138 Goniometric Vroblems. 



shows also the great care that he took in measuring the 

 angles, and in conducting the whole of the operations. 



It cannot be too stron<rlv recommended to observers to 

 measure all three of the angles, several times, on diflerent 

 parts of the arc of the instrument, and then to take a mean 

 of them all. If time will permit, this should be repeated 

 for several successive days, at all hours of the day; for it 

 has been strongly suspected that there exists a lateral as well 

 as a horizontal refraction. 



It sometimes happens that the sun illuminates only one- 

 half of an object ; and the observer, if he is not on his 

 guard, will bisect the dark part of the object instead of 

 takinor its centre. This may be avoided by waiting till the 

 sun is obscured, or causes an equal illumination on both 

 sides of it; or bv choosing, if possible, such objects as are 

 projected on the sky by rays drawn from the observer's eye ; 

 then the object appearing dark, and the sky behind it being 

 liorht, he cannot fail of bisecting it properly with a little 

 attention. 



The height of a signal is of more consequence than its 

 width in geodesic operations ; for it is evident, the wider it 

 is, the more uncertainty there will be in bisecting it. De- 

 lambre took -^^^x; ^^ 'he greatest distance for the height 

 of his signals, whence its height appeared under an angle 

 of 3l". Or if D = the greatest distance of a signal, H= its 

 required heiglit; then he made H = D 5, 3l" = 000015 D, 

 and the base he made one-third of the height. 



Care sh )uld be takea that ibe sides of the triangles are not 

 chosen too long or too short in comparison of the length of 

 the base. A side should never subtend a less angle than 25" 

 on any account. When the chain of triangles is long be- 

 tween the first base and the base of verlllcation, the sides of 

 the trianii;les may be so chosen as to increa-;e in length gra- 

 dually till about the middle, and then to decrease in the 

 same manner from the middle to the base of verification. 

 By this means one or two triangles may be saved without 

 sensibly diminishing the accuracy; and the advantage will 

 be, that so much trouble and conipiitatlon will be saved. - 



The strictest attention possible should be paid to the ad- 

 justment 



