{"id":716,"date":"2024-07-04T16:44:34","date_gmt":"2024-07-04T11:14:34","guid":{"rendered":"https:\/\/study.madeeasy.in\/?p=716"},"modified":"2025-07-16T14:57:02","modified_gmt":"2025-07-16T09:27:02","slug":"computation-of-latitude-and-departure","status":"publish","type":"post","link":"https:\/\/www.madeeasy.in\/study\/ce\/surveying\/computation-of-latitude-and-departure","title":{"rendered":"COMPUTATION OF LATITUDE AND DEPARTURE"},"content":{"rendered":"<ul>\r\n<li style=\"text-align: justify;\">The latitude (L) of a line is the orthographic projection of the line on the N-S axis representing the Meridian.<\/li>\r\n<li style=\"text-align: justify;\">It is considered positive when the projection of the line is on the north called as northing (N) and negative when on south side called a southing (s).<\/li>\r\n<li style=\"text-align: justify;\">The departure (D) of a line is the orthographic projection of the line on the axis perpendicular to the Meridian i.e. E-W axis.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-430 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/Meridian.jpg\" alt=\"Meridian\" width=\"677\" height=\"434\" \/><\/p>\r\n<p style=\"text-align: justify;\">Note that in the expression for<\/p>\r\n<p style=\"text-align: center;\">Latitude = <em>l <\/em>cos0,<\/p>\r\n<p style=\"text-align: center;\">Departure = <em>l <\/em>sin0<\/p>\r\n<p style=\"text-align: center;\">Where 0 = angle measured from N \u2013 S axis.<\/p>\r\n<p style=\"text-align: justify;\">if, in place of quadrant bearing angle, we use whole circle bearing, the value so obtained will have the necessary sign. For example, if the line OC ha 0<sub>3<\/sub> = 30\u00b0, the whole circle bearing will be 210\u00b0.<\/p>\r\n<p style=\"text-align: justify;\">Hence<\/p>\r\n<p style=\"text-align: center;\">latitude = <em>l<\/em>3 cos210\u00b0 = \u2013 0.866 <em>l<\/em>3(i.e. \u2013 ve)<br \/>departure = <em>l<\/em>3 sin210\u00b0 = \u2013 0.5 <em>l<\/em>3 (i.e. \u2013 ve)<\/p>\r\n<p style=\"text-align: justify;\"><strong>Consecutive and Independent Co-ordinate<\/strong><\/p>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-431 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/consecutive.jpg\" alt=\"Consecutive\" width=\"416\" height=\"205\" \/><\/p>\r\n<h5 style=\"text-align: justify;\">Consecutive Co-ordinates<\/h5>\r\n<ul style=\"text-align: justify;\">\r\n<li>Co-ordinates of end point of a line w.r.t to its initial point are called consecutive co-ordinate or dependent co-ordinates of the end point of the line.<\/li>\r\n<li>Consecutive co-ordinate of end point 2 of line 1 \u2013 2 will be \u2013 <em>L<\/em><sub>1<\/sub> and <em>D<\/em><sub>1<\/sub>.<\/li>\r\n<\/ul>\r\n<h5 style=\"text-align: justify;\">Independent co-ordinates<\/h5>\r\n<ul style=\"text-align: justify;\">\r\n<li>Co-ordinates of a point w.r.t to a common origin are called independent co-ordinates.<\/li>\r\n<li>Independent co-ordinate of point 1 = <em>y<\/em><sub>1<\/sub> and <em>x<\/em>1.<\/li>\r\n<li>Independent co-ordinate of point 2 = <em>y<\/em><sub>2<\/sub> and <em>x<\/em>2.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\"><strong>NOTE:\u00a0\u00a0\u00a0<\/strong><\/p>\r\n<p style=\"text-align: center;\"><em>x<\/em>2 = <em>x<\/em>1 + <em>D<\/em>1<br \/><em>y<\/em>2 = <em>y<\/em>1 \u2013 <em>L<\/em>1<br \/><em>x<\/em>3 = <em>x<\/em>1 + <em>D<\/em>1 + <em>D<\/em>2<br \/><em>y<\/em>3 = <em>y<\/em>1 \u2013 <em>L<\/em>1 + <em>L<\/em>2<\/p>\r\n<ul style=\"text-align: justify;\">\r\n<li>Total latitude of any point (say point no. 3) = Total latitude of starting point + algebraic sum of the all latitude of all lines upto that point 3.<\/li>\r\n<li>Total departure of any point (say point number 3) = Total departure of starting point + algebraic sum of the departures of all lines upto that point 3.<\/li>\r\n<\/ul>\r\n<p style=\"text-align: justify;\"><strong>Mid-ordinate Rule<\/strong><\/p>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-432 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/mid-ordinate.jpg\" alt=\"Mid Ordinate\" width=\"658\" height=\"427\" \/><\/p>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-433 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/trapezoid.jpg\" alt=\"Trapezoid\" width=\"466\" height=\"180\" \/><\/p>\r\n<h3 style=\"text-align: justify;\">Simpson\u2019s One Third Rule<\/h3>\r\n<p style=\"text-align: justify;\">Here it is assumed that the boundaries between the two extreme ends of three consecutive offsets is parabolic and the axis of parabola is parallel to the offsets.<\/p>\r\n<p style=\"text-align: justify;\">Now, Area of figure = Area of trap. <em>ABDC <\/em>+ Area of parabolic portion <em>CHDPC<\/em><\/p>\r\n<p style=\"text-align: justify;\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-434 aligncenter\" src=\"https:\/\/study.madeeasy.in\/wp-content\/uploads\/2024\/07\/simpson-one-third-rule.jpg\" alt=\"Simpson\u2019s One Third Rule\" width=\"645\" height=\"561\" \/><\/p>\r\n<p><strong>Note:<\/strong><\/p>\r\n<p style=\"text-align: justify;\">In order to apply Simpson\u2019s one-third rule, the areas must be divided in even number i.e., number of offsets must be odd i.e., <em>n <\/em>term in the last offset \u2018<em>O&#8217;<\/em><em>n<\/em>\u00a0should be odd. If offsets are even in number, then in this case average of offsets is taken between any two adjacent offsets and hence the number of offsets become odd.<\/p>\r\n\r\n<p style=\"text-align: center;\"><a class=\"btn btn-danger\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/surveying\/law-of-accidental-error\/\" target=\"_blank\" rel=\"noopener\">&lt;&lt; Previous<\/a> | <a class=\"btn btn-success\" role=\"button\" href=\"https:\/\/study.madeeasy.in\/ce\/surveying\/horizontal-curve-s\/\" target=\"_blank\" rel=\"noopener\"> Next &gt;&gt;<\/a> <br \/><strong> Must Read: <\/strong> <a href=\"https:\/\/study.madeeasy.in\/subjects\/what-is-surveying\/\" target=\"_blank\" rel=\"noopener\"><strong>What is Surveying?<\/strong><\/a><\/p>\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>The latitude (L) of a line is the orthographic projection of the line on the N-S axis representing the Meridian.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[203,2],"tags":[243,244,245,246],"class_list":["post-716","post","type-post","status-publish","format-standard","hentry","category-surveying","category-ce","tag-consecutive-co-ordinates","tag-independent-co-ordinate","tag-mid-ordinate-rule","tag-simpson-one-third-rule"],"_links":{"self":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/716","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/comments?post=716"}],"version-history":[{"count":0,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/posts\/716\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/media?parent=716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/categories?post=716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.madeeasy.in\/study\/wp-json\/wp\/v2\/tags?post=716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}