86 



These two rays form the basis of this method of measuring, and the distance from 

 the telescope to any given point will be proportional to the space between the lines at 

 that point (see Fig 2). 



Fig. 2. 



In the prismatic stadia the two spider-lines are dispensed with, and in their stead a 

 prism is used in such a way that a double image of the target is formed. The observer, 

 by means of a suitable adjustment, then brings the two images to coincide, whereupon 

 the desired distance is read, either directly or indirectly, upon the rod. 



Since the angle, Fig. 2, between the bent ray and the direct ray is constant, the 

 employment of the prism obviates the variation to which the angle is subjected by the 

 use of the spider lines. 



The telescope for use with this stadia must be chosen to suit the purpose in view. 

 For a hand telescope, 10 diameters magnifying power is quite powerful enough. On the 

 other hand, if a substantial tripod be used, the higher the power, up to 60 diameters, 

 the better. However, telescopes of 20, 30 or 40 diameters do excellent work. The 

 telescope should give ample light, and upon a tripod an inverting telescope can be used 

 quite as handily as a terrestrial one, provided an agreement is made with reference to 

 the targets so as to avoid confusion. 



The two images, produced by the direct and bent rays respectively, have a strong 

 analogy to the two images in a sextant. The sea captain brings down the sun's image 

 with one glass till he gets contact between the sun's disk and the horizon, and the angle 

 is then read from the vernier of the instrument. With the prismatic stadia-telescope 

 the lower image is brought into juxtaposition with the upper one, and we read the 

 amount that the lower image has cut off upon the upper one. This reading gives us the 

 displacement of the image, and from this we can compute the distance. 



Prof. Richards found that a prism having an angle of 1 : 100 gives the best re- 

 sults for long or short distances, and that a telescope of about 30 diameters is the best 

 power, although good results can be obtained with other powers. 



The advantages claimed for this prismatic stadia-telescope as compared with the 

 usual forms read by spider-lines in the telescope are : 



1st. The starting-point for the measurement is within the prism, instead of being at 

 an imaginary point some distance in front of the objective. 



2d. Only one observation is required for measuring a distance, and there is there- 

 fore only one personal equation instead of two. 



3d. The portion of the self-reading target which is to be read is the only part that 

 is distinct. It is therefore unnecessary to hunt for the reading. 



4th. The prismatic stadia-telescope can be used in the hand for short distances. 

 This is impossible with the spider-line instruments. 



5th. Long distances can be satisfactorily measured by the tape and sliding-targets, 

 but not with the spider-line. 



6th. The extreme variation of this Instrument as found by Prof. Richards is from 

 .2 per cent to .052 per cent. The extreme error will therefore be from + .1 per cent 

 down to + .026 per cent, diminishing as the distance increases, while the error of the 

 spider-line stadia may be as high as .4 per cent, and often is .2 per cent, and does not 

 diminish with distance. 



In making an observation we must first focus the two images, next rotate into 

 juxtaposition, and finally read the distance. 



The target is made in two forms, the self-reading rod and the tape-target. 



Self-reading rods should be prepared for each prism according to its ratio or factor ; 

 but it appears probable that prisms can- be made that will vary only between the ratios 

 1 : 100.2 and 1 : 99.8, and thus vary not more than 0.2 from the ratio of 1 : 100 

 Measures will, therefore, be taken for preparing rods with standard graduation of 1 : 

 100, which will be near enough for most purposes. 



If it is desired to attach this prismatic arrangement to an instrument already made 

 it will be necessary to s"nd us the telescope. 



For a pamphlet Riving a detailed description and method of using apply to either 

 Prof. Richards, Massachusetts Institute of Technology, Boston, Mass., or to us. 



