84 UV'JSfUlAUI* 



with the "Profile of Quantities," of which a short example 

 is engraved, but it is done completely and accurately. 



The method of the profile of quantities was originated by 

 Bruckner, a Bavarian engineer. It was presented by Cuhlman 

 in his "Graphical Statistics" in 1868, and translated from that 

 by P. Reineker, then (1871-3) Principal Assistant Engineer of 

 the Pennsylvania Co., at Pitsburg, Pa., for the use of his de- 

 partment. This translation was procured there by the writer, 

 and the method adapted to American practice in a great variety 

 of railway work, and is here given with an example of work 

 as actually executed. 



The subject is presented, for convenience and clearness, in 

 three steps: 



1st. The Compilation of the Data. 2d. The Plotting of the 

 Profile. 3d. The Taking Off of the Results. 



1. The Compilation of the Data. The paper containing the 

 data is ruled in five vertical columns, see page 83. 



The first column contains the station numbers. In practice 

 the elemental volume is the total excavation or embankment 

 in a full station, whether the station distance is 100 ft, 66 ft, 

 or a number of meters. Plusses are not used, excepting at an 

 occasional beginning or end of a subsection, although the sys- 

 tem is flexible enough to apply to any regular or irregular sub- 

 division of these elemental volumes. 



In columns 2 and 3 are now entered the total increments 

 or volumes of earthwork in excavation or embankment in suc- 

 cessive stations. When excavation and embankment both oc- 

 cur within the limit of the same station the net amount only 

 need be entered. If there is a special price for casting within 

 the station another column may be introduced for it. Excava- 

 tion is considered plus and embankment minus. The latter 

 may be entered in red ink. 



Columns 4 and 5 are now filled up by algebraic addition of 

 columns 2 and 3. The ordinate at any point of the "Profile of 

 Quantities" is equal to the algebraic sum of the volumes as far 

 as to that point, and should be verified by use of this princi- 

 ple, at convenient points, as the summation proceeds. 



2. The Plotting of the Profile. The horizontal part of the 

 plotting is the same as used in the ordinary profile, and it may 



