Mr. Rumker’s Method of reducing Lunar Observations. 373 
GENUS AND SPECIES. STRATA AND LOCALITIES. 
New genus allied to Scopelus ... Engi, canton Glaris. 
E Placoid fish not yet named.... ae Shale.) North Stafford. 
E Placoid fish not yet named.... (Coal Shale.) North Stafford. 
E Placoid fish not yet named.... (Coal Shale.) North Stafford. 
E Placoid fish not yet named.... (Coal Pier North Stafford. 
Scomberoid not yet named ... (London Clay.) Sheppey. 
c Ten species not yet named.... (London Clay.) Sheppey. 
c New genus not yet named.... (Tertiary Beds.) QEningen. 
LXIX. On a new Method of reducing Lunar Observations 
Jor the Determination of the Longitude. By Cuaries 
RumkeEr, Esq., F.R.A.S.* 
To Lieut.-General Sir Thomas Macdougall Brisbane, K.C.B., 
Pres. RS. E., F.R.S.L., F. Ast. S., §c. 
Sir, 
HE lively interest which you took in the determination of 
the longitude by lunars, and the success which attended 
your observations, animate me to submit the following me- 
thod, admitting of greater accuracy when either altitude is 
low, to your approval and patronage. Allow me to remind you 
here, that already when I had the honour of accompanying 
you on your passage to Australia, I had occasion to allude to 
the necessity of a more strict method, suitable to the circum- 
stances. ‘This subject has since been treated by a celebrated 
astronomer. His method appears to me, however, not likely 
to be generally adopted by seamen, and requires, moreover, a 
particular ephemeris, which becomes useless on ordinary oc- 
casions, when the usual methods answer every purpose. 
I hope, therefore, that the following method, which re- 
quires no other tables than the Nautical Almanac, and may, 
according to circumstances, be computed with more or less 
precision, will meet your approbation. 
The object of the present lines is to correct the error com- 
mitted in the usual methods of clearing the apparent di- 
stance between sun and moon by taking out the refraction 
for the central altitude of both bodies, whereas it is the re- 
fraction for those points of their limbs, the distance of which is 
actually measured, that should be used in the calculation. 
As introduction, it may not be useless to remark, that the 
usual methods of clearing the distance, supposing the alti- 
tudes known from observation, can be classed into direct and 
approximative ones. For thus, as all the former methods 
are derived from the equation existing between the sides of 
* Communicated by Sir Thomas M. Brisbane, K.C.B., &c.. A portion 
of this paper was inserted in our Number for October last : this having re- 
quired some corrections, we now give the Communication entire. 
