencil. These areas were measured with an equidistant point grid (point-counting method), a digital planimeter (planimetric method), and for the paper weighing method they were cut and weighed with a precision scale. For the computerized method, ImageTool software was used. In order to perform a validation test of the methods, all of them were applied to slide projections of geometric figures with known dimensions. The correlation tests showed high correlation values (r = 0.82 to 0.99) among the methods. The validation test (ANOVA) showed no statistically significant differences among the values obtained from the measurement of figures using all four quantitative methods and the real dimensions of these geometric figures. Quantitative methods were efficient and reliable for measuring quantity of biofilm in complete dentures, and may be useful in experimental studies on the efficacy of hygiene products. The computerized method was fast and easy to perform. Este estudo comparou a aplicação e a confiabilidade de quatro métodos de quantificação de biofilme (computadorizado, pesagem de papel, contagem de pontos e planimétrico) em próteses totais, verificando a correlação entre eles. As superfícies internas de 62 próteses totais foram coradas (eritrosina a 5%) e fotografadas. Os diapositivos foram projetados em papel, e as áreas (total e com biofilme corado) foram contornadas com grafite. Estas áreas foram medidas com uma grade de pontos eqüidistantes (método de contagem de pontos), um planímetro digital (método planimétrico) e, para o método de pesagem de papel, foram recortadas e pesadas em balança de precisão. No método computadorizado, foram medidas com um software (ImageTool). Com o objetivo de realizar um teste de validação dos quatro métodos, estes foram aplicados também em diapositivos de figuras geométricas de dimensões conhecidas. Os testes de correlação mostraram altos valores de correlação (r = 0,82 a 0,99) entre os métodos. O teste de validação (ANOVA) não mostrou diferença estatisticamente significante entre as medidas reais dos desenhos geométricos e aquelas obtidas pelos quatro métodos quantitativos. Os métodos quantitativos mostraram-se eficazes e confiáveis na mensuração dos níveis de biofilme em próteses totais, podendo ser úteis em estudos experimentais da eficiência de produtos de higiene. O método computadorizado mostrou-se rápido e de fácil aplicação.

The Prytz planimeter is a simple example of a system governed by a non-holonomic constraint. It is unique among planimeters in that it measures something more subtle than area, combining the area, centroid and other moments of the region being measured, with weights depending on the length of the planimeter. As a tool for measuring area, it is most accurate for regions that are small relative to its length. The configuration space of the planimeter is a non-principal circle bundle acted on by SU(1,1), (isom. to SL(2,R)). The motion of the planimeter is realized as parallel translation for a connection on this bundle and for a connection on a principal SU(1,1)-bundle. The holonomy group is SU(1,1). As a consequence, the planimeter is an example of a system with a phase shift on the circle that is not a simple rotation. There is a qualitative difference in the holonomy when tracing large regions as opposed to small ones. Generic elements of SU(1,1) act on S^1 with two fixed points or with no fixed points. When tracing small regions, the holonomy acts without fixed points. Menzin's conjecture states (roughly) that if a planimeter of length L traces the boundary of a region with area A > pi L^2, then it exhibits an asymptotic behavior and the holonomy acts with two fixed points, one attracting and one repelling. This is obvious if the region is a disk, and intuitively plausible if the region is convex and A >> pi L^2. A proof of this conjecture is given for a special case, and the conjecture is shown to imply the isoperimetric inequality., AmS-TeX, 23 pages, 12 figures in 2 *.gif files. To appear in Reports on Mathematical Physics. Part of proceedings of Workshop on Non-holonomic Constraints in Dynamics, Univ. of Calgary, Aug. 1997

The purpose of this study was to establish intratester and intertester reliability of four methods of measuring wound surface area from transparency film tracings. Wound area measurements were obtained in 31 subjects with venous stasis ulcers. After tracing each wound on transparency film, wound area was calculated by (1) multiplying length and width measurements with a ruler, (2) placing the transparency film over graph paper and counting the squares, (3) using a planimeter, and (4) using a digitizer. Intraclass correlation coefficients (ICCs) for intratester measurements were .99 for each method. The ICC values for intertester measurements ranged from .97 to .99. The results of this study indicate that intratester and intertester wound measurements can be taken reliably with the graph paper, planimeter, and digitizer methods. The graph paper technique may be preferable in most clinical settings, because it is low in cost and easy to use.

Two systems of measuring the areas obtained from the filter paper press method (Grau & Hamm) on meat (beef) were compared: by planimeter (method A) and by optical-electronic system (Video Image Analyzer; method B). Data obtained by three operators, measuring 15 samples twice, were utilized to estimate the ‘precision’ of the two methods. The general mean area of ring zone resulting from method A was 6·69 cm 2 . Analysis of variance demonstrated a significant influence both for ‘operator’ factor and for the interaction operator-sample. Repeatability and reproducibility were 0·1706 and 0·2580, respectively. By method B the general mean area was 6·67 cm 2 . The variance among operators was significant, but lower than in the method A, and there was no interaction. The repeatability and reproducibility were 0·03055 and 0·07234, respectively. It would appear, therefore, that the optical-electronic determination is more precise than the planimetric method.

This study was conducted to determine the accuracy and repeatability of beef carcass longissimus muscle area (LMA) measurements obtained by three different methods. Longissimus muscle area for beef carcass sides (n = 100) randomly selected in a commercial packing plant was determined: 1) independently by three USDA grading supervisor experts using the grid method to obtain triplicate measurements of the same longissimus muscle (LM); 2) by three different Colorado State University personnel tracing the LMA on acetate paper and subsequently measuring the area via a polar planimeter three different times (total of 3 x 3 = 9 observations/LM); and 3) by use of two identical video image analysis (VIA) instruments making triplicate measurements for each LM using three different procedures. Video image analysis Procedure 1 required that LMA be measured by placing the camera head unit over the LM and collecting three sequential images without moving the camera head unit while carcasses were in a stationary position; Procedure 2 required measurement of LMA by placing the camera head unit over the LM and collecting three images, but removing and repositioning the camera head unit between collection of each image while carcasses were in a stationary position; and Procedure 3 required that LMA be measured by placing the camera head unit over the LM and obtaining an image while carcasses were in continuous motion (chain speed of 360 carcasses/ h) during three different circulations past the grading stand. Overall, VIA-derived LMA measurements were highly accurate for all three procedures compared with expert-gridded (R 2 = 0.92, 0.90, and 0.84 for Procedures 1, 2, and 3, respectively) and acetate/planimeter-traced (R 2 = 0.94, 0.93, and 0.86 for Procedures 1, 2, and 3, respectively) LMA measurements. Instrument LMA repeatability also was comparable to expert-gridded and acetate/planimeter-traced LMA repeatability, as the means of the absolute differences between individual measurements and the average of those same measurements per LM were 1.29, 1.35, 0.52, 0.84, and 1.87 cm 2 for expert-gridded, acetate/planimeter-traced, and VIA Procedures 1, 2, and 3, respectively. Therefore, VIA instrumentation can be used to assess beef carcass LMA in both a stationary and operational scenario with high levels of accuracy and repeatability.

The area of sway, which is believed to be one of the most important parameters reflecting standing ability, be measured by planimeter. The Japanese Equilibrium Research Association recommends that. On the other hand, the product of the maximum widths in both X and Y directions is also used, since measurement by planimeter is difficult to use clinically. This paper aims to clarify the relationship between two methods. The area measured by plani meter and the product of the maximum widths in both X and Y directions are called A and B, respectively.Statokinesigrams of 500 patients aged 5 to 80 years with eyes open and eyes closed were analyzed and the correlation between A amd B was analyzed statisticaliv.1 ) With regression analysis, the correlation coefficient of A associated with B was determined to be: r=0.953 in the group with eyes open, r=0.968 in the group with eyes closed. Relationships between A and B in both groups were statistically significant at the level of 0.001.2) The data were fitted to the following regression equation: Y=0.443X-20.47 in the group with eyes open, Y=0.441X-5.689 in the group with eyes closed. (X=B, Y=A) The regression coefficients in both groups were significant (P

We measured central corneal endothelial cell density and area from contact specular photomicrographs of ten normal and ten abnormal corneas, comparing the precision, cost, and speed of four methods: a rectangle, planimeter, digitizer, and cell sizer. The rectangle, planimeter, and digitizer gave results that differed less than 10% from each other; therefore, the three methods can be used interchangeably for clinical purposes. There are statistically significant differences among the three techniques that may be important in basic research. The cell sizer gave a rapid, less precise estimate of mean cell area and cell density. The planimeter and digitizer measured individual endothelial cell size, and the latter entered data directly into a computer that printed both a copy of the endothelial mosaic and a histogram of cell size frequency, and computed cell density and mean cell area. We make the following recommendations: Count cells in a rectangle used for routine clinical measurement. use a cell sizer for rough estimation, as in an eyebank setting. Use a computerized digitizer to study individual endothelial cell size.

SummaryThoracic and abdominal surface areas have been measured by planimeter on 340 photogrammetric somatotype photographs of 15 boys of the Harpenden Growth Study followed at regular intervals from 3 to 20 years of age. Mean distance and velocity curves are given, estimated by Patterson's method for extracting maximum information from mixed longitudinal data. Both areas showed a marked adolescent growth spurt with the age at peak coinciding with the age of peak height velocity of the same children.The correlation coefficients between thorax and abdominal surface areas rose from an average of about 0·3 at ages 5–8 to 0·5 at ages 9–12 and 0·7 at ages 13–19. Trunk index (thorax/abdomen area) fell gradually with age from 5 to 9 and thereafter remained constant.

The remarkable area measurement property of the hatchet planimeter is proved directly and easily by a series expansion. The previously known correction terms are readily generated and extended by a new analysis which now easily shows any blade misalignment to be of minor effect. This allows rationalizing the design for adjustment to give the best precision for the size of the figure. A new operating scheme, illustrated by an example, attempts to ensure accuracy at the minimum of user sophistication and calculation, to realize the hatchet planimeter’s enormous advantage in cost, mechanical simplicity and ruggedness over the Amsler planimeter. This is the background to an attempt to popularize this planimeter for rural engineering (Farthinget al 1985).

Left ventricular systolic pressure volume area (PVA) has been proposed as a reliable predictor of cardiac oxygen consumption per beat (VO2). PVA is the area in the pressure-volume (P-V) diagram that is circumscribed by the end-systolic and end-diastolic P-V relation curves and the systolic segment of the P-V loop trajectory. It represents the total mechanical energy required for the ventricle to contract, to change its wall's elastic state from end diastole to end systole, and to eject blood against afterload. PVA has so far been measured manually with a planimeter applied to the P-V diagram. To measure PVA more accurately and on line during experiments, we devised a new method of computing PVA with a digital computer. The method consists of integrating during systole the infinitesimally narrow triangular pressure volume area swept by the straight line segment connecting Vd (ventricular volume at which peak isovolumic pressure is zero) and the instantaneously counterclockwise moving P-V data point in the P-V plane, and adding a small area between the end-diastolic P-V relation curve and the line connecting Vd and the end-diastolic P-V point. This method has proved useful in our study of the relation between VO2 and PVA to evaluate the PVA's ability to predict VO2.

This note describes an improvement to a method of harmonic analysis described by F. B. Daniels. Both the original and improved methods use only a planimeter and a set of ruled grids. An approximate value of a sine or cosine coefficient is obtained from a single tracing of the plotted function and the accuracy may be improved by means of correction terms from the higher-order harmonics. In the improved method described here the number and importance of the correction terms is much less than in Daniels's original method.

The need to measure accurately the area of several thousand apple leaves in connection with a study of the deposit of spray residues led to a search of existing methods of leaf area measurement. The several methods described in the literature failed to satisfy the requirements, inasmuch as accuracy in area measurements was apparently to be secured only by methods too lengthy to be of use in this study. Existing methods for measuring leaf areas include the following: (1) Measurement of the leaves along their axes, the area obtained by multiplying these figures being corrected by a factor; (2) planimeter measurements; (3) tracing or otherwise transferring the leaf outline to paper of known weight per unit of area and later determining the area of the tracings by their weight; (4) leaf -punch methods, in which definite areas of the leaf surface are removed by a punch or die. The first of these methods is not sufficiently accurate, since variations in leaf shape among individual leaves of the same species is sufficient to introduce gross errors into the calculation. The second and third methods are extremely time-consuming, depend largely for their accuracy on the skill and dexterity of the person using them, and are adapted only for measuring the areas of small numbers of leaves. Circles or other geometric figures cut from the leaf surface with a punch or die are subject to errors arising from the obvious fact that the leaf presents neither a uniform surface nor an interior structure free from gross tissue differentiation. The use of the photoelectric cell in a variety of ways in recent years led the writer to consider the possibility of such a device for measuring leaf areas, inasmuch as the area would be a direct function of the amount of light intercepted if the leaf were placed in the path of a beam of light. While a device was being perfected, a short news article appeared describing a similar apparatus, built by Withrow, and it was learned that a paper describing a similar apparatus had been presented at the Boston meeting of the American Society of Plant Physiologists. Definite information concerning the construction of this apparatus could not be secured, however, and the present apparatus has been developed independently, and has been used satisfactorily for the past season. 1 Publication authorized by the Director of the Pennsylvania Agricultural Experiment Station, as Technical Paper no. 677.

A new method for finding the center of an area and a practical application to stability calculations is given. The procedure presented makes possible collection of data for cross curves with a minimum of labor and apparatus. The paper contains an ideal and a practical theorem along with mathematical proof for acceptance of the method in calculations for GZ. Worked examples are illustrated for geometric forms and hull sections. Notes for development of mathematical devices are included.

SUMMARY THE PROBLEM OF finding Fourier coefficients can be solved readily if the equation of the curve for which the coefficients are desired is known. Usually the equation is not known if the curve is obtained from experimental data. Therefore, a method must be found which will give the coefficients from the curve at selected points on the curve. It is shown that any method which is based on fitting a polynomial to the data of a curve can introduce errors that might be significant for any particular problem. The method used for finding the coefficients is based on the fundamental definitions of the Fourier coefficients and involves integration under derived curves for each harmonic for the area. The coefficient is a function of the mean ordinate which by a neat manipulation of Simpson's Rule is readily obtained. For those who prefer, the area can be obtained by use of planimeter and the coefficients determined. Both methods give engineering order accuracy which is dependent on the faithfulness of the representation of the area using Simpson's Rule or the mechanical fineness of the planimeter.

This paper deals with the nature of the sampling errors which may occur in measurement of area by a square pattern 'dot planimeter'. The important conclusion is that the relative error of measurement is small if the count of points is of the order of 100 per parcel. The authors recommend the use of different sizes of point pattern for the measurement of different sizes of parcel, rather than the use of a single overlay for the measurement of every parcel on a given map. The theoretical work is supported by some results of measurements made on the McKay Pattern Map using the MK Area Calculator.

The leaf-area indices (LAI) of simulated swards of three populations of Festuca arundinacea Schreb. were estimated by use of an inclined point quadrat and an air-flow planimeter. Both for comparisons of leaf areas before defoliation, and for comparisons of leaf areas removed by defoliation, very highly significant relationships were found between estimates by the two methods. In five out of six cases the airflow-planimeter estimates of leaf area became greater than those from the inclined point quadrat as sward leaf area increased. It is suggested that the major factor responsible for departure from complete agreement between the methods is a difference in leaf areas actually measured by the two methods; in addition, there was some indication of operator error with the inclined point quadrat. The results indicated that these factors were not greatly influenced by leaf canopy arrangement.

Automatic planimeters described in the literature have, with one exception (Winter et al., 1956), been analogue devices measuring some continuously variable quantity (light interception, air flow) related to area. This system is simple in principle but elaborate precautions are required to eliminate errors arising from variations in mains voltage, non-linearity and fatigue of photo cells, stray light, contamination by mud from the leaves, non-uniformity of the light beam, and variations in leaf transmission. Some of these sources of errors are avoided by using air instead of light. Unfortunately, the airflow planimeter (Jenkins, 1959) is unsuitable for estimating large areas because of the great air flow required and because the null adjustment limits the speed of operation. In crop studies the total area of a number of leaves in a sample is usually of more interest than the individual values. Unfortunately, it is impossible to make an analogue device give the total of a series of determinations unless the information is first converted into digital form. A digital instrument has greater potentialities ; such a device would count the number of elements (unit areas) in the leaf, or series of leaves, and register the result. As the relation between counts and leaf area depends only on the size of the element, which is fixed by the dimensions of the instrument and the accuracy of the counting, it is independent of the sources of error mentioned above. These advantages are offset by the increased complexity of the system and it was decided to construct a digital planimeter suitable for sugar-beet as a test of the method. Manual methods based on this principle were described by Winter et al. (*956).

This paper presents a method of determining by means of a polar planimeter the probability of falling inside a plane area when the distribution of “hits” in the plane of this area is a normal bivariate distribution centered at some fixed point in the plane. The method presented is especially useful when the area involved is irregular.

Saline extracts of minced normal canine lungs varying in sample weight from 0.25 to 3.0 gm. were prepared and the areas of hysteresis loops inscribed by the pneumatic surfactometer determined by planimeter. Using the variables of sample sizes and cycle times of 1.5, 3, 6, and 9 minutes a multiple linear regression analysis was performed to generate a three dimensional fitted polynomial surface. Maximum loop area differences between samples sizes were observed at a cycle time of 1.5 minutes and sample size of 2.0 gm. Sequential dilutions of a 2.0-gm. sample cycled at two minutes showed linear correlation with decreasing areas of the hysteresis loops. Superimposition of the dilution points on the computed polynomial surface showed good correlation for concentrations other than 50%. Quantitation of surface activity on the basis of hysteresis loop area is feasible as a rapid and convenient technic for study of whole lung samples.

1. The area of eye muscle cross-section of beef carcasses may be accurately measured by tracing the boundary and measuring the tracing with a planimeter. Taking a single area measurement from each of duplicate tracings increases the accuracy by some 30%. If a planimeter is not available, the area may be estimated by superimposing a grid on the tracing and counting squares; although this method is some 25% less accurate than the planimeter method it is sufficiently repeatable for experimental use.2. Area estimated by combinations of linear measurements is highly repeatable, but predicts true area with insufficient accuracy for experimental use. The standard error of prediction is about 7% of the mean area. Regression equations relating planimeter area and combinations of measurements for various cuts and animals are given.

An indirect and less time consuming method to estimate synchrony ratios in EEGs from voltage is described. The relationship between the voltages of referential and simultaneous bipolar leads is used to develop a regression equation which allows the calculation of the synchrony ratio. A nomogram is constructed to simplify the procedure. For determining average voltage, we used a relatively inexpensive planimeter, as previously described. Any other method to find the average voltage with sufficient accuracy would be suitable too.

The video differential planimeter is an instrument which measures variations in the projected area of any remote object with the aid of a flying spot scanner or television camera system. The composite video signal, caused by the scanning of the object and its contrasting background, is shaped to yield a sequence of constant amplitude rectangular pulses that are negative going during a scan of the object, and positive going at all other times. The average of this sequence of pulses is obtained from a point on a bleeder resistance returned to the negative supply, and is fed into an integrator. The net integration voltage is read off and the integrator is returned to zero at the end of each field. If the object's projected area remains fixed, the sum of the positive and negative pulse areas entering the integrator will be constant. Hence, the change in integration voltage from field to field will be zero. If the object's projected area varies, the sum of the positive and negative pulses entering the integrator will change, and the readout voltage of the integrator will vary proportionately. The V.D.P. is applied here to the measurement of the vibration of a speaker cone, and to the measurement of the human respiration and plethysmogram.