90 Proceedings of the Royal Society of Victoria. 



^are also adapted to tins method. At sea, the reductions are 

 generally made on the differential principle, mostly by the 

 aid of Thomson's tables, which give in a convenient shape, 

 the result of an immense amount of labour, as the author 

 stated that he solved more than (S0,000 lunar distances in 

 their construction ; but for hydrographic and land observa- 

 tions, they are not sufficiently precise. In these cases, the 

 rigid formula v/as, until lately, generally applied. Aljout 

 thirty years ago, however, Chauvenet, in his great work on 

 •Special and Practical Astrononi}', gave a new investigation 

 and tables for its application, by means of which tiie vvliole 

 of the corrections can be taken into account, and the result 

 obtained with nearly the accuracj^ of the laborious method 

 of Bessel, who, as Chauvenet remarks, is the unly one who 

 has given a theoretically exact solution of tlie problem. 



From the many hundreds o+" lunar observations I have 

 taken in Australia, T select ray observations of the last three 

 years, as I wish to show the degree of dependence on them 

 in the present state of the Nautical Almanac. They were 

 ■all observed at my quarters, a little to the south-west of the 

 Observatory. The insti'ument was a pillar sextant, Trough- 

 ton No. 1139, it was made at the beginning of this century, 

 •and has been in my possession nearly forty years, during 

 the whole of which time the index error, which is measured 

 at each observation, has barely varied half a minute of arc, 

 and the greatest excentric error is about twenty seconds. 

 The objects observed, have been in every instance the sun 

 and moon, which, from their slower relative motion, are 

 theoretically less suitable than the moon and a star ; but I 

 find the results to be actually better, owing to the delicate 

 •contacts that can be made with two discs, and the advantage 

 of daylight in noting the time and reading off the arc. 

 Only one coloured glass has been used in all the observa- 

 tions, the equality of brightness of the two images having 

 been obtained by altering the distance of the telescope from 

 the plane of the instrument. No special selection of time 

 has been made for observing, indeed from the fact that I 

 keep my sextant at home, most of the observations have 

 been made before 8 a.m. oi- after 5 p.m., when one of the 

 •objects is usually rather low, whereas on board ship the 

 most favourable times could always be chosen. The baro- 

 meter and thermometer liave been read immediately after 

 -each observation for the proper correction of the refractions, 

 iind the reductions have been made by means of Chauvenet's 



