 Hi, dear learners, best greetings of the time to all of you. I am Mr. Seshikant B. Gosavi, Assistant Professor, Department of Civil Engineering at Valkhanda Institute of Technology. I am going to take a session on adjustment of feudalite travers as a part of the online educational resource. At the outset, let us learn about what are the learning outcomes of this session. The first learning outcome is the learners will be able to compare the use of rules for feudalite travers. In addition to that, the learners will also be able to select the best suitable rule for adjustment of the feudalite travers. All of us are familiar with the types of travers. This is a closed traverse. As you can see, there is a starting point over here and then the traverse is moving in an anticlockwise direction. In feudalite travers, it is mandatory to run in anticlockwise direction and it is actually supposed to end up over here. In absence of all types of error, it will end up over here. If there is a presence of some angular error or linear error, it may fail by a certain amount of closing error. This is what is the closing error. The field procedure for the feudalite traversing consists of measurement of included angles by repetition method at all these stations as well as measurement of magnetic bearing for each of the side of the traverse in forward direction as well as in backward direction, which we call as the forebearing and backbearing. In addition to that, we are also measuring length of the sides of the traverse with utmost precision. As you are familiar with from the earlier session, that there is a standard shape of a Gale-Straver stable, which is used for entering the data of feudalite travers. As you can see, the Gale-Straver stable consists of these many number of columns beginning with serial number, name of the station, name of the line, name, sorry, the length of the line, the observed included angle corresponding to that particular station. Then by calculation, we will be working out the corrected included angle. There will be observed forebearing and observed backbearing corresponding to this particular line. The bearings will be corrected with the help of release of the local attraction as well as because of the known included angle and finally we will be getting the corrected forebearing. These corrected forebearing which are in the whole circle bearing system will be converted into reduced bearing system because that is how the rest of the calculation of the coordinates of feudalite travers are carried out. Here I have shown the consecutive coordinates. These are the coordinates of every station with reference to its preceding station. You can see here, even though the station is P, I have not given a name as PQ, I have given a name as VP, assuming that V is the preceding station and P is the succeeding station and therefore when I am calculating the consecutive coordinate of station P, these are actually the coordinates of P calculated with reference to V and therefore length VP and quadrantal bearing of the line VP are used for calculating the consecutive coordinate of station P. In the consecutive coordinate, there are two columns. One is latitude, the other one is departure. In the latitude, we have two subcolumns, northern and southern. As well as in departure, we have two subcolumns, easting and westing. The latitude can be calculated with a very simple formula L cos theta and departure is calculated by using a formula L sin theta, where L is length of the respective side VP and theta is the quadrantal bearing which we have got under this particular column for the same line VP. This is how the data is entered into the Gale-Stravers table. Here you can see from the calculated L cos theta, L sin theta, latitudes and departures, we can at the bottom of the table do the summation of all the latitudes as well as all the departures. Remember very well, northern latitudes are treated positive, southern latitudes are treated negative, easting latitudes are treated positive and westing departures are treated negative. And therefore, when we are trying to find out whether the closing error is present or not, normally we will take summation latitude and summation departure. Theoretically speaking, if we are starting from a particular station and coming back to the same station, the gross moment may be this much, but the net moment will be coming back to the same station and therefore, the latitude summation must be 0 as well as summation of the departure should also be 0. But practically it may not happen and therefore, there may be a failure of closure in the form of p dash p o as has been shown in the figure. This length of the closing error can be calculated by using the formula E is equal to square root of dL square plus dD square or square root of summation L square plus summation D square. One can deduce or conclude regarding what is the degree of accuracy that has been achieved in this particular case. It is equal to the length of error of closure divided by total perimeter of the traverse. This ratio gives us idea about what is the degree of accuracy that we have achieved. In first order work, it is expected that it must be 1 as to 10,000. In 10,000 meter, 1 meter error is permissible. In second order, it is 1 as to 5000. In first order, it will be 1 as to 2000 and therefore, depending upon the order of the accuracy desired from the work, we can make a decision about whether the error is acceptable or not and if it is within the acceptable limit, then we can proceed further for redistribution of that error or removal of that error. The other thing that has been shown over here is theta is equal to tan inverse dD divided by DL or theta is equal to tan inverse summation D by summation L. This is the angular position of the closing error. As you can see over here, this is theta, angular position of the closing error which is ratio of tan inverse of ratio of summation D by summation L and thus we can get an idea about what is the angle in quadrantal system as well as we will get an idea about which quadrant is there in which the closing error falls. Actually the theme of today's session is comparison of the rules for adjustment of these errors. There are two rules which are normally used in case of theodolite traverse. The first one is Bowditch's rule and the other one is transit rule. The Bowditch's rule is used when the angular measurements are equally precise to the linear measurements. The total error in latitude and departure is distributed in proportion to length of each side of the traverse. Thus if CL or CD is correction to latitude or correction to departure, it will be equal to correction to latitude of any side. Similarly, summation L or summation D is equal to total error in latitude or departure. Summation L has been shown over here that is equal to length of perimeter of the traverse, summation of length of all sides of the traverse. L is length of any side and thus CL that is correction to latitude will be equal to summation of latitude multiplied by length of the side divided by the perimeter of the traverse which is summation L. Similarly, correction to departure is equal to summation D into ratio of length of the respective side divided by summation of the respective departure and thus summation of respective length of sides of the traverse which is nothing but perimeter. Because the correction to latitude and correction to departure can easily be known to us. The other rule which is transit rule is given a name as transit because it is particularly useful for the very precise tuorites. If angular measurements are more precise than the linear measurements, we will opt for the transit. If correction to latitude is denoted as CL or correction to departure is denoted as CD, total error in latitude or departure is denoted as summation L or summation D. Latitude or departure of the line is denoted by L or D and arithmetic sum of latitude or arithmetic sum of departure is indicated by LT or DT. Then the formula which is used in the transit rule is correction to latitude is equal to summation L which is nothing but total error in latitude. Try and understand this is a algebraic sum of latitude. Northern treated positive, southern treated negative multiplied by latitude of the side divided by LT which is nothing but arithmetic sum of latitude. That means, northern and southern both of them are added together irrespective of any sign conventions. So LT is arithmetic sum, summation L is algebraic sum. Similarly, CD is equal to summation departure into D divided by DT. Correction to consecutive coordinates are supposed to follow these rules about whether it should be added or detected from the earlier latitude or departure. The balancing part of Gail Straver's table has been shown over here wherein you can enter the latitude departure, you can enter the values of the corrections in the respective columns and finally corrected consecutive coordinates can be calculated. Pause the video and answer the following multiple choice questions. These are the answers of the questions that I have asked. I have referred to National Program of Technology Enhancement as reference material. Thank you very much.