Heights of the principal Hills of Dent, fyc. Yorkshire. 87 



equal to U minus P, and the correction must be applied to P 

 with the negative sign, in order to make USP greater than 

 UTP by the angle of correction SPT. These corrections 

 being applied to the readings for the different signals, we 

 form a new register, whence we can immediately find by sub- 

 traction (as before) the angular distance of any two of the sig- 

 nals as observed from S in lieu of T. 



On referring to the distances of some of the more remote 

 signals from the theodolite-stations as measured from different 

 bases, discrepancies, amounting'in some instances to upwards 

 of 100 feet, will be remarked. These differences were occa- 

 sioned in a great measure by the signals having a diameter 

 too inconsiderable for the distance, so that the vertical wire 

 in lieu of bisecting, appeared to efface them *. The formula 

 adopted for obtaining a proper mean of such of the different 

 measurements of a distance as were remarkably discordant, 

 requires to be explained. 



In order to find the distance between the point e and the 

 inaccessible object a, measure from e in different directions 



any number of bases, as ABC, and observe at the two ex- 

 tremities of every base the inclination of that base to a line 

 passing through the point of observation in the direction of 

 the inaccessible object. With these data we shall be able to 

 calculate from each base an independent measure of the re- 

 quired distance ;— but supposing the observations to have been 

 subject to a small uncertainty, limited, for instance, to one 

 minute, required the probable error of each of the respective 

 calculated dist'dnces ? 



By trigonometry, 180° minus the sum of the angles taken at 

 the ends of any* one of the basjes will be equal to the subtense 

 of that base at a. Then if we restrict ourselves in our calcu- 



* At a distance of 60,000 feet a tower 6 feet in diameter appears under 



an angle of only 21". * 



"O lations 



