302 



REPORT — 1865. 



Fig. 1. 



its length, expressed in parts of the moon's 

 semidiameter, m the same measured in 

 revolutions of the micrometer, C the point 

 of the second order whose position is to 

 be ascertained, and AC the line whose 

 length is to be determined for this purpose. 

 The position angles of the lines AB and 

 AC being determined at the time of ob- 

 servation, the angle yp or inclination of AC 

 to A B is known, and the angle <p, or in- 

 clination of AB to the line of abscissae 

 being determined by the formula 



tan <p— x_ x , > 



where X and Y represent the coordinates 

 of A, and X' and Y' the coordinates of B, the inclination of A C to the Hue 

 of abscissae =p — \p. Now if the true distance between A and C in micro- 

 meter revolutions = m", then AC=- — , expressed in parts of the moon's 



m 



semidiameter. 



Kesolving AC into the coordinates x' and y', we have x'=ACcos (<£—»//) 

 and y'=AC sin (0 — 1/>). Now X and Y are the coordinates of the point A, 

 and x and t those of the point C, therefore x=X— x', and t=Y— y'*. "We 

 have consequently for the latitude sin /3=x, and for the longitude 



sin X=t sec /3. 



In consequence of the greater foreshortening of the lunar features in pro- 

 portion as they may be removed from the middle of the disk towards tbc 

 limb than as represented in the true orthographical projection, Beer and 

 Miidler considered it necessary to limit the points to be determined by mea- 

 surements of the second order to such as lie near the sides of their measured 

 triangles, of which they give the sides and angles in ' Der Mond,' pp. 78-83. 

 These measured triangles amount to 176. They also considered it important, 

 both for convenience and accuracy, that the angle \p should be small ; and if 

 it were necessary to include a larger angle, the distance AC should be 

 shorter than if the angle were smaller. It would appear from the example 

 given on p. 87 of ' Der Mond,' that their measurements were effected on the 

 line AB, from the point A 



towards B as far as D (see Fig. 2. 



fig. 2), at which point they 

 were stopped by the micro- 

 meter wire at right angles to 

 AB, bisecting the point of the 



second order, C. This measure, in', from A to D, they called the curtate 

 distance ; and from this they determined the true distance, m", by the for- 

 mula m"=m' sec \p. Beer and Miidler's measures of the second order were 

 made when the points were near the terminator, or boundary behveen light 

 and darkness. 



The Committee has not only given a considerable share of its attention to 

 the preparation of Forms Nos. 1, 2, 3, and 4, but also to the subject matter 

 to be entered in them. The resolution appointing the Committee states, 

 " That the Forms are for registering the various craters and visible objects 



* Or, as in the figure, X -(- x' and Y + y'. 



