342 Mr Galbraith on Trigonometrical Surveying 



4. Prop, log m = log cosec t + log cos X + prop, log p, in 

 which m is the azimuth reckoned from the north reduced to the 

 horizon, which, compared with a referring lamp * by means of 

 the horizontal circle, gives the azimuth along with the lati- 

 tude at any point of the star's revolution. The usual formula 

 for computing the effect of a level reading from a central 

 zero upon the zenith distance is 



lJfi~*>* .... (C) 

 2 n 



in which / is the effect, e the sum of the readings of the scale 

 at the eye-end of the telescope, o that of the object-end, a" 

 the value of one division of the scale of the level in seconds, 

 and n the number of observations. The scale of my level 

 originally read to three seconds, but on considering the pre- 

 ceding formula (C) should it become 2", then the formula itself 

 becomes 



1 = 0=1 .... (D) 

 n 



Whence, in this case, it is neither necessary to multiply by the 

 value of the divisions of the scale, nor to double the number of 

 observations, to get the effect of the level, but merely to divide 

 the difference of the sums of e and o by the number of obser- 

 vations simply, at the same time taking care of the sign to 

 correct the zenith distance for the effects of the level. On 

 this account I got Mr John Adie to redivide the scale of my 

 level in accordance with these views previous to commencing 

 my observations this season. 



Having made these preliminary remarks so that every thing 

 relative to my operations may be fully understood, I shall re- 

 cord the first series of observations, and perform the compu- 

 tation at full length, so as to render the whole operation clear 

 and distinct to every one having a very ordinary knowledge 

 of such subjects. 



* A distant lighthouse will frequently answer the purpose of a referring 

 lamp very successfully. 



