270 Mr. S. Sharpe on the Reduction to the Meridian. 



of the gorge below this point should have been a precipitous 

 ravine uniformly incrusted with travertin, such as now covers 

 the site of the actual cascade : instead of this, we have a valley 

 included by gentle slopes, except at its upper extremity, where 

 its sides for a short interval become more steep ; nor is there a 

 single particle of the travertin which, on the theQry, ought to 

 have prevailed through its whole extent, except in the neigh- 

 bourhood of the artificial cascatelli, which of course must ne- 

 cessarily produce it, just as the natural cascade does. 



I have now concluded the cursory view which I proposed to 

 take of the phaenomena of geology bearing on theoretical 

 points, and of the inferences which the observers of the school 

 to which I am attached, have thought themselves justified in 

 deducing from them. And I am now happy to leave, I hope for a 

 long time, the field of theoretical, and especially controversial 

 discussion. Having heartily tired myself, and I fear far more 

 tired your readers, I can well say with the copyists of the 

 middle ages: "Explicit, expliceat; ludere Scriptor eat." 



XLVI. On the Reduction to the Meridian. By S. SHARPE, 



Esq. F.G.S* 



TN the well-known formula for the reduction to the meridian 

 " of a zenith distance observed near to the meridian (see 

 Baily's Tables, page 93) : 



x being correction required ; 



P hour angle ; 



L latitude of the place ; 



A polar distance of the body observed; 



Z zenith distance of ditto ; 



_ . e P/cosLsinA\ . , P/cosLsinA\ 2 , 



sm,r=2sin 2 -( r ~ ) 2sm 4 -( ^^ Vcot Z. 



2 \ sin Z / 2 V sin Z / 



When the sun or a planet is the body observed, the additional 

 term + 8.P is usually added: SP being its change of de- 

 clination, proportional to the time P. 



But when this is done, the first term ought to be 



2 sin ^(-^gz + gp > r > wha < is th e same thing, 

 we should add a fourth term 



2 sin*-|sin(PS)-^. 

 Remembering that these two terms containing 8 are to be of 



* Communicated by the Author. 



different 



