LUNAR CALCULATIONS. 



iible circumstances ; that is to say, when the air holding 

 a, certain quantity of water in solution, shall be forced to 

 deposit it all at once in the solid form. We see conse- 

 qucnlly that in this case, without hav ing recourse to the 

 existence of a frigorific principle, the hoarfrost falling on 

 the sides of the funnel will be guided toward the edges of 

 the plate, where a ring of ice will be formed before the 

 middle shall become congealed. 



253 



XVI. 



Practical Rules for reducing the apparent Distance of 

 the Moon from (he Sun or a fixed Star to the true Dis^ 

 tance^ for the Purpose of ascertaining the Longitude 

 of the Place of Observation, Bj/ a Correspondent. 



-A.T some former periods of my life I was not unfre- origin of the 

 quently in the habit of amusing myself with practical Investigation, 

 astronomy, and, amongst other departments of it, with 

 what are usually called the common lunar observations. 

 In the course of these it was impossible to avoid remarks 

 ing that none of the rules given atth« end of the " He- Former rules 

 quisite Tables" for reducing the apparent to the true dis- Jhensome to 

 tances are by any means so short, or so easy to be remem- the memory. 

 bered, as might be wished; and that it would be highly 

 desirable to diminish the labour of this process. I was, 

 indeed, previous to the investigation of the methods here- 

 after described, usually accustomed to prefer the direct 

 solution of the two triangles, in the former of which the 

 apparent co-altitudes and observed distance are given, 

 and the vertical angle required, and in the other of which ^ 



the true co-altitudes and azimuthal angle are given, and 

 the base or true distance required. The following me- 

 thods of performing this reduction, which I then hit upon, 

 appearing however to me to be somewhat more eligible 

 than any others which I have seen, I shall venture to 

 communicate them to the public through the medium of 

 the Philosophical Journal. They are all founded on the Analogies on 

 t>ro following well-known analogies, viz. Tliat the r«ct- which the fol- 

 angle of the sines of the sides containing the vertical a'J^Jfounded* 

 Vot.XV.— Nov. 1806. L 1 angle ^ ^ ^ 



