244 * New Method of reducing Luna?- Observations. 



apparent distance of the limbs from the highest point in the 

 distance — or its prolongation, that is, from that point in a great 

 circle drawn through sun and moon, where the effects of pa- 

 rallax and refraction in distance is 0, — then is 



tang A= tT^¥ i?tL^ it s and A ' = \d + r + A-iD, 



b tangi (H + h). tangi D * 2 ' 



whence we obtain the apparent altitudes of the points of con- 



which can also be found by 

 H'— H = r. tang H tang (|D-A) and h 1 ' -h = r' tang h . 

 tang (JD'+A) and adding H/ — H and h! — h to the 

 apparent altitudes of the centre above the sensible horizon 

 and subtracting from the sun the change of refraction from 

 H' to H and K to h. But if A >£ D, H'-H is to be sub- 

 tracted from the greater altitude, and the change of decli- 

 nation to be added thereto. The same is to be observed when 

 the distance of the moon's remote limb from a star is ob- 

 served. It being, however, not so much an error in the alti- 

 tude as an error in the refraction which materially affects the 

 calculation, and this refraction not being sensibly altered by 

 a few seconds of change of altitude, the change produced by 

 a change of refraction in the altitude may safely be neglected. 

 For the apparent altitudes of the points of contact of the sun 

 and moon above the horizon, compute strictly the refraction 

 g and g' with regard to barometer and thermometer, and add 

 the sums of these refractions in altitude to the apparent di- 

 stance of their limbs. From the same apparent altitudes of 

 the points of contact above the sensible horizon, find, by ap- 

 plying thereto the above-stated reduction, the altitudes H' and 

 H with respect to the true zenith, and deduct from each the 

 corresponding refraction p found before, and compute for the 

 rest the parallax in altitude i: and ir f , and subtract their sums 

 x + tt' from the observed distance augmented by the refractions, 

 and call the rest d + g + g' — 7r — if — 8. 



Find also for each altitude the corrections g— it and §' — n' ; 

 then is 



= 8 cos(H' + jtf-A').(g-») cos {N + jd + A 1 ). (j-J) 

 cosH' cos (id— A') cos^cos^d + A/) 



cos (H' + \d- A') cos [H'-(j- d- A')] {q -**) . sin l" 



+ 2tangdcos 2 H'cos*(£tf--A') ~ 



cos {h' + %d + A) cos [#— (1 d + A 1 )] (g 1 - n')\ sin 1" 



+ 2 tang d cos 2 h! cos 2 (£ d- A') + + 



[To be continued.] 



C. RUMKER. 



