Surveying engineer stations
Railroads and Highways use E(ngineer) S(tations) to locate on maps or plats a drawing of where their route is on the ground. An ES is 100 feet in length denoted as 1 + 00. Thus one mile would be 52 + 80 feet on a drawing which normally shows the scale of the drawing, for instance, 1 (one) inch = 100 (one hundred) feet. My descriptions are for those uses of ES's that were employed on Southern Pacific lines including predecessor companies but they will conform to the majority of railroads in the US. A survey for a railroad would be in conformance with an order by the Board of Directors or someone with authority to order same and would instruct a survey crew what termini were desired, such as Podunk, (state) to Greater Butterflyville, (state). For terrain with no great physical obstacles only one survey might possibly be necessary, and if these towns or cities were 10 miles apart by the line taken by the surveyors the ES's would start at ES 0 + 00, most commonly used, and run to ES 520 + 00. Railroad lines not only are measured in feet and ES's but also in miles. In our example the M(ile) P(osts) would start at MP 0 and run to MP 10. Where terrain contains physical obstacles such as rivers or mountains or where acquisition of property is a problem more than one survey may be necessary. In such cases the first survey might be identified by placing a letter with the ES's such as A0 + 00, the second survey might show B0 + 00, etc. On longer surveys where multiple survey lines are used it is often the case where the surveyed lines meet or cross that ES equations are used to identify which survey lines are which. Thus in our examples we might start a new survey 3 miles from the start at (ES) 158 + 40 and rejoin the first line 3 miles further on but with a saving of 500 feet in length. The new line would be shown as (ES) 158 + 40 to (ES) 311 + 80=(ES) 316 + 80. Equations are also used where subsequent surveys of the same line find differences or a surveyed line is undertaken by more than one survey party to speed up the work.
In the first years of railroad construction curved track was constructed using "simple" curves, that is, the curved portion was all two degrees or whatever was the degree of curvature used. When William Hood was appointed Chief Engineer in mid 1880's he developed what were called "Hood's Taper Curves". These "transition" curves eased the locomotive and cars into the "main" curve. After Hood's departure as Chief Engineer Southern Pacific and affiliated lines used "spiral" curves employed by many other railroads. The use of taper and later spiral curves resulted in small reductions in track length with the consequent need for (ES) equations.
This is a much simplified description of engineer stations. If you have further questions I will be happy to attempt an answer for them.