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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

Photovoltaic (PV) panel was used to develop a simple and practical leaf area meter. Components of the developed PV leaf area meter include a PV panel as sensor, a wooden cabinet as enclosure, a flashlight as light source, and a commercial digital multimeter for voltage measurement. The principle of projected area measurement is the voltage generated by the PV panel varies directly with sample area, when corresponding panel surface is exposed to incident radiation. The PV leaf area meter performance was evaluated using cardboard cutouts of various geometrical shapes of known areas and the voltage generated had good correlation (r = 0.9911) with sample areas. Linear fits adequately modeled the areas from non-dimensional voltages (R2 > 0.98). Leaf samples from mango, sapodilla, guava, custard apple, and cotton covering a wide array of natural shapes were tested and compared among the existing graphical, scanner-based electronic leaf area meter, and digital planimeter methods. Digital planimeter produced bett...

We show how the planimeter is used for the estimation area. For example, it could be used for measuring the area of trees’ leaves, the size of a city or the area of a planar section of a human’s organ cut. Suponga que usted tiene un mapa del lago Arenal y desea medir su superficie. Si usted tiene la información que brinda la escala del mapa, podría usar un magnífico aparato llamado planímetro para determinar el área del lago. El planímetro es un aparato de ingeniería usado para medir el área de una región plana acotada por una curva cerrada. Por ejemplo, se podría usar un planímetro para medir el área de hojas de árboles, el tamaño de una ciudad o el área de una sección planar del corte de un órgano humano. En este artículo mostraremos como funciona un planímetro. Utilizaremos el Teorema de Green para explicar la teoría matemática detrás del concepto planímetro.

According to the Merriam-Webster dictionary, a planimeter is `an instrument for measuring the area of a plane figure by tracing its boundary line'. Even without knowing how a planimeter works, it is clear from the definition that the idea behind it is that one can compute the area of a figure just by `walking' on the boundary. For someone who has taken calculus, this immediately suggests Green's Theorem. The aim of this note is to clarify for others why this principle works. We do this by using points of view from linear algebra to elementary plane geometry in order to obtain an intuitive justification for Green's Theorem. As an application, we show how the reader can easily construct a `software planimeter'. The idea behind this is certainly not original; the formula for the area of a polygon used in this process (see Theorem 1.2 and Remark 1.5 (3)) is surely folklore for experienced programmers (1). What we would like to emphasize is, on the one hand, the beautiful interplay between various branches of mathematics and elementary computer graphics in this case. On the other hand, since our application is (in our view) particularly fun to work with, we hope that this approach can be successfully used in class as an aid in teaching Green's Theorem, or in a calculus lab, or even to show younger and more inexperienced students that sometimes deep mathematical results can be surprisingly accessible and entertaining.

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.

The purpose of this study was to evaluate the validity and reliability of coating methods (plaster bandage, inelastic tape, and the alginate method) and an indirect method using a three dimensional (3D) whole body scanner. The surface area of geometric solids was measured five times using the three coating methods, and analyzed through 2D scanning and a planimeter. Second, to examine the accuracy of the alginate method more closely, the surface areas of boards with different surface properties at various inclines were measured and compared. Lastly, the surface area of a human arm was measured using the three coating methods and a 3D scanning method. The results are as follows: 1) The three coating methods were statistically valid and reliable for measuring the surface area of geometric solids. 2) The planimeter was rejected because the mean error was bigger than in 2D scanning. 3) The method showing the least error was the inelastic tape method, but that method was not recommended because it was too tiresome and laborious. 4) The greater the curvature and smaller the size of a geometric solid, the greater the error. 5) In measuring surface area using the alginate method, the objects that were smoother and had steeper angles showed a greater surface area: however, the mean error was less than 1%. 6) In measuring a human arm, the surface area obtained by 3D scanning was less than any other surface area obtained in the three coating methods, because the 3D scanner could not discern the armpit and fingers. In conclusion, the method using alginate was statistically valid and reliable in the measuring of surface area both of geometric solids and real human skin.

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.

Objectives This study tested the hypothesis that the impact of a stenotic aortic valve depends not only on the cross-sectional area of its limiting orifice but also on three-dimensional (3D) valve geometry. Background Valve shape can potentially affect the hemodynamic impact of aortic stenosis by altering the ratio of effective to anatomic orifice area (the coefficient of orifice contraction [Cc]). For a given flow rate and anatomic area, a lower Cc increases velocity and pressure gradient. This effect has been recognized in mitral stenosis but assumed to be absent in aortic stenosis (constant Cc of 1 in the Gorlin equation). Methods In order to study this effect with actual valve shapes in patients, 3D echocardiography was used to reconstruct a typical spectrum of stenotic aortic valve geometrics from doming to flat. Three different shapes were reproduced as actual models by stereolithography (computerized laser polymerization) with orifice areas of 0.5, 0.75, and 1.0 cm2 (total of nine valves) and studied with physiologic flows. To determine whether valve shape actually influences hemodynamics in the clinical setting, we also related Cc (= continuity/planimeter areas) to stenotic aortic valve shape in 35 patients with high-quality echocardiograms. Results In the patient-derived 3D models, Cc varied prominently with valve shape, and was largest for long, tapered domes that allow more gradual flow convergence compared with more steeply converging flat valves (0.85 to 0.90 vs. 0.71 to 0.76). These variations translated into differences of up to 40% in pressure drop for the same anatomic area and flow rate, with corresponding variations in Gorlin (effective) area relative to anatomic values. In patients, Cc was significantly lower for flat versus doming bicuspid valves (0.73 ± 0.14 vs. 0.94 ± 0.14, p Conclusions Three-dimensional valve shape is an important determinant of pressure loss in patients with aortic stenosis, with smaller effective areas and higher pressure gradients for flatter valves. This effect can translate into clinically important differences between planimeter and effective valve areas (continuity or Gorlin). Therefore, valve shape provides additional information beyond the planimeter orifice area in determining the impact of valvular aortic stenosis on patient hemodynamics.

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.

A method was developed for assessing the three dimensional (3-D) geometric structure of white clover canopies. 3-D co-ordinates of pre-defined points on leaves, petioles and stolons were measured using a Polhemus Fastrak electromagnetic 3-D digitiser. Digitising progressed downwards from the top of the canopy and plant parts were removed after they have been digitised. Leaflets were treated as four quarter-ellipses, and petiole and stolons were treated as cylinders. Leaf dimensions and areas calculated from 3-D co-ordinates were within about 5% and 20% of direct measurements made with a ruler and a planimeter, respectively. Special software and freeware POV-Ray were used to reconstruct a virtual canopy from digitiser records and to calculate canopy characteristics such as leaf area index (LAI), petiole intersection area, and profiles of leaflet areas and inclinations with height. It took between 3 and 7 h to digitise 10 × 10 cm stands of clover and the resulting information was considerably more comprehensive and accurate than could have been obtained by the alternative ‘point quadrat’ or ‘stratified clipping’ methods.

図形の面積を求めるソフトウェアを提示する。面積を求めたい図形はマウスを使って, ディスプレイ画面に取り込む。図形入力はマウスを使うことにするため, 精度の面ではやや劣るが, パソコンの標準入力装置であり, 簡便に使用できる利点を持つ。プログラム言語には初心者にとって理解しやすいN88BASICを用いた。このため中学校におけるプログラミングの学習にはよい教材となりうると考えている。, A mouse is a convenient device which is attached to the personal computer system. A mouse is primarily the device for the sake of indicating a point on the computer display. But we used a mouse as an input device for capturing the geometric figure on the display. We made the computer program with the N88BASIC language which can calculater the area of this plane geometry enclosed with a curved line captured on the display. We can compute the distance between two points in a map by use of this program also.

Measurement or estimation of leaf area is essential for simulation of light interception and photosynthate production. Leaf shape is an important factor in describing how leaf area is distributed in the canopy. When defined mathematically, leaf shape can be used to calculate leaf area of individual leaves as well as how leaf area varies along the length of the leaf. The objective of this study was to evaluate several methods used to describe leaf shape (the variation in leaf width with distance from the ligule or stem) and to analyze variations in shape coefficients. Measurements of leaf width every 10 cm along fully expanded leaves were made over a number of years, sites, plant densities, and nitrogen treatments with normal, leafy, and reduced-stature hybrids. These measurements were fitted to a number of polynomial equations which related leaf width to distance from the ligule. Leaf area was calculated by integrating these equations. In all, 10 methods were used to calculate areas of individual leaves, but one method, based on a second order polynomial equation which could easily be integrated for total leaf area or area along the leaf, was chosen as a standard. All other methods were compared with this standard and leaf area estimates were found to be similar (R 2 > 0.98). Planimeter measurements of individual leaf area also compared well with estimates using the standard method (R 2 = 0.96) but planimeter measurements had more scatter than estimated values. The most useful equation was the second order polynomial with two dimensionless shape coefficients using maximum leaf width and total length. Integrating this equation produced the well known length × maximum width × alpha equation for calculating leaf area where alpha was 0.743 for all hybrids and 0.734 for normal hybrids. A method was developed to use this equation for calculating leaf area as a function of leaf length.

The objective of this study was to examine the feasibility of using a semiautomated computer-vision system to quantify the percentage of voids in mineral aggregates (VMA%) of bituminous mixtures. The system used a hybrid procedure which utilized a digital image analysis scheme and a planimeter surveying instrument. Thirty-nine Marshall specimens were prepared using limestone and gravel aggregates. Values of VMA% were obtained using the ASTM conventional procedure and the computer-vision procedure. To compute VMA% using the computer-vision procedure, normal case photography with uniform scale images was used to map horizontal and vertical cross sections of Marshall specimens. Image domain measurements were corrected for distortion. Spatial filters and image processing operations were used to enhance the aggregate edges. Experimental results showed slight variations between VMA% computed using conventional and the computer-vision procedures. The average differences of VMA% between conventional and the computer-vision procedures were 0.81% and 0.006% for gravel and limestone specimens, respectively. Measurements of VMA% for limestone mixtures were more precise than those for gravel mixtures because of the angular edge shape of limestone particles. Variations in VMA% were due to the anisotropic properties of asphalt mixtures, aggregate distribution in the asphalt mixture, and different shapes of aggregates. Using the computer-vision-based technique, VMA% of horizontal and vertical cross sections were 50% consistent. The existence of fine aggregate in the asphalt mixture affected the accuracy potential of the developed system because a low-resolution camera was used. Increasing the camera resolution and automating the area computation of aggregate are expected to enhance the potential accuracy of the procedure. The proposed method for VMA quantification is anticipated to improve field quality control of hot-mix asphalt (HMA). The use of computer-vision technology with bituminous mixtures can open the doors to a wide variety of applications.Key words: bituminous mixtures, voids in mineral aggregate, computer vision, automation, image processing.

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

In-field estimates of green leaf area index for treatments with varying amounts of yellow rust (Puccinia striiformis (Westend.)) were directly proportional to laboratory measured green leaf area index (R2 = 0.75). The field technique depended on shoot counts and a leaf form factor (F = 0.83) which was derived from 20 varieties of winter wheat by relating the product of their leaf lengths and widths to leaf areas measured by a planimeter (R2 = 0.95). In two experiments at ADAS Terrington, UK, on the susceptible winter wheat variety Slejpner, epidemics of yellow rust ranged from nil to severe with 60 (1994) and 52 (1995) different combinations of fungicide dose and timing. Assessments of disease severity (%) integrated as the area under the disease progress curve accounted for yield differences within each season, but the relationship differed markedly between seasons. In-field assessments of green leaf area index integrated over time, or healthy area duration, showed a curvilinear relationship with grain yield (1994, R2 = 0.63; 1995, R2 = 0.73), but any healthy area duration value in the brighter year of 1995 related to larger yields than the equivalent value in 1994. Intercepted radiation by green leaf tissue accumulated after flowering (20 June in both years), estimated through the Beer’s Law analogy from field-measured green leaf area index and total incident radiation (i.e., healthy area absorption), accounted for more variation in grain yield (1994, R2 = 0.80; 1995, R2 = 0.92). There was no seasonal difference in the conversion coefficient between grain dry matter and the amount of incident radiation absorbed by green leaf tissue (1.4 g/MJ) but the intercepts of the relationships were sensitive to the date from which integration began. It is suggested that in-field green leaf area index assessments, interpreted through a simple model which provides estimates of differences in intercepted light energy, may prove useful in the analysis of experiments on disease control. © 1997 Elsevier Science B.V.

This work describes a dedicated software which detects and characterizes disease lesions on leaves to provide data on the number and type of lesions and the percentage of leaf area diseased (severity). The software, written in C, can be used with a standard computer in combination with a colour CCD camera and a frame grabber for image acquisition. The usefulness and adaptability of the software was evaluated using two foliar diseases, Alternaria blight of sunflower and oat leaf rust (Puccinia coronata f.sp. avenue), which differ in symptoms. Using image segmentation and classification techniques, the software discriminated disease symptoms from the healthy leaf area. The number and size of lesions and severity, obtained using the image processing software, were compared with those calculated using a software planimeter or visual assessment. Significant linear relationships between planimeter and the imaging software were obtained for lesion number and severity in oat leaf rust and for severity in sunflower blight. Artefacts, mistakenly classified as blight lesions by the imaging software resulted in an over-estimation of the number of lesions. Future research is aimed at improving accuracy through better illumination during image capture. A dedicated, compact and portable hardware is currently being developed for field use as a self-contained device for disease assessment.

The electromagnetic planimeter is a non-disturbing detector which allows, by magnetic flux measurement, determination of the area enclosed by the average current line of an electric arc in a three-dimensional configuration. In the vicinity of industrial devices such as circuit breakers, there appear induced currents and ferromagnetic effects which disturb the flux measurement. The effect of the induced currents is to delay the measured magnetic flux, which is no longer zero when the current is zero. A theoretical model of the induced current is provided which yields a numerical method by which to compensate that delay and allows one to retrieve the flux due to arc current.

On mental maps, at all scales, there is a tendency to exaggerate the size of the home area. To see whether there was a home continent exaggeration on sketch maps of the world, we used a subset of 438 maps from a world wide study of mental maps of the world. The subsample consisted of 20 maps from each of 22 sites, selected to include locations within each continent and dispersion latitudinally and longitudinally. On each map, the areas of the continent were calculated by means of a Numonics electronic planimeter attached to a computer. We compared the proportion of the total areas devoted to each continent to the actual proportions. Thus, we determined whether each contient tended to be exaggerated or diminished in size. The home continent was generally exaggerated. In addition, two unforeseen results were that Europe is always exaggerated, and Africa always diminished in size.

OZET: Bu calismanin amaci nazofarengeal hava yolu blokaji sonucu gelisen agizdan solunum sendromunda adenoidektomi endikasyonu konulmasinda sefalometrik analizin degerini orta ya koymaktir. Arastirmamiz, adenoidektomi oncesi ve sonrasi 10 bireyden elde edilen 20 lateral sefalogram uzerinde yurutulmustur. Sefalometrik degerlendirmede; hava yolu orani, AD1-PNS, AD2-PNS ve Ptv-AD mesafeleri olculmus ve normlar ile karsilastirilmistir. Hava yolu oraru planimetre ve bilgisayar yardimi ile hesaplanmistir. Postoperatif olcumlerde adenoid blokajin ortadan kalktigi ve bulgularimizin Michigan Universitesi tarafindan saptanan normlarla uyum icerisinde oldugu saptanmistir

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.

Differences in the proportion of the breast occupied by mammographic densities have been shown to be associated with differences in breast cancer risk. However, estimation of these densities by radiologists may be subject to error, and it is likely that quantitative measurement will reduce misclassification of densities and strengthen their association with risk of breast cancer. The objective of this study was to compare the extent of mammographic densities estimated subjectively by an experienced radiologist with the measured extent of densities using a digital planimeter. A total of 225 sets of mammograms from women aged 40-49 years and enrolled in the Canadian National Breast Screening Study (NBSS) were selected. The extent of the radiological densities was estimated visually by one radiologist. Independently, the total area of the breast and the areas of density were traced and measured using a digital planimeter. Visual estimations and measurements of mammographic densities were then compared to determine the extent of agreement between the two methods. In general, the two methods showed good agreement (kappa = 0.78). The measured area of mammographic densities tended to be slightly greater than the radiologist's estimations. Both methods were highly reproducible (radiologist-dependent method, kappa = 0.89; quantitative method, r = 0.95, P = 0.0001). Our results indicate that measurement of the area of mammographic density using a quantitative method is reliable, and correlates well with assessment by an experienced radiologist. The method may be useful for identifying women at increased risk of breast cancer.

The postnatal growth of the maxillary sinus was analyzed in 20 male and 20 female skulls of orang-utan (Pongo satyrus borneensis) in 5 age steps. Coronal CT scans were carried out of all skulls using a computed tomograph Siemens SOMATOM DR. The distances between the CT scans were always 4 mm. The outline of the maxillary sinus was surrounded on the CT scans with a planimeter and then the volumes were calculated. Using a growth model introduced by Fanghänel (1974), growth functions for the volume measurements for male and female animals were calculated separately. The growth curves showed a particular course, which was characterized by a quick rise until the age of 15 years. After the age of 20 years the curves for females orang-utan became gradually flat. At the age of 21 to 23 years the confidence intervals of the growth curves for male and female orang-utan began to drift apart, indicating the appearance of a sexual dimorphism. Using the basicranial length as an indicator of skull size, it becomes evident, that the sexual difference in the maxillary sinus' volume is probably based on the fact, that the maxillary sinus' volume of the male orang-utan increases further on following a common growth pattern.

PURPOSE To determine the effects of single radial or horizontal suture placement in 2-step clear corneal incision (CCI) wound apposition and permeability to particles of India ink. METHODS Five fresh human globes were included. Two 25-gauge needles connected to a saline solution bag and to a digital manometer were inserted through the limbus, 120 degrees apart from each other. Four 2-step CCIs (2.75 mm wide and 3 mm length) were constructed in each cornea. Incisions were divided into 3 groups: single radial suture (SRS), single horizontal suture (SHS), and unsutured group. Optical coherence tomography (OCT) was performed before and after suture placement. With a preset 10 mm Hg intraocular pressure (IOP), India ink was applied to the incision site and a standardized sudden IOP fluctuation was induced. OCT and superficial images were recorded before and after suture placement. India ink inflow and internal and external CCI gapping were outlined and measured by planimeter. RESULTS The area and linear distance of India ink inflow after pressure challenge in all study groups were higher when compared with pre-pressure measurements; however, this increase was significant in the SRS and SHS groups (P < 0.05). Additionally, SRS placement significantly increased inner wound gapping (P = 0.018), and SHS significantly widened outer wound gape (P = 0.02). CONCLUSIONS Well-constructed unsutured 2-step CCI seems to be more efficient at preventing bacterial-sized particles inflow during sudden changes in IOP, and it seems to offer better wound apposition as assessed by OCT.

The development of the human medial superior olivary nucleus was studied in serial sections of 10 fetuses at 12-35 weeks of gestation (WG), an infant at 2 months of age and an adult of 63 years using an electronic planimeter with a computer. Morphometric analysis suggested that the development of the human medial superior olivary nucleus accelerates between 16 and 21 WG in terms of columnar lengths and volumes, neuronal sizes and circularity ratios, while it matures gradually in terms of the amount of Nissl bodies.

OZET: Arastirmamizin amaci, adenoidektomi operasyonunun iskeletsel ve dental yapilara olan etkisini longitudinal olarak incelemektir. Calismamiz, nazal obstruksiyon nedeniyle adenoidektomi endikasyonu konmus 26 birey uzerinde gerceklestirilmistir. Bu bireylerin 13'u birinci yil icerisinde adenoidektomi operasyonu gecirmis, 13'u ise bu ameliyati cesitli nedenlerle yaptiramamislardir. Adenoidektomi operasyonu olan 13 birey tedavi grubunu, geriye kalan non-opere 13 birey ise kontrol grubunu olusturmuslardir. 6 yil sonra tekrar cagrilan bireylerden lateral ve antero-posterior sefalogramlar ile alci modeller elde edilmistir. Lateral sefalogramlar uzerinde baslangicta oldugu gibi, nazal direnc olcumleri planimetrik olarak hesaplanmistir. Ayrica lateral ve antero-posterior sefalogramlar uzerinde iskeletsel ve dental olusumlarin olcumleri yapilmistir. Alci modellerde ise dental degisiklikler incelenmistir. Elde edilen olcumler istatistiksel olarak degerlendirilmistir. Sonuc olarak, nazal obstruksiyonlu bireylerde...

A controversial point in the management of patients undergoing anterior cervical discectomy is whether an interbody bone graft should be used. Proponents of interbody grafting claim that without a graft, the disc height and the area of the foramina at that level will decrease postoperatively with the potential for persistent symptoms and/or the development of a radiculopathy. Using a two-dimensional digital planimeter, we measured the cross-sectional area (cm2) of cervical foramina on preoperative and postoperative oblique films in patients undergoing anterior cervical discectomy. Group A patients underwent the insertion of an interbody graft after the discectomy; Group B patients did not. Our results indicate that in all the patients in Group A, there was a statistically significant increase in the area of the foramina (P 0.8). There was no statistically significant difference (P = 1.000) in the outcome between the two groups. From an anatomical standpoint, our data support the insertion of an interbody graft if the surgeon wishes to increase the area of the foramen. However, the overall magnitude of change is not significant, which may be a factor in why the clinical outcome is similar in both groups.

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.

OZET: Calismamizda, Angle sinif III malokluzyonlu, erken karma dentisyondaki bireylerde Frankel 3 apareyinin Nasal Direnc'e olan etkisi incelenmistir. Arastirmamizda 7'si kiz, 13'u erkek toplam 20 birey tedavi grubunu, 7'si kiz, 7'si erkek toplam 14 ise kontrol grubunu olusturmuslardir. Her iki grubu olusturan bireylerden, tedavi oncesi ve sonrasi alinan lateral sefalometrik filmier uzerinden planimetrik olcumler elde edilmistir. Sonucta, Frankel 3 apareyinin uygulandigi bireylerde Nasal direnc'in azalmis oldugu, “Mann Whitney U” testi ile, dil konumunun ve mandibulanin etkilenmedigi ise, “Student t” testi ile saptanmistir.

The purpose of this study was to investigate whether there are relationships between the cross-sectional surface area (CSSA) of the lips and the sagittal structure of the skeletal parts of the face and the dentition in the midsagittal plane and whether the sagittal structure of the face and the dentition is related to the class of malocclusion. The CSSA of the upper and lower lip was measured with a planimeter on the lateral cephalograms of 156 patients before their orthodontic treatment with a closed lip relation in rest. They were divided into 18 groups according to their age, sex, and Angle classification. The Quick Ceph program (Orthodontic Processing, Chula Vista, Calif.) was used to digitize and analyze 23 dental and skeletal parameters. The parameters were tested by an analysis variance to show differences between the three classes of malocclusion. The regression analysis was used to look for relations between the CSSA and the skeletal or dental parameters. It appeared that the mean and the variance of the lip line and the inclination and the sagittal position of the incisors are significantly different between the three classes of malocclusion ( p p p p p p p

An integration technique for EPR spectra working similar to a planimeter is presented. A brief description of the mathematical background and of the program is given. By means of a few examples it is shown how this technique works and what has to be considered applying it to experimental EPR spectra.

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.

The use of stone surface area measurements obtained from standard radiographs provides a more accurate and reproducible assessment of stone burden when reporting results and treatment recommendations for staghorn calculi. Techniques for determining stone surface area include use of graph paper, planimeter or computerized image analysis. The use of graph paper is inefficient while planimeters suffer from significant variation for areas less than 500 mm.2 (more than 5%). Computer image analysis is accurate, rapid and easiest to perform. Software programs compatible with microcomputers are readily available making assessment of stone surface area practical and inexpensive. Stone surface area showed close correlation to stone volume as measured by 3-dimensional computerized tomography (correlation coefficient 0.84, p = 0.005). Stone surface area determination enables more accurate reporting of treatment results and, thus, recommendations based upon stone burden. Comparison of data between institutions becomes more meaningful if stone surface area is used. Stone surface area also provides a useful basis to study and compare trends of treatment within a single institution.

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.

A microcomputer based technique of area measurement is described. The method measures the polar co-ordinates of points along the perimeter of the area and uses simple trigonometry to compute the total area. The microcomputer does this job very swiftly and displays the result almost instantaneously. All the sources of error in the method are statistical in nature and are expected to give a very low average error. Apart from the higher accuracy and an excellent resolution the method has the advantages of simplicity of working and high speed of response.

The aim of this research was to determine effect of genotype (Holstein, Simmental and their crossbreeds), sex and slaughter weight groups (SW1= 150-160 kg and SW2=190-200 kg) on veal longissimus muscle area (LMA). Between the12th and the13th rib, two ultrasound LMA (ULMA) images were taken from each animal and carcass LMA (CLMA) traced on transparent foil was measured by planimeter. For both measures, Simmental calves had larger LMA than Holstein (P

The purpose of this study was to evaluate apical extrusion of root canal content using ultrasonic and hand instrumentation. Forty-nine tooth models were fabricated with clear resin. Each model contained a canal in the center. Each tooth model was mounted in a plastic cube (1 x 1 x 2 cm) with white dental plaster so that the coronal 2-3 mm of the model was exposed for instrumentation. Methylene blue dye with glycerin was used as a marker for root canal content. The study consisted of three groups. In group I, Enac ultrasonic instrumentation was used 1 mm from the apex; in group II, Enac ultrasonic instrumentation was used 3 mm from the apex; in group III, K files were used with a push-pull instrumentation technique, 1 mm from the apex. After instrumentation the resin models were extracted and the plaster blocks were sectioned through the long axis of the models. Photographs were made of the area of apical leakage and the amount of dye penetration was measured using a planimeter. There were no differences between hand instrumentation and both ultrasonic groups. At p less than 0.05, ultrasonic instrumentation 3 mm from the apex leaked significantly more than the ultrasonic instrumentation 1 mm from the apex.

OZET: Bu calisma lateral sefalometrik grafiler uzerinde, hipofiz bezini icinde barindiran sella turcica'nin alanini iki degisik yontemle belirleyerek, bu yontemleri birbirleri ile karsilastirmak gayesiyle yapildi. Bu amacla, 16 erkek, 14 bayana ait toplam 30 radyografi uzerinde sella turcica'nin alani planimetre ve milimetrik kareli kâgit kullanmak suretiyle iki arastirici tarafindan ayri ayri belirlendi. 2 hafta sonra tum cizim ve olcumler iki arastirici tarafindan tekrarlandi. Herbir arastiricinin soz konusu yontemlere iliskin 1. ve 2. olcumleri arasinda istatistiksel olarak onemli farklilik bulunamadi. Arastiricilarin planimetre ile belirledikleri degerlerin birbirleri ile ve kareli kagit yontemi ile belirledikleri degerlerin birbirleri ile karsilastirilmasinda onemli farklilik tesbit edilemezken, arastirici farki gozetmeksizin planimetre ile belirlenen ortak degerlerin, kareli kâgitla belirlenen ortak degerlerle karsilastirilmasinda istatistiksel olarak onemli fark bulundu.

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 genus Hypericum has attracted scientific interest for recent years, since it is a source of a variety of compounds including hypericin. The present study was conducted out to develop leaf area prediction models for some Hypericum species containing hypericin, namely H. pruinatum, H. perfoliatum, H. aviculariifolium subsp. depilatum var. depilatum (endemic), H. montanum, H. montbretii, H. linarioides, H. triquetrifolium, H. bithynicum and H. perforatum growing wild in Northern Turkey. Lamina width, length and leaf area were measured without destroying 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 formulised as LA = (a) + (b1 × L) + [b2 × (L × W)] + (b3 × L2) + (b4 × W2) + [b5 × (L × W2] + [b 6 × (L2 × W)] + [b7 × (L 2 + W2)] where LA is leaf area, Wis leaf width, L is leaf length and a, b1, b2, b3, b4, b 5, b6, and b7 are coefficients. R2 values varied with species from 0.80 in H. aviculariifolium subsp. depilatum var. depilatum to 0.97 in H. pruinatum. All R2 values and standard errors were found to be significant at the p < 0.001 level. © 2008 Akadémiai Kiadó.

The evolution of the area of a deformable current loop is measured from the magnetic flux collected by a coil and the current flowing in the loop. This planimetry method is non-intrusive, and its application to an arc running on parallel rails gives results that are easy to interpret.

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...

Clay tablets from Mesopotamia and papyri from Egypt provide evidence that work with area has been part of mathematics since its early history. These Ancients knew how to find areas of squares, circles, triangles, trapezoids, and a number of other shapes for which we no longer have names. Like many other physical quantities, we usually measure area indirectly. That is, we measure something else, such as lengths, a radius, or angles. Then we do some calculations to find area based on appropriate formulas. The object determines the formula we use and the measurements we make. There are a number of methods to measure volumes. Some of them are indirect, as for areas, involving linear and angular measurements and the use of formulas. Interestingly, some of them are more direct. One example is the measurement of liquid when cooking, using calibrated measuring cups. Similarly, the volume of a non-porous solid can be measured by submerging it in water to see how much water it displaces (it helps if the solid doesn’t float). Many instruments are cleverly designed devices that convert a value we want to measure into some scale that we can read directly. For example, thermometers (the bulb type, not the digital ones) convert the volume of the liquid (this used to be mercury, but now it is usually tinted alcohol) in the bulb into a length. When the liquid expands or contracts with the temperature, the calibrations along the tube let us read the temperature that corresponds to volume. Our goal is to learn how to make and use a simple device called a planimeter that measures area more directly without having to measure lengths or angles or to make any calculations. A second goal is to understand the mathematics behind how planimeters work.

PURPOSE To compare conventional angiography (CA) and rotational angiography (RA) to assess the degree of angiographically-measured stenosis versus cross-sectional area (CSA) stenosis in an in vitro carotid model. METHODS Various grades of stenosis were created by adhering different amounts of silicone rubber sealant onto the inner wall of clear, radiolucent tubes. Following 2- and 3-projection CA and 20-projection RA, the tubes were transected at the actual maximum stenosis. The cross-sectional areas were digitally photographed, and CSA stenosis was calculated using ImageJ planimeter software. The differences among CA, RA, and CSA stenosis measurements were compared statistically. RESULTS There was no significant difference between RA and CSA stenosis measurements (p=0.46). Conventional angiography with 2 or 3 projections between 0 degrees and 90 degrees underestimated the severity of disease in 19 (63%) of 30 samples. The maximum stenosis percentage was significantly lower in CA versus RA (p

Objective The objective of the study was to assess the role of uterine activity on fetal outcome. Study Design Intrauterine pressure (IUP) recordings from consecutive term singleton, vaginal deliveries collected between June 1, 1993, and July 1, 2004, were analyzed. One thousand four hundred thirty-three recordings were included. IUP data were obtained using HP 8040A and HP M1350 cardiotocographs. For each recording the uterine contraction curve was analyzed, and the following contraction parameters were determined: relaxation time; contraction duration, frequency, amplitude, and surface; Montevideo units; and active planimeter units and contraction frequency. IUP recordings and contraction parameters from deliveries ending with an umbilical artery pH of 7.11 or less were compared with those ending with an umbilical artery pH of 7.12 or greater. Statistical analyses were performed using Student’s t test and logistic regression. Results An umbilical artery pH 7.11 or less at birth is associated with significant more uterine activity during the first and second stage of labor. Conclusion Increased uterine activity is significantly associated with a higher incidence of an umbilical artery pH of 7.11 or less.