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onds and tenths of seconds； it rarely happens that the accordance is perfect。
The transit instrument used by Captain Sabine was thirty inches in length； and the wires are stated to be equi…distant。 Out of about 370 transits； there are eighty…seven； or nearly one…fourth； which have the intervals between all the wires agreeing to the same； the tenth of a second。 At Sierra Leone； nineteen out of seventy…two have the same accordance； and of the moon culminating stars； p。 409； twelve out of twenty…four are equally exact。 With larger instruments； and in great observatories； this is not always the case。
Captain Kater has given； in the Philosophical Transactions； 1819； p。 427； a series of transits； with a three and a half foot transit； in which about one…eleventh part of them only have this degree of accuracy； and it should be observed that not merely the instrument； but the stars selected； have； in this instance； an advantage over Captain Sabine's。
The transit of M。 Bessel is five feet in length； made by Frauenhofer； and the magnifying power employed is 182； yet； out of some observations of his in January； 1826； only one…eleventh have this degree of accordance。 In thirty…three of the Greenwich observations of January； 1828； fifteen have this agreement； or five…elevenths； but this is with a ten…feet transit。 Now in none of these instances do the times agree within a tenth of a second between all the wires； but I have accounted those as agreeing in all the wires in which there is not more than four…tenths of a second between the greatest and least。
This superior accuracy of the small instrument requires some explanation。 One which has been suggested is； that Captain Sabine employs a chronometer to observe transits with； and that since it beats five times in two seconds； each beat will give four…tenths of a second； and this being the smallest quantity registered； the agreement becomes more probable than if tenths were the smallest quantities noticed。 In general； the larger the lowest unity employed the greater will be the apparent agreement amongst the differences。 Thus； if； in the transit of stars near the pole； the times of passing the wires were only registered to the nearest minute； the intervals would almost certainly be equal。 There is another circumstance； about which there is some difficulty。 It is understood that the same instrument；the thirty…inch transit； was employed by Lieutenant Foster； and it has not been stated that the wires were changed； although this has most probably been the case。 Now； in the transits which the later observer has given； he has found it necessary to correct for a considerable inequality between the first and second wires （See Phil。 Trans。 1827）。 If an erroneous impression has gone abroad on this subject； it is doing a service to science to insure its correction； by drawing attention to it。
Should these observations be confirmed by other observers； it would seem to follow that the use of a chronometer renders a transit more exact； and therefore that it ought to be used in observatories。
Among the instruments employed by Captain Sabine； was a repeating circle of six inches diameter； made by order of the Board of Longitude； for the express purpose of ascertaining how far repeating instruments might be diminished in size：a most important subject； on which the Board seem to have entertained a very commendable degree of anxiety。
The following extract from the 〃Pendulum Experiments〃 is important：
〃The repeating circle was made by the direction； and at the expense of the Board of Longitude； for the purpose of exemplifying the principle of repetition when applied to a circle of so small a diameter as six inches； carrying a telescope of seven inches focal length； and one inch aperture； and of practically ascertaining the degree of accuracy which might be retained； whilst the portability of the instrument should be increased； by a reduction in the size to half the amount which had been previously regarded by the most eminent artists as the extreme limit of diminution to which repeating circles； designed for astronomical purposes； ought to be carried。
〃The practical value of the six…inch repeating circle may be estimated； by comparing the differences of the partial results from the mean at each station； with the correspondence of any similar collection of observations made with a circle； on the original construction； and of large dimensions； such； for instance； as the latitudes of the stations of the French are； recorded in the Base du Systeme Metrique： when； if due allowance be made for the extensive experience and great skill of the distinguished persons who conducted the French observations； the comparison will scarcely appear to the disadvantage of the smaller circle； even if extended generally through all the stations of the present volume； but if it be particularly directed to Maranham and Spitzbergen；at which stations the partial results were more numerous than elsewhere； and obtained with especial regard to every circumstance by which their accuracy might be affected； the performance of the six…inch circle will appear fully equal to that of circles of the larger dimension。 The comparison with the two stations； at which a more than usual attention was bestowed； is the more appropriate； because it was essential to the purposes for which the latitudes of the French stations were required； that the observations should always be conducted with the utmost possible regard to accuracy。
〃It would appear； therefore； that in a repeating circle of six inches； the disadvantages of a smaller image enabling a less precise contact or bisection； and of an arch of less radius admitting of a less minute subdivision； may be compensated by the principle of repetition。〃
Captain Sabine has pointed out Maranham and Spitzbergen as places most favourable to the comparison。 Let us take the former of these places； and compare the observations made there with the small repeating instrument of six inches diameter； with those made by the French astronomers at Formentera； with a repeating circle of forty…one centi…metres； or about sixteen inches in diameter； made by Fortin。 It is singular that this instrument was directed； by the French Board of Longitude； to be made expressly for this survey； and the French astronomers paid particular attention to it； from the circumstance of some doubts having been entertained respecting the value of the principle of repetition。
The following series of observations were made with the two instruments。 ＇I have chosen the inferior meridian altitude of Polaris； merely because the number of sets of observations are rather fewer。 The difference between the extremes of the altitude of Polaris； deduced from sets taken above the pole by the same observers； amounts to seven seconds and a half。＇
Latitude deduced from Polaris； with a repeating circle； 16 inches diameter。BASE DU SYSTEME METRIQUE； tom。 iv。 p。 376。 1807。
Number of Latitude Names of Observers。 Observations。 of Formentera。
deg。 min。 sec。 64 38 39 55。3 Biot 100 54。7 Arago 10 56。2 Biot 88 56。9 Biot 120 56。7 Arago 84 54。9 Biot 100 56。5 Arago 102 57。1 Arago 80 54。5 Biot 88 53。3 Arago 90 53。6 Arago 88 53。8 Arago 92 53。7 Arago 42 55。6 Chaix 90 54。1 Chaix 80 53。9 Arago
Mean of 1318 Observations； 38deg。 39min。 54。93sec。
*
Sets of Observations made with a six…inch repeating circle； at Maranham。
Star。 Number of Latitude Observer。 Observations。 deduced。
deg。 min。 sec。 alpha Lyrae 8 2 31 42。4 Capt。 Sabine alp