1 Eberhard, W. G Behavioral flexibility in orb web construction : Effects of supplies in differen t silk glands and spider size and weight. J. Arachnol., 16 : BEHAVIORAL FLEXIBILITY IN ORB WEB CONSTRUCTION : EFFECTS OF SUPPLIES IN DIFFERENT SILK GLAND S AND SPIDER SIZE AND WEIGH T William G. Eberhard Smithsonian Tropical Research Institute and Escuela de Biologia, Universidad de Costa Ric a Ciudad Universitaria, Costa Rica ABSTRAC T Comparisons of webs spun in the field when both sticky and non-sticky silk supplies were complete, when both were recently depleted, and when only non-sticky supplies were depleted show tha t Leucauge mariana and Micrathena sexspinosa vary design features of their orbs such as numbers o f radii and sticky spiral loops, web area and proportion covered with sticky spiral, sticky spira l symmetry, and spaces between sticky spiral loops in response to changes in the amounts of both stick y and non-sticky silk that they have available. Spider size, spider weight and possibly website als o influence L. mariana web designs. INTRODUCTIO N The orbs of araneid spiders are composed of a sticky spiral, produced by th e aggregate and flagelliform glands, and a network of non-sticky supporting line s (radii, frames, hub and temporary spiral) drawn from the ampullate gland s (Kovoor 1977; Kavanagh and Tillinghast 1979). Several aspects of orb web desig n have been thought to be species- or genus-specific (Savory 1952 ; Witt and Bau m 1960; Reed and Jones 1965 ; Witt et al. 1968; Risch 1977; Foelix 1982 ; Ramouss e and LeGuelte 1984 ; Tyshchenko 1984). Individual spiders appear however, t o adjust some web characteristics on the basis of their silk supply. Laboratory experiments using drugs that stimulated non-sticky silk production altered or b sizes and designs (Witt et al. 1968), as did manipulation of non-sticky sil k production by altering the spider's demands for non-sticky silk (Reed et al. 1970). These studies did not take into account, however, other possible effects of th e drugs, or possible effects of changes in silk supplies in other glands. The present report of field observations of the araneids Leucauge mariana (Keyserling) an d Micrathena sexspinosa (Hahn) shows that recent expenditure of sticky as well a s non-sticky silk influences web designs. Spider size, spider weight and possibl y websites are also shown to influence web design in L. mariana. MATERIALS AND METHOD S Individual spiders were followed during the course of a day by markin g websites rather than spiders, as spiders were generally several meters from each
2 296 THE JOURNAL OF ARACHNOLOGY other, and usually did not change sites during the day (spiders that did mov e were not included). L. mariana was observed in second growth near San Antoni o de Escazu, San Jose Province, Costa Rica, and M. sexspinosa at the edge of a large clearing at the La Selva field station near Puerto Viejo de Sarapiqui, Heredia Province, Costa Rica. All individuals observed were mature females. Webs were measured in the field, and then collapsed by cutting all but three radi i near their outer ends with a scissors, leaving all silk still in the web, and th e frame and anchor lines intact. Web area was estimated by multiplying vertical length times horizontal width measured from frame to frame. By weighing paper cutouts of 53 photographed L. mariana webs, it was determined that suc h estimates correlate strongly with area (r = 0.80). The number of sticky loops wa s the average of the number above and below the hub in M. sexspinosa, and the average of those above, below, and to the right and left of the hub in the les s symmetrical webs of L. mariana. The average space between sticky spiral loop s was the distance from the inner to the outer loop divided by the number of loops. Those L. mariana spiders which were to be weighed were placed in individual plastic vials with fresh leaves within 1-2 hours of finishing their first webs of th e day, and weighed to the nearest 0.1 mg less than 12 hours later on an electrica l balance. Using the average rate of weight loss for nine spiders kept in vials fo r seven hours (0.05 mg/ h spider weights averaged about 45 mg), each spider' s estimated weight when it spun its web was calculated. Each spider was placed i n alcohol after being weighed, and cephalothorax and tibia I lengths were measure d later using a dissecting microscope. Website effects on orb design were investigated by measuring the first webs o f the day for a series of spiders. These spiders were then removed (with little or no damage to the webs) and were replaced the same morning by other spiders take n from finished orbs of their own; the first webs made by the replacement spiders a t the same sites were measured the 'next morning. When possible, statistical tests were performed comparing different webs spu n by the same spider on the same day and at the same site, allowing the spider t o act as its own control. RESULT S Normal webs. Both L. mariana and M. sexspinosa replaced damaged webs hours after their original webs were destroyed at hours. The second, replacement webs of both species were consistently smaller in area, had fewer radii, and fewer loops of sticky spiral (Table 1). The average spaces between sticky spiral loops were unchanged. Third webs of L. mariana spun the same day to replace destroyed second webs (all third webs were built <15 hours after th e first web) showed further reductions in numbers of radii and loops, increase d spaces between loops, but no further change in web area (Table 1). The relative portion of L. mariana webs within the outermost loop of sticky spiral also varied. The distances from the outermost sticky loops to the oute r ends of the radii were greatest in third, smaller in second, and smallest in firs t webs (Fig. 1) (first and second webs differed comparing numbers of distance s both <0.6 cm and >1.5 cm with Chi Square p < 0.05, p < respectively) ; second and third differed comparing both <1.1 and >2.0 cm both p < with Chi Square).
3 EBERHARD-FLEXIBILITY IN ORB DESIGN 29 7 Table I.-Averages and standard deviations of characteristics of normal first, second and third web s and experimental second webs, and statistical comparisons of ratios from webs spun by the sam e spiders on the same days at the same sites (two sets of first webs are used in the comparisons of L. mariana webs). Differences between values followed by the same letter are highly significant (p < 0.001) with Mann-Whitney U-test. Number of Number of Area Space Betwee n Web Radii Sticky Loops (cm) 2 Loops (cm) N Micrathena sexspinosa First 38.3 ± ± ± ± Second 26.2 ± ± ± ± Experimental 32.0 ± ± ± ± Second/First 0.66 ± 0.16a 0.75 ± ± 31b 1.06 ± Exptl. / First 0.83 ± 0.09a 1.09 ± 0.31b 3 5 Leucauge mariana First 30.2 ± ± ± ± Second 23.4 ± ± ± ± Third 20.7 ± ± ± ± Experimental 26.2 ± ± ± ± Second / First 0.79 ± 0.1 lc 0.70 ± 0.14d 0.64 ± ± 0.13e 4 0 Third / First 0.62 ± 0.12c 0.53 ± 0.14d 0.65 ± ± 0.25e 40 Second / First 0.82 ± 0.08f 0.67 ± ± 0.19g 1.05 ± Exptl. / First 0.92 ± 0.07f 0.96 ± 0.28g 29 Sticky spiral asymmetry was reduced in second and third L. mariana orbs. Absolute values of differences between the average number of loops and th e numbers of loops in the four sectors were summed for each web in 44 cases i n which the same spider made three successive webs at the same site on the same day. The sums for first webs ((. = 8.4 ± 5.0) were larger than those in second (x = 5.0 ± 4.6) and third (x = 4.4 ± 4.2) webs (both p < with Mann-Whitne y U-test). In addition, when the difference between the maximum and minimu m number of loops in each web were compared between first, second and thir d webs, those in first webs (x ± 3.3) were larger than those in second (x = 3.4 ± 3.2) and third (x = 3.0 ± 2.7) webs (both p < with Mann-WhitneyUtest), and the proportion of webs with differences of >4 loops was greater amon g first than in second or third webs (both p < with Chi Square). Since spider s often reused frame lines from previous webs, the sticky spirals of later orbs ma y have been more symmetrical because these webs tended to have relatively large r frame areas as compared to sticky spiral areas, making fewer turnbacks in th e sticky spiral necessary (Eberhard 1969). Experimental modification of relative amounts in glands.-the relative amounts of sticky and non-sticky silk available to the spider when the second we b was begun were modified experimentally by allowing the spider to finish addin g non-sticky lines to the first web (radii, frame, hub, temporary spiral), but the n cutting the radii as above, thus preventing the spider from laying any sticky silk. The spider's non-sticky silk supply was thereby reduced, while the sticky silk supply was left intact. The experimental second webs that followed did not have reduced areas; they had fewer radii and, in L. mariana, fewer sticky loops than first webs, but the reductions in both were significantly less than those in normal second webs of both species (Table 1). The relative portion of the web enclose d within the outermost sticky spiral loop was not reduced as in normal second web s
4 298 THE JOURNAL OF ARACHNOLOG Y 30 > 2 0 U Z W 1 0 W 11ill] >3.5 DISTANCE OUTER LOOP TO FRAM E Fig. 1.-Frequencies of distances between outer loops of sticky spiral and ends of radii in norma l first (white), second (hatched) and third (black) webs (N = 44 in each case) that were spun by L. mariana females (three webs / female, all on the same day). Distributions are significantly different with Chi-Square Test. (predicted distances from outer loops were calculated for experimental webs usin g the percentages for normal second webs in Fig. 1). By cutting radii as soon as they were laid, L. mariana spiders wer e experimentally induced to lay more than one additional set of radii during construction of replacement webs (radii represent approximately 20-30% of th e non-sticky silk in a finished orb Eberhard 1986), confirming that or b construction of normal second webs does not completely empty the ampullat e glands of this species, just as in the first webs of Araneus diadematus Clerc k (Kong 1951 ; Witt et al. 1968), L. mariana and Gasteracantha cancriformis (Linneaus) (Eberhard 1986), and the unidentified araneid studied by Hingsto n (1920). Correlations with spider size and weight. Correlations between spider size an d weight and dimensions of first webs of 138 L. mariana showed that larger an d heavier spiders made webs with more closely spaced sticky spiral loops, an d somewhat larger webs (Table 2). Partial correlations showed that both weight and a combination of body size measures (x = tibia/ average tibia + cephalothorax / average cephalothorax) had significant correlations with sticky spiral spacin g (partial correlation coefficients were and respectively, both p < 0.001). Partial correlations with web area were not significant. Website effects. There were strong positive correlations between the slants an d areas of successive webs at the same site spun by different spiders (r = 0.46, p <
5 EBERHARD FLEXIBILITY IN ORB DESIGN 299 Table 2. Correlation coefficients between web and body measurements of 138 adult femal e Leucauge mariana (* p < 0.05, ** p < 0.001). Area Number Sticky Loops Space betwee n Sticky Loops Numbe r Radii Cephalothorax 0.206* ** Tibia ** Wet weight 0.267** ** Slant and r = 0.335, p < 0.01 respectively for 63 pairs of webs). Other web features showed no significant relationships, nor was there a significant correlation between the weights of successive spiders occupying the same sites. DISCUSSIO N It might be thought that differences between first and second webs were due t o the first webs usually being spun in darkness and the second in daylight (Ramousse and LeGuelte 1979 on Araneus diadematus). The differences between second and third webs of L. mariana and experimental and second webs of both species (all built during the day) indicate however that light conditions durin g construction do not explain the changes in design. The reduced numbers of radii in both normal and experimental second orbs o f L. mariana and M. sexspinosa suggest that, as in A. diadematus, non-sticky silk in the ampullate glands probably influences their web designs. The experimental webs show, however, that the supply of sticky silk can partially "over-rule" th e effect of non-sticky silk availability. A. diadematus may also respond to cues from its sticky silk glands. Preliminary evidence shows similar reductions may occur in radius and sticky spiral loop number and web area when webs are buil t in close temporal succession (Ramousse 1977). Slight reductions of numbers of sticky spiral loops occurred in webs spun by spiders which had been milked o f non-sticky silk, but prevented from laying sticky silk for three weeks (presumably gland output was reduced when demand ceased) as compared with controls whic h had spun normal webs (21.0 vs. 26.5, N = 6 for both, significance levels were no t given) (Reed et al. 1970). Sticky silk forms a large fraction of an orb. Its length ranged from about 36 t o 54% of the total length of silk in more or less typical orb designs (Eberhar d 1986). By weight it may be an even larger fraction. The non-sticky scaffolds o f Argiope aurantia webs weighed only about 16% of the dry weight of the finishe d orb (Tillinghast et al. 1984). Taking into account the non-sticky stabilimentum, which was included along with the sticky spiral in the remaining 84%, it i s probable that the sticky lines account for 70-80% of the dry weight of an orb (E. K. Tillinghast, pers. comm.). Sticky silk is also, of course, a key web componen t in trapping prey. In sum, it is perhaps not surprising that the supply of sticky sil k influences web design. The relatively smaller portions of later webs occupied b y sticky spiral, the big proportion occupied in experimental second webs, and th e spiders' ability to lay many extra radii during second web construction all sugges t that sticky rather than non-sticky silk sometimes limits web size (see als o Eberhard 1986).
6 300 THE JOURNAL OF ARACHNOLOG Y It is tempting to postulate that non-sticky gland contents determine the desig n of non-sticky web components, and sticky silk supplies affect sticky silk desig n features. There are, however, probably "crossovers" in cues from the two types o f glands; for instance, web area (a design feature of non-sticky lines) was no t reduced in experimental second webs of either species, even though supplies o f non-sticky silk had been reduced. Individual araneids sometimes produce non-sticky lines with varying diameter s (e.g., Christiansen et al. 1962; R. W. Work pers. comm.), and the sizes and space s between sticky balls on the sticky spiral of L. mariana webs varies substantially even within a single web (Eberhard unpub.). Thus the web measurements give n here may not accurately reflect total amounts of material in different webs. The probable trend in diameter modification (smaller diameters when gland less full ) suggests that the trends documented here give underestimates of the differences i n the amount of material in successive webs. Several previous studies have analyzed the relationships between spider size and weight, but many comparisons include the possibly confounding effects of specie s or age (instar) differences. Comparisons of webs of conspecific mature female s with different weights (Christiansen et al. 1962; Risch 1977) and different bod y sizes (Risch 1977) suggest that both factors have effects on web design in othe r araneid species. Variations in L. mariana web designs associated with greater spider weight were similar to those associated with relatively greater supplies o f sticky silk (decreased spaces between sticky loops, greater area), but differed i n showing no relations with numbers of radii or sticky loops (Table 1). Larger spider weights might be associated to some extent with greater recent feedin g success and thus, presumably, greater amounts of material in the glands, but a female spider's weight is probably largely determined by the stage of developmen t of its eggs. Thus the weight effects documented here may be largely independen t of the gland-filling effects. Website may be still another factor causing L. mariana web designs to vary. Spiders often reuse some of the frame lines from previous webs (Eberhard, unpub.), and the correlations in slant and area of successive first webs could b e due to frame reuse. It is also possible that other website characteristics wer e important. Adjustments of web design to local conditions are undoubtedly advantageous for orb weavers; they are suggested by field data (Leborgne an d Pasquet 1987), and have been documented in confinement (Tilquin 1942 ; Szlep 1958; LeGuelte 1966). The intraspecific variations documented here are substantial. For instance, eve n when one controls for possible effects of spider size, weight, and website in L. mariana, first webs average 146% more radii, 185% more sticky spiral loops, an d 166% more area than third webs ; some individual spiders, of course, showed even greater variations. The magnitude of this variation, the existence of similar variation in other species (Ramousse and LeGuelte 1979 ; Leborgne and Pasquet 1987), and the correlations between these and other web characters (Leborgn e and Pasquet 1987) weaken the old hope that orb designs can provide reliable species-specific characters (e.g., Savory 1952; Foelix 1982). If such web characters exist, they may be associated with more subtle details such as number and patter n of hub loops, relative size of free zone, etc. (see Coddington 1986 for examples of useful generic characters in webs of Theridiosomatidae). It is possible tha t different species have different ways of adjusting to changes in factors such as
7 EBERHARD FLEXIBILITY IN ORB DESIGN 30 1 supplies of sticky and non-sticky silk and spider size and weight, but proof of thi s will require much more information that is presently available. Intraspecifi c variation seen in other studies- (LeGuelte 1966 ; Risch 1977; Ramousse and LeGuelte 1979, 1984; Nentwig 1983, 1985 ; Tyschenko and Marusik 1985, Tyshchenko et al. 1985; Buskirk 1986 ; Leborgne and Pasquet 1987) may be du e at least in part to the factors discussed here. In light of these findings, the probable nervous mechanisms controlling orb construction appear to be extraordinarly complex. Both internal factors (weight, body size, contents of sticky and non-sticky silk glands) and external factor s (website and / or previous lines present there) are integrated in determining a variety of design features, ranging rom basic characteristics such as numbers o f radii and sticky loops and web area, to more subtle aspects such as the relativ e symmetry of the sticky spiral and the relative fill of the web area with stick y spiral. Different features are modified at least partially independently. The influence of gland contents and perhaps that of the website may incorporate feed - back loops involving amounts of silk and web designs used previously (Reed e t al. 1970; Tillinghast and Townley 1986 ; this study). During actual constructio n several other factors, such as gravity, leg length and distances and angles between lines, and memories of distances and directions travelled (Hingston 1920 ; Tilquin 1942; LeGuelte 1966 ; Vollrath 1986, 1987 ; Eberhard 1987, 1988) also influence th e paths taken and the lines laid. The reasons why spiders opt for different or b designs when they have different amounts of silk available are not yet clear ; but there is no doubt that we must discard once and for all the old image of or b weaving spiders spinning out the same rigidly programmed, inflexible geometri c patterns in their webs day after day. ACKNOWLEDGMENT S I thank H. W. Levi for identifying the spiders, M. Spivak for measurements o f photographs of L. mariana webs, J. A. Coddington, F. G. Stiles, E. K. Tillinghast, M. A. Townley, F. Vollrath, and M. J. West-Eberhard for criticism s of earlier drafts, and the Vicerrectoria de Investigacibn of the Universidad d e Costa Rica for financial support. LITERATURE CITE D Buskirk, R Orb-weaving spiders in aggregations modify individual web structure. J. Arachnol., 14 : Coddington, J. A The genera of the spider family Theridiosomatidae. Smithsonian Contrib. Zool., 422 :1-96. Christiansen, A., R. Baum and P. N. Witt Changes in spider webs brought about by mescaline, psilocybin, and an increase in body weight. J. Pharmac. exp. Ther., 136: Eberhard, W. G Computer simulation of orb-web construction. American Zool., 9 : Eberhard, W. G Effects of orb-web geometry on prey interception and retention. Pp , In Spiders Webs, Behavior and Evolution (W. A. Shear, ed.). Stanford Univ. Press, Stanford. Eberhard, W. G The effect of gravity on temporary spiral construction by the spider Leucauge mariana (Araneae, Araneidae). J. Ethol., 5 : Eberhard, W. G Memory of distances and directions moved as cues during temporary spira l construction in the spider Leucauge mariana (Araneae : Araneidae). J. Insect Behay., 1 : Foelix, R Biology of Spiders. Harvard Univ. Press, Cambridge.
8 302 THE JOURNAL OF ARACHNOLOG Y Hingston, R. W. G A Naturalist in Himalaya. H. F. & G. Willoby, London. Kavanagh, E. and E. K. Tillinghast Fibrous and adhesive components of the orb webs of Araneus trifolium and Argiope trifasciata. J. Morph., 160 : Kbnig, M Beitrage zur Kenntnis des Netzbaues orbiteiler spinnen. Z. Tierpsychol., 8 : Kovoor, J La soie et les glandes sericigenes des arachnides. Ann. Biol., 16: Leborgne, R. and A. Pasquet Influences of aggregative behaviour on space occupation in th e spider Zygiella x-notata (Clerck). Behay. Ecol. Sociobiol., 20 : LeGuelte, L Structure de toile de Zygiella x-notata CI. (Argiopidae) et facteurs que regissent l e comportement de 1'araignee pendant la construction de la toile. These Publ. Univ. Nancy, Nancy. Nentwig, W The non-filter function of orb webs in spiders. Oecologia (Berlin), 58 : Nentwig, W Prey analysis of four species of tropical orbweaving spiders (Araneae : Araneidae) and a comparison with araneids of the temperate zone. Oecologia (Berlin), 66 : Ramousse, R Organisation spatio-temporelle du comportement constructeur chez Araneus diadematus (Araigneae, Argiopidae). These Univ. Claude-Bernard de Lyon, Lyon. Ramousse, R. and L. LeGuelte Relations spatio-temporelles da ps le comportement constructeur ches 1'Epeira diademe. Rev. Arachnol., 2 : Ramousse, R. and L. LeGuelte Strategies de construction de la toile chez deux espece s d'araignees (Araneus diadematus et Zygiella x-notata). Rev. Arachnol., 5 : Reed, C. F and R. L. Jones The measuring function of the first legs of Araneus diadematus Cl. Behaviour, 25 : Reed, C. F., P. N. Witt, M. Scarboro and D. B. Peakall Experience and the orb web. Develop. Psychobiol., 3 : Risch, P Quantitative analysis of orb-web patterns in four species of spiders. Behay. Genet., 7 : Savory, T. H The Spider's Web. Frederick Warne, London. Szlep, R Influence of external factors on some structural properties of the garden spide r (Aranea diademata) web. Folia Biol. (Praha), 6 : Tillinghast, E. K., S. F. Chase and M. A. Townley Water extraction by the major ampullat e duct during silk formation in the spider Argiope aurantia Lucas. J. Insect Physiol., 30 : Tillinghast, E. K. and M. A. Townley The independent regulation of protein synthesis in th e major ampullate glands of Araneus cavaticus (Keyserling). J. Insect Physiol., 32 : Tilquin, A La Toile Geometrique des Araignees. Presses Univ., Paris. Tyshchenko, V. P The catching webs of orb-weaving spiders 1. The substantiation of th e method of standard webs with reference to two species of the genus Araneus (Aranei, Araneidae). (in Russian) Zool. Zhurnal, 63 : Tyshchenko, V. P. and Y. M. Marusik Catching webs of orbweaving spiders 3. Geographic variation of webs in Araneus marmoreus (Aranei, Araneidae). (in Russian) Zool. Zhurnal, 64 : Tyshchenko, V. P., Y. M. Marusik and C. K. Tarabaev The catching webs of orb-weaving spiders 2. Comparative study of the webs in the genus Nuctenea (Aranei, Araneidae). (in Russian) Zool. Zhurnal, 64 : Vollrath, F Gravity as an orientation guide during web-construction in the orb spider Araneus diadematus. J. Comp. Physiol., 159 : Vollrath, F Altered geometry of webs in spiders with regenerated legs. Nature, 328 : Witt, P. N. and R. Baum Changes in orb webs of spiders during growth (Araneus diadematu s Clerck and Neoscona vertebrata McCook). Behaviour, 16 : Witt, P. N., C. E Reed and D. B. Peakall A spider's web. Springer Verlag, New York. Manuscript received October 1987, revised January This paper was included in the Spider Silk Symposium held during the 1987 America n Arachnological Society Meeting at Harvard University ; a part of the funds raised at this meeting was used to defray publication costs.
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9.8 Factor Polynomials Completely Before You factored polynomials. Now You will factor polynomials completely. Why? So you can model the height of a projectile, as in Ex. 71. Key Vocabulary factor by grouping
LAUE DIFFRACTION INTRODUCTION X-rays are electromagnetic radiations that originate outside the nucleus. There are two major processes for X-ray production which are quite different and which lead to different
Natural Neighbour Interpolation DThe Natural Neighbour method is a geometric estimation technique that uses natural neighbourhood regions generated around each point in the data set. The method is particularly
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity- 8G1-8G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
Lab 7: Rotational Motion Equipment: DataStudio, rotary motion sensor mounted on 80 cm rod and heavy duty bench clamp (PASCO ME-9472), string with loop at one end and small white bead at the other end (125
-NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has
SEISMIC DESIGN Various building codes consider the following categories for the analysis and design for earthquake loading: 1. Seismic Performance Category (SPC), varies from A to E, depending on how the
UK Junior Mathematical Olympiad 206 Organised by The United Kingdom Mathematics Trust Tuesday 4th June 206 RULES AND GUIDELINES : READ THESE INSTRUCTIONS CAREFULLY BEFORE STARTING. Time allowed: 2 hours.
INTERNATIONAL HOCKEY FEDERATION PERFORMANCE REQUIREMENTS AND TEST PROCEDURES FOR HOCKEY BALLS Published: April 1999 CONTENTS 1 Introduction 2 Test Procedures General 3 Standards and Specific Test Procedures
Introduction Rotational Motion There are many similarities between straight-line motion (translation) in one dimension and angular motion (rotation) of a rigid object that is spinning around some rotation
Name: Teaching Motion with the Air Puck Objective: In studying motion of objects, many times it is difficult to quantitatively measure objects on Earth because of ever-present friction issues. Often, our
LEARNING Unit Descriptions USER GUIDE Pre-K - KINDERGARTEN UNITS Counting Build 1 to 10 Optimally. Students build and identify numbers from static and flashed sets of 1 to 10 objects using the least number
Lab #1 Measurement of length, Mass, Volume and Density Readings Before you begin this laboratory read chapter 1 of the textbook. Objectives After completing this lab, you will be able to: 1. Make measurements
Introduction to the Practice Eams The math placement eam determines what math course you will start with at North Hennepin Community College. The placement eam starts with a 1 question elementary algebra
USING SPECTRAL RADIUS RATIO FOR NODE DEGREE TO ANALYZE THE EVOLUTION OF SCALE- FREE NETWORKS AND SMALL-WORLD NETWORKS Natarajan Meghanathan Jackson State University, 1400 Lynch St, Jackson, MS, USA email@example.com
Rocket Activity Foam Rocket Objective Students will learn about rocket stability and trajectory with rubber band-powered foam rockets. Description Students will construct rockets made from pipe insulating
Vern Lindberg 1 Making Graphs A picture is worth a thousand words. Graphical presentation of data is a vital tool in the sciences and engineering. Good graphs convey a great deal of information and can
a. Using Faraday s law: Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION The overall sign will not be graded. For the current, we use the extensive hints in the
THE EFFECT OF BLADE ANGLE AND SIZE ON WIND TURBINE PERFORMANCE Anish Bhattacharya, 8 th Grade, Unity Point School District 140 PURPOSE We have experienced a major fall in the economy in the recent past.
Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost
NCSU PHYSICS 205 SECTION 11 LAB II 9 FEBRUARY 2002 Spring Force Constant Determination as a Learning Tool for Graphing and Modeling Newton, I. 1*, Galilei, G. 1, & Einstein, A. 1 (1. PY205_011 Group 4C;
Selecting Receiving Antennas for Radio Tracking Larry B Kuechle, Advanced Telemetry Systems, Inc. Isanti, Minnesota 55040 firstname.lastname@example.org The receiving antenna is an integral part of any radio location
Modeling the Seasons Students model the seasons with their own earth globes. Materials For the whole group, you ll need: a 150 200 watt light bulb (not frosted) or a flashlight a lamp or socket for the
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
PholC60 September 001 DATA INTERPRETATION AND STATISTICS Books A easy and systematic introductory text is Essentials of Medical Statistics by Betty Kirkwood, published by Blackwell at about 14. DESCRIPTIVE
Analysis of the Potential for a Heat Island Effect in Large Solar Farms Vasilis Fthenakis 1,2 and Yuanhao Yu 1 1 Center for Life Cycle Analysis, Department of Earth and Environmental Engineering, Columbia
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Chapter 27 Solutions PSS 27.2 The Electric Field of a Continuous Distribution of Charge Description: Knight Problem-Solving Strategy 27.2 The Electric Field of a Continuous Distribution of Charge is illustrated.
Source: Frerichs, R.R. Rapid Surveys (unpublished), 2008. NOT FOR COMMERCIAL DISTRIBUTION 3 Simple Random Sampling 3.1 INTRODUCTION Everyone mentions simple random sampling, but few use this method for
GEOLOGY 306 Laboratory Instructor: TERRY J. BOROUGHS NAME: Patterns in the Solar System (Chapter 18) For this assignment you will require: a calculator, colored pencils, a metric ruler, and meter stick.
NUMERICAL MODELLING OF PIEZOCONE PENETRATION IN CLAY Ilaria Giusti University of Pisa email@example.com Andrew J. Whittle Massachusetts Institute of Technology firstname.lastname@example.org Abstract This paper
F09 Biol 322 chi square notes 1. Before proceeding with the chi square calculation, clearly state the genetic hypothesis concerning the data. This hypothesis is an interpretation of the data that gives
Mensuration (3-D) Total Time: 90 mins Practise Exercise no. 1 Total no. Of Qs: 51 Q1. A wooden box of dimensions 8m x 7m x 6m is to carry rectangular boxes of dimensions 8cm x 7cm x 6cm. The maximum number
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Description Lab 5: Projectile Motion In this lab, you will examine the motion of a projectile as it free falls through the air. This will involve looking at motion under constant velocity, as well as motion
Steps to draw 3D Worm Gear using SolidWorks 2013 EGN 1110C: Engineering Drawing 1.) Draw two circles on the Front Plane centered at the origin, give the correct dimension using Smart Dimension and Click
END OF PRIMARY BENCHMARK MATHEMATICS WRITTEN PAPER 80 marks 1 hour 15 minutes Mathematics Written Paper End of Primary Benchmark 2013 Page 1 of 13 WRITTEN PAPER 1. Work out: a) 142 + 241 = b) 1000 = 243
Physics 182 - Spring 2012 - Experiment #8 1 Experiment #8, Magnetic Forces Using the Current Balance 1 Purpose 1. To demonstrate and measure the magnetic forces between current carrying wires. 2. To verify
Chapter 4: Data & the Nature of Graziano, Raulin. Research Methods, a Process of Inquiry Presented by Dustin Adams Research Variables Variable Any characteristic that can take more than one form or value.
Student Outcomes When students are provided with the angle measure of the arc and the length of the radius of the circle, they understand how to determine the length of an arc and the area of a sector.
The Calculus of Functions of Several Variables Section. Introduction to R n Calculus is the study of functional relationships and how related quantities change with each other. In your first exposure to
The 2 Test Use this test when: The measurements relate to the number of individuals in particular categories; The observed number can be compared with an expected number which is calculated from a theory.
International Journal of Research Studies in Biosciences (IJRSB) Volume 3, Issue 1, January 2015, PP 104-109 ISSN 2349-0357 (Print) & ISSN 2349-0365 (Online) www.arcjournals.org Aspects of Reproduction
VOLATILITY AND DEVIATION OF DISTRIBUTED SOLAR Andrew Goldstein Yale University 68 High Street New Haven, CT 06511 email@example.com Alexander Thornton Shawn Kerrigan Locus Energy 657 Mission St.
Asexual Versus Sexual Reproduction in Genetic Algorithms Wendy Ann Deslauriers (firstname.lastname@example.org) Institute of Cognitive Science,Room 22, Dunton Tower Carleton University, 25 Colonel By Drive