H. LENGTH. 51 



The curve scale is intended for engineers, steani boiler makers, surveyors, 

 architects, and others, for copying maps, plans, &c. 



It will be of great advantage in the projection of railway lines, the 

 curve scale requiring only to be adjusted to the situation in order to ascer- 

 tain how the line can be most favourably traced, and expensive cuttings 

 avoided. In regard to such surveys, as well as in the control or examination 

 of railway lines already traced and sketched (for which purposes either the 

 bow, cut out according to certain radii, or compasses, are used at present), 

 the employment of the curve scale will save the tedious trouble of experi- 

 menting, since the correct curve can be immediately determined and read by 

 means of this instrument. 



Boiler manufactures, also, and almost all technical pursuits, will find the 

 curve scale very useful for determining the radius of part of an arc of a circle, 

 of Avhich three points are given, as, for instance, in arched steam boiler 

 bottoms. 



In fact, in all cases where part of an arc of a circle, or three points of the 

 same, is given, the radius can be read direct, and without loss of time, in a 

 manner hitherto unknown. 



If it be desired to take the radius of a given curve by means of the scale, 

 the middle bar of the same is placed on the curve line, and the scale is then 

 moved so far upwards or downwards until the curve line meets in three com- 

 mensurably described points of the scale. The number indicated gives the 

 radius of the curve in centimeters, if the curve is drawn in its natural size. 



If, however, the drawing of which the radius of the curve is to be deter- 

 mined is sketched, as is usually the case, in a reduced scale, the radius 

 indicated must be multiplied with the proportional number of the reduced 

 scale. 



For example, if the drawing should be sketched in ^^ scale of the natural 

 size, and the curve radius on the curve scale is indicated with 52 5 cm., the 

 actual radius of the curve will be 52 -5 x 2,500 = 131,250 cm., or 1,312-5 meters; 

 or, should the drawing be sketched in -^ scale, and the curve scale indicates 

 43 cm., the radius of the curve will be 43 x 500 = 21,500 cm., or 215 meters. 



The curve scale can likewise be used as a reduction scale of every other 

 measure which is to be calculated in meter measure, as the radius in meters 

 can always be read directly, no matter in what scale the drawing is made. 



This is a great saving of labour, which is very much facilitated if, as often 

 is the case, old maps and drawings are to be made use of. 



In using the curve scale it will sometimes happen that the curve to be 

 ascertained does not exactly meet the line drawn on the scale, but will fall 

 between two lines. In this case the smaller division can, as the radii are 

 marked progressively by 0'5 cm., be easily estimated with the naked eye after 

 a little practice. 



For example, the curve of the radius of 1,110 meters, at a proportionate 

 scale of t2 00 ; lies between 88*5 and 89 '0 of the curve scale, and amounts to 

 nearly 88 '9. 



As, however, in most cases, round numbers, without fractions, are chosen 

 for the radii, the radius can always be determined with the greatest accuracy. 



291. Calliper Apparatus, for accurately determining dia- 

 meters and lengths up to 150 mm. 



A. Meissner (If. Muller and F. Reinecke), Berlin. 



The calliper apparatus is to be employed for the exact determination of 

 diameters and lengths, as far as 150 millimeters ; the y^- part of a milli- 

 meter by estimation, and -^~ millimeter by direct reading by means of a 

 microscope. 



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