A NEW FORM OF TELEMETEK. 617 



horizontal distance. In this respect the instrument has. OA-er the 

 tacheometer type of instrument, the same advantage that is pos- 

 sessed by the omnimeter. 



Any pairs of vahies of y that makes the factor in = g[i' j {g ^ (/') 

 a simjile integer as 100, 80, 50, &c., are to be preferred for con- 

 yenience. For example, if a staff be graduated to -Olft., the 

 horizontal distance will be as many feet as there are hundredths 

 in the difference of the staff readings, provided a pair of grades be 

 selected such as will make m = 100. 



With a view doubtless of facilitating in this way the use of the 

 telemeter, the inventor has marked the circle with grade values, 

 which greatly vary in different parts of the instrument. For tele- 

 metric purposes greater precision could be attained by graduating 

 the circle in the ordinar^y way and carrying a table of grades with 

 the corresponding circle readings ; to these the index might be 

 set with great accuracy by means of a vernier in the usual way. 



The grade limit is double the angle of inclination between the 

 axes, and in general it is obvious that this inclination is a funda- 

 mental constant governing the operations of the instrument. The 

 angle of inclination of the telescopic sight-line at any part of the 

 arc may be thus found — 



In the figure suppose the sight-line to be turned from the 

 initial position through the arc 6, measured on the inclined 

 graduated circle P P', so as to occupy the position O P' (O is the 

 intersection of the inclined axis and the sight-line, and O' the 

 centre of the graduated circle). By projecting P' on O' P, and 

 observing that if p" be vertically above P' and in the horizontal 

 plane through O P, jo 2^'=p" P •> it is evident that the angle />" O P' or 

 7 is given by the equation 



sin. 7 =: /: vers. .... (2) 

 in w^hich, if we put i for the angle of inclination between the axes, 



k = i sin. 2 I (3) 



The equation (2) may also be written 



this last being required for computing the graduation reading 

 corresponding to required grades. Thus with its aid we can select 



