168 Mr Galbraith on Trigonometrical 



\ (I + 0=51° 13' log M (tab. IV.) 7.994069 x gives log. P=7.992935 

 M' =184282.44 log. . 5.205484 P=427511. 43 log. 5.630948 



»»"= 0' 30' 17".8 log. 3.259553 p"=l°10' 6".l log. 3.623883 



l=ol 28 38.5 



Xrr50 58 20.7 COS . . 9.79913 1 (Z+^')cosec. 0.10817' 

 /'&Xcor = — 53. 1,/' Prop. log. 0.40954 I 



V =50 57 27. 6, «=1 51 19.6 p. 1.0.20867 . • 0.20867 



c . . . = 1 26 47.0 Prop. log. . . 0.31684 



Calais bears , S. 66 40 52.0 E. from Greenwich. 



Greenwich bears N. 65 14 5.0 W. from Calais. 



The corrections from Table III. for tangents would be — 2".2 for u, 

 and — 1".2 for c, -which are too great, making these 1° 51' 17".4, and 1° 26' 

 45".8 respectively, and even for such considerable distances, these are less 

 than would arise from a slight variation in the values of the earth's axes. 



Hence this last method of computing /, u, and c, is sufficiently accurate 

 for cases of the greatest nicety, is by far the most simple ; and on that 

 account, it is recommended to nautical surveyors, who have always a 

 table of proportional logarithms. 



By some surveyors, the log. sine of / or /', as the case may happen, is 

 employed to compute c, and this plan is certainly very simple, since that 

 Jog. sine is already found by a previous calculation, but it is not suffi- 

 ciently accurate for nice purposes, as in our first example the error would 

 be -f- 6" ; and if this source of error be continued through a considerable 

 series of triangles, in nearly the same direction, the accumulated error 

 would be quite inadmissible in very ordinary operations. 



In making the necessary observations, the instruments employed should, 

 by judicious management, be used, so as to produce the most accurate 

 results of which they are susceptible. Borda's repeating circle, and the 

 repeating theodolite, as constructed and employed on the continent, pos- 

 .vess considerable facilities for this purpose. The smaller classes of cir- 

 cles made in this country, do not, in general, possess the property of re- 

 petition ; but to gain this, when thought necessary, a repeating stand has 

 jjeen frequently supplied. It adds, however, greatly to the price, as well 

 ns to the weight of carriage, and consequently, this addition is frequently 

 dispensed with. To reduce or destroy any small error in the azimuth 

 circle, Troughton directed the observer to " turn the whole instrument a 

 ^'mall quantity on its stand, and, upon readjusting it, again to measure 

 the required angle." This method, no doubt, is advantageous, but it 

 does not give all the advantage of which it is susceptible. To gain this, 

 I propose to suggest the following method, which I have frequently used 

 to advantage. Let r be the number of repetitions required, v the num- 

 ber of verniers, or reading microscopes, and c the change of position of 



QgAO 



the first vernier, as A, then c = (10) 



