313 SURVEY OF THE COAST 



It is evident that the luminous point which was observed 

 on the tin cone depended on the angle which the sun sub- 

 tended with the line from the observer to the signal, and 

 required of course a small reduction to the centre of the sig- 

 nal. To obtain this element of reduction easily, 1 observed 

 always at intervals the sun to the nearest degree only, as 

 no great accuracy is required, by placing the telescope of 

 the instrument in the shade formed by itself, and reading the 

 stand of the microscope A on the limb. Calculating the ap- 

 parent angle subtended by the mean radius of the signal cone 

 for each distance, 1 formed a small table, and placed it at 

 the head of each station in the Journal of Results. The re- 

 duction was very easy, and was quickly made by a construc- 

 tion and a short multiplication of decimals, of which it is 

 proper to give here the explanation, as well in principle as 

 in practice. 



In Plate VI. fig. 5, let a be the station point of the obser- 

 ver, c the centre of a signal observed from this station, Ibd 

 the mean circumference of the tin cone, and os the direction 

 in which the sun is seen from the station, at the time of the 

 observation. 



For the purpose here intended, it is perfectly allowable to 

 omit the correction of the azimuth of the sun, between the 

 station point and that of the signal (which would be propor- 

 tionate to the convergency of the meridians,) and also to 

 suppose the lines drawn from the different parts of the sig- 

 nal to the observer as parallel, which would vary always less 

 than the apparent radius of the signal.) This permits us to 

 suppose, das=cas—ccs'=fds" . 



By the principles of reflection, the point on the circumfe- 

 rence of the cone which will be reflected to the point a, will 

 lie at d the middle of the angle s'ca, supplement to the angle 

 observed between the sun and the signal. The correction 

 will therefore be proportional to de the sine of acd=i.s'ca, 

 or to the cosine of the complement of it, that is to cosine 

 icas, or half the angle between the sun and the signal. 



