178 



♦ KNOWLEDGE ♦ 



[Aug. 29, 1884. 



The apparatus being constructed, it only remains to use 

 it. At 200 metres Jistance station one or more men, and, 

 where you are standing, allow an assistant to hold the 

 instrument at the height you direct him to. Now proceed 

 10 a distance of exactly four paces, of 0'7.5ni. each, from 

 your figures, and ascertain whether their general aspect, as 

 regards height and width, corresponds to that of the men 

 stationed 200 mitres off. If the resemblance is perfect, 

 you are in possession of one of the timplefet and most port- 

 able of telemeters ; if it is not, you will have to begin all 

 over again. You may renew the operation by placing your 

 men at 300 metres, and taking six paces instead of four 

 (Fig. 1). 



The arrangement adopted permits, on holding the instru- 

 ment away from the eye, of diminishing the ditficulty that 

 the latter has of seeing the objective and image simulta- 

 neously. Besides, it lessens the trembling of the hand that 

 holds the apparatus, and which would render observation, 

 impossible in an ordinary stadium placed at OG m. from the 

 eye. 



What is the value oi —1 In the majority of -proportional 



base telemeters the distance sought is .50 times greater than 

 the base. Such a ratio is'very convenient, since it necessi- 

 tates a base of only 20 mfetres for a distance^of^l kilometre 



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Fig. 1 — lleth)d of Estimating Distances. 



Supposing that the apj)aratus has been constructed satis- 

 factorily, the manner of using it for estimating distances 

 •will be readily understood. Let an assistant hold the in- 

 strument in the direction of the troop th;it serves as an 

 oVijective, while you move backward in keeping your eye 

 upon the silhouettes and the objective, and stopping when 

 the figures and men exhibit the same aspect and seem to 

 form part of one and the same group. Then returning to 

 your assistant, you count the number of paces that 

 separated your eye from his hand. Upon multiplying this 

 number by 50, you will obtain a product that will give you 

 in metres the distance sought. 



Notwithstanding the wonderful simplicity of the instru- 

 ment, it is easy to control the accuracy of the principle 

 upon which it is based, first, by reasoning, and then by 

 experiment. 



In the similar triangles, ABC and DEC (Fig. 3), we 

 have the ratio : 



(«) 



x = l—- 

 h 



H and h being constants, I will have to vary -with x, that is 

 to say, with the distance. 



However, as the observer can scarcely measure the bas*- 

 otherwise than by pacing it off, it has seemed preferable, in 

 order to expedite the operation and avoid a conversion of 

 pace measurements into mitre ones, to take a mean pace 

 of 07.5 m. as unity, and to modify the formula so as to all 

 once obtain the distance in metres. 



In formula a, on substituting wxO'75 for I, and making 



-T-x 075=50 (H being equal to 1,6&5) we shall have 



0'249 m. as the value of /(. 



If, however, greater precision were required in the 

 results, the metre might be preserved as the unity of 

 measurement of the base, the silhouettes be given a height 

 of 33 millimetres, and a cord about 30 metres, with knots 

 1 mitre apart, be employed. But it will be readily under- 

 stood that this process, although more accurate, is much 

 less practical. 



Let us now examine the causes of error, as well as their 

 limits. 



The height of a soldier, taken as a base, varies between 

 l'-t5m. and LSm. As the mean height generally ad- 

 mitted is 1'665 m., we should, upon taking this as a basis 



