Hello, welcome to this part of geometric leveling where we will address a certain number of definitions, what is an altitude, and see the principle of measuring with a level and a rod. The first definition that we will address is the true altitude; what is an altitude? We have seen in the part that deals with Geodesy the definition of a geoid; I remind you, the geoid is the reference surface for altitudes, its a physical surface that depends on the gravitational field. Then I can draw a topographic surface and the altitude is the distance measured by the vertical; if I consider her the point <i>A</i>, I have my distance here along the vertical is the altitude of point <i>A</i>, so the orthometric height or true altitude, is this distance. If I consider here a point <i>B</i>, I do the same exercise I have my distance here <i>HB</i> that is the true altitude at this point. What you should know is that the gravitational field will vary so we will have here at point <i>A</i> a vector of gravity with its orientation and at point <i>B</i> I have another vector with its orientation and the other orientations of these two vectors are not necessarily parallel, there may be variations in the gravitational field, thus these variations must be taken into account to have a rigorous model of the altitudes. In the definition of the altimeter system we have to go back to what we call a fundamental point, in this case to define this mean sea level we will use a tide gauge that will be placed on the coastline, particularly, in this case, in Marseille, and then we will use a method of measurement, in this case leveling, in order to propagate this horizontal reference to the country. This is what we did for Switzerland, where we went from Marseille, on a route along the Rhône valley to finally arrive here in Geneva that is our fundamental point for the Swiss system. The third definition, the geometric leveling. Geometric leveling is a direct measurement method for height differences that is also called vertical drop. This is a small example where I draw a topographic surface and along this surface I will place the vertical rods that permits us to measure the difference in levels. Between each rod, in a section here, I can draw a horizontal and what interests me is the total of these vertical drops, which will allow us to define a height difference between two points of interest in the field. The problem of altitudes, we have noticed, depend on the gravitational field; I redraw here my reference surface, in this case the geoid, and the surface that interests me, namely, the topographic surface here; and I place myself on two points of interest here in the field, the point <i>A</i> here and the point <i>B</i>, and the problem I have is that we are not on a common vertical so the vertical at <i>A</i> and at <i>B</i> is not necessarily parallel. I remind you here the gravitational field at <i>A</i> and the gravitational field here at <i>B</i>. Therefore the first assumption to make our lives simpler, and this is often the case on construction site operations, or of the work across a neighborhood or a city, is that the two surfaces here passing through point <i>A</i> and point <i>B</i>, so these surface levels, are parallel because we made an assumption that the gravitational field here is uniform and that we are on the same vertical. We speak in this case of usual altitude, it is what we will use in most topometric work. The usual altitude, is based on a fundamental point, as we have seen, it is the point that is attached to the mean sea level, we have here materialized in Geneva at "Pierre du Niton". a base point, as a reference, for our Swiss altitude system. The altitude system consist of, as seen on this map, this is not the roads but in fact it is the leveling paths that have been made across the country on the federal level, so we have here a series of paths with points which are documented where we find information about the altitude. We talk here of an altimetric network. The reference frame was defined early in the twentieth century, in 1902, and it is called the Federal leveling, NF02, and it is effectively connected to this "Pierre du Niton" as a horizontal reference for our country. I will remind you that it is a non rigorous system, the gravitational field influence the leveling measurement. We will stop now for a small quiz where we will look at two different paths across Switzerland. We will leave here in Lausanne and we will do a first route along the plateau to reach Zurich. We will consider a second path that will go through the Valais, through the Alps, the canton Uri, and also reach Switzerland. The question that arises here is is the <i>ΔH</i> between Lausanne and Zurich across the plateau, or across the Alps, is this <i>ΔH</i> equal? That is the question that is posed in this quiz. In 1995 Switzerland upgraded its national Geodesy, in particular a rigorous system was defined for altitudes, namely the system <i>RAN95</i> which is the new national altimetric network. It is a rigorous orthometric system, so the altitude measurements according to the theory of potential gravitational field. We apply to the raw leveling measurements the orthometric corrections and we have now a perfect model for our altitude in Switzerland. If we now compare the model defined in 1902, <i>NF02</i>, with this new model, we have the following map which shows these differences. We can note in the plateau region, so here in this area, I see that the altimetry differences are near zero or a few centimeters; in contrast if I go to the Alp region where the geoid is more disturbed by steeper slopes, and well, in this case, I see that I may have these differences between the two models up to 40-50 cm. So these elements are now documented and we have a rigorous network of altitudes for Switzerland. When talking about documentation, each of the points along the federal and cantonal leveling, is documented in the records in which we will find a certain number of information, namely, identification of the point, we have its region, we have a number corresponding to the national map, then you will obviously have the approximate coordinates to situate the point on a map; associated with this, you have a photo that can identify this point in the landscape in this case here, at the foot of a building, we have an indication of the materialization, in this case a pin that was realized by the Federal Office of Topography and we obviously have the value of the altitude here in the system <i>NF02</i> with an estimated precision here of 3 millimeters. We also see in this record that there are regular updates and the controls here of these altitude points, which are made by the Federal Office of Topography. The measuring principle: to be able to measure with the level, it is necessary that the line of sight is horizontal. We remind you here that the spirit level used to calibrate the level, we have here the guideline; once the bubble is in the upper portion of the tube, the tangent in this upper portion here gives the guideline. If the level is adjusted, this guideline will be parallel to the line of sight and thus enable us to make measurements on an horizontal plane. The measures is done on the staff; the graduations of the staff are as following: you have first the meters, the decimeters and then the centimeters that are given here by the small black and white markers. The millimeter will be estimated by eye with a precision of plus or minus one millimeter. In this example here, we can say that we have one meter, we have two decimeters and we can count the number of centimeters starting from here to here and we have seven centimeters, and the estimation of millimeters we give here is about eight millimeters, so that the height reading is 1,278 meters. The measurement principle is as following: you have the level that is placed here in the middle of the range, between point <i>A</i> and point <i>B</i>, on point <i>A</i> we place a vertical rod we will make a so-called back reading, then this rod will move with its operator to point <i>B</i> and we will make a front reading; here we define a direction of measurement and direction of travel, that will give an indication of the height difference + if we ascend, - if we descend and height difference is, as we have already shown, the difference between the back reading and the front reading. Now if we place it in the context of a path, we will move on to a known point in altimetry, for example, and make a series of spans here until reaching the point <i>B</i> and the sum of these height differences will give us the difference in elevation between <i>A</i> and <i>B</i> ; so we have here in the first section a <i>Δh1</i>, in the second section you have a <i>Δh2</i>, etc., to finish at <i>Δhn</i> and terminate at the point <i>B</i>, and the sum of these differences of level or vertical drops give the height between point <i>A</i> and point <i>B</i>. For the field operations of a geometric leveling routing we generally use the following formula where we see the different points with the back readings and the front readings, that we have here in a first span, and we will directly calculate the difference in level with its sign, it helps the along a path to sum these differences of level positive and negative and finally have the height difference along this section of the path. To summarize this part dedicated to geometric leveling we have seen a certain number of definitions of altitudes: the usual altitudes, orthometric altitudes, so an update of our system that takes into account the gravitational field, and we have seen the principles with the description of the level, the description of the staff on which we make a reading and the principle of the path. I invite you to see the different videos shot on location that illustrate and complete these theoretical principles.