806 DESCKIPTION OP BANG'S PLATOMETER. [1854. 



the cone is that line in which a plane parallel to the grooves of In practice it bus been found convenient to make the readings 



the frame .A would intersect the cone ; and with two binding give square inches, tenths, and hundredth pan of square inches, 



screws to retain it. al that height. The weights of .-ill the pans Jn the instrument represented in Pig. 1, a complete revolution 



are so arranged thai the tracing point just presses lightly on the of the wheel indicates 20 square inches, and in order to carry on 



map without snatching it. the indications as far as 100 inches, a second toothed wheel T, 



is placed so as to receive motion from a pinion oh the arbor of 



The effeel of this construction is thai a Blight force applied to i. i„ manufacturing the instruments, the diameters of the in- 

 to the handle H, which is grasped in the hand like a common dez wheels are adjusted so that the divisions may accurately in- 

 pen, maj cause the whole instrument to roll along the paper dicate square inches, by trying them frequently on the outline of 

 forwards or backwards; or may merely cause the frame F, an oblong figure of about 100 square inches engraved on a cop- 

 with the tracing point and index wheel to move sideways to the ,„. r plate. The diameter of the wheels are slightly lessened at 

 right or left; or may cause a combination of these motions, so each trial, until al length they indicate precisely the area which 

 that the tracing point may he guided along any line drawn on had previously been ascertained by means of very .■.curate mea- 

 the map. When the tracing point is moved to the right or left, surements with a standard scale tinder a microscope, to be tl at 

 the rollers, B 15, remaining stationary, the index wheel is merely f t ] le figure engraved on the copper. They are then ready to 

 carried along the edge of the cone without receiving any revolv- indicate in standard square inches the area of any other figure, 

 ing motion. But when the tracing point is moved forwards or 



backw aids, a forward or backward' revolving motion is imparted Itia found that in passing the tracer over lines oblique to the ma- 

 through the rollers and cone to the index wheel. The ratio of this Ihine, there is a slight retardation of the index wheel, so that the 

 motion to the forward or backward motion of the tracing point is reading is a very little more or less than the tnie area, depending 

 not uniform, but depends on the diameter of that part of the °n the position in which the figure is presented to the instrument. 

 cone with which the index wheel happens to be in contact, which This retardation is very small, and practically it is destroyed by 

 again depends on the distance from the apex of the cone. If turning the figure half round, and again tracing it and noting the 

 we suppose the index wheel to be at the apex of the coDe, and area. The effect of the retardation is now equal, and contrary 

 imagine a line to be drawn on the map through the tracing point to that in the first tracing, and the average of the two is the true 

 and perpendicular to the axis of the cone, then as the tracing area; and this result was found on experiment to be a little 

 point and index wheel have the same lateral motion, it is obvious more accurate than the results of very careful measurements 

 that the revolving motion of the index wheel will be in propor- m ade by scales and calculations in the ordinary manner. As a 

 tion to the backward or forward motion of the tracing point mul- practical test of the value of the Platometer in this respect, an 

 tiplied by its distance to the left of that line, which we will call enclosure of an estate plan was measured very carefully by scale 

 the zero line. From this it follows that if the tracing point be and calculations. It was then rc-measured. The small differ- 

 guided completely round the boundary of any enclosure, the ence between the two results was an indication of the degree of 

 resulting forward revolving motion of the index wheel will be accuracy obtained. The same enclosure was then measured 

 proportional to the area of that enclosure. This becomes more tw >ce by the Platometer, and the difference between its results 

 clear, if we imagine the enclosure to be divided into very narrow being in like manner an indication of their degree of accuracy, a 

 sections by lines parallel to the grooves of the frame A, and attend comparison between the two differences gave the means of judging 

 to the effect on the index wheel when the tracer passes over the of the accuracy of the two methods. In an experiment made on a 

 ends of one of their sections. When the tracer passes over one SIn gl e enclosure, it happens sometimes that this indication is in 

 of the ends, the index wheel revolves forward a distance propor- favour of the scale, and sometimes in favour of the instrument; 

 tional to the breadth of the section, multiplied by the distance but the aggregate indications of a number of experiments was 

 of that end from the zero line; as it continues its journey round always found to be m favour of the instrument Thus, in an es- 

 the enclosure, it reaches the other end of the narrow section, and tate plan containing 90 enclosures, each enclosure being measured 

 in passimT over it, the index wheel revolves through a distance separately, there was found: 



proportional to the breadth of the section, multiplied by the dis- By Scale. By Platometer. 



tance of that end from the zero line ; the motion is, however, now Sum of the means of each pair 740-92 ... 741-01 



backward with respect to the former, so that the effect with re- Sum of the differences 2 79 ... 2-44 



o-ard to the section is that the index wheel has revolved forward Greatest difference -17 ... -09 



through a space proportional to the difference between the dis- Least difference -00 ... -00 



tances of the ends of the section from the zero line (that is to This aggregate is in favour of the Platometer as 279 is to 244. 

 sav. the length of the section), multiplied by its breadth, which .,, ' . , , ,. . , . , . , . , 

 is the area of the section. And as the same thing happens with M f^ tna ' s f *f f natl "- e havl ?? completely shown the trust- 

 reeard to each of the sections, into which we have conceived the worthiness of the Platometer, and U being of great value in re- 

 enclosure to be divided, it follows that when the tracer has made s P e . ct J° the SA ] ln S of . time - experimental alterations were made 

 a complete circuit, the sum of the forward and backward revolv- ln lts f°™> wlth f th . e v ! ew cble ^ , of doln ? away altogether with 

 ing motion of the index wheel is a forward motion proportional tbe Ration of the index wheel ,n passing over oblique lines. 

 to the whole area of the enclosure. 0ne , of tbem » presented in Fig. 2. In this the rollers, B B, 



are lessened in diameter; and in order to make the lessening 



This happens with regard to every enclosure, whatever its shape possible they are raised up on another pair of rollers, G G, instead 



or however irregular its outline, so that in calculating an area by of coming in contact with the map. As the space representing 



means of the instrument, we have only to make a small mark a square inch on the index wheel is inversely as the diameter of 



with the tracer on the outline, observe the reading of the index the rollers, by this means the divisions were increased in size, so 



wheel, lead the tracer along the boundary of the enclosure that they read thousandths instead of hundredth parts of an 



till it again reaches the small mark, and again observe the read- inch. It was not found that advantages commensurate with the 



in" - of the index. The difference of the two readings is the area, increased expense of the machine were obtained from this form. 



