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The Planimeter, 



An instrument for measuring the areas of plane surfaces, by passing a pointer 

 around their periphery. It is of great convenience to all classes of engineers, and 

 practically applicable to a great variety of purposes. To measure the areas of 

 figures that are bounded by irregular lines, such as : drainage areas ; lots bounded 

 by rivers or creeks ; contour lines of ponds, etc. ; to get the true average of obser- 

 vations taken at irregular intervals; to measure indicator and other diagrams, and 

 for many other portions of engineering work. As these instruments will not only 

 give the area of any figure, but also any multiple of such area, and the sum of any 

 number, or series of such multiples, at one operation, they may be used to very- 

 great advantage in the calculation of the cubical contents of solids ; as in the cal- 

 culation of earth- work, etc. See on this point an article by Clemens Herschel, Esq., 

 in the Journal of the Franklin Institute for April, 1874. The planimeters graduated 

 by us are rated to read square inches of area, square centimeters of area, any mul- 

 tiple of these areas, and so as to give the cubic yards in any cut or fill, if used 

 according to the directions that will accompany each instrument, Two consecu- 

 tive measurements of the same area need never differ by more than 0.02 of a square 

 inch ; and by repeating the measurement in the same manner that angles are re- 

 peated with a transit instrument, the error of observation may be reduced to but a 

 small fraction of one hundredth of a square inch of area. 



The above illustration represents the planimeter, as sold by us, ready for 

 use. The total length of the instrument is about nine inches. The graduated 

 bar g h can be slid in and out in a socket formed at the top of the frame, the thumb- 

 screw/being used for fine movements of this sort; by this means, and by the 

 sensible form of graduation adopted, the planimeter may be made to dp the various 

 operations spoken of above. Theory requires that the pointer d, which is moved 

 around the periphery of the figure whose area is to be measured, the pivot , at 

 the junction of the two arms g &and i j, and the main axis a 6, upon which turns 

 the measuring and counter wheel c should all be in one and the same straight line ; 

 for this purpose, our instruments have both the pointer d and the rear part 

 of the frame which carries the rear bearing of the axis a 6, adjustable. Kadi 

 reading of the instrument consists of a record of the number of revolutions of the 

 counter-wheel c read to three places of decimals; the whole revolutions are ivad 

 on the wheel Z, the tenths and hundredths on the wheel itself, and the thousandth 

 on the vernier m. With such simplicity of construction and of operation, the a cu- 

 racy of work done by this instrument is one of the most surprising things about it. 

 The figures given above in relation to accuracy of work are, however, reliable; 

 being derived from the experience of several years in the use of the planimeter for 

 many kinds of work. 



A brass scale sent with our planimeters can be used to prove the correct working of the instrument. T* 

 u*e it drive a fine needle as an axis through one of the small holes of the scale rtHo the paper, then put the 

 tracer into one of the other holes and describe a circle. In this manner large and small circles of known areas 

 can be circumscribed with perfect accuracy. This operation should be repeated in the opposite direction, and 

 if the results agree the instrument is correct. However, if the results differ correction maybe mad* by 

 means of the two adjusting screws by which the tracer can be moved to right or left of the graduated bar, as 

 the case may be. 



