CIRCLE, MURAL. 



CIRCULATING DECIMALS. 



focal length of 1U feet. The circle is 6 feet in diameter. The 

 divisions are read off by means of six microscopes firmly imbedded in 

 too* piers. The material used in the construction of the instrument 

 w cast-iron. A aimilar instrument ha* been subsequently made by 

 Mr. Simms, for the Royal Observatory at the Cape of Good Hope. 

 The Inuuut-circlc used by Mr. Carrington in the observation of the 

 tars for his Redhill catalogue, has also been constructed upon the 

 plan of the Greenwich instrument. 



An altitude and azimuth circle has been recently introduced at the 

 Royal Observatory, Greenwich, for the special purpose of observing 

 the moon whan aha is out of the meridian. Two distinct circumstances 

 suggested the expediency of this step. In the first place it frequently 

 happens, that when the moon is on the meridian she is concealed from 

 observation by the unfavourable state of the weather; secondly, the 

 moon cannot be seen on the meridian for several days before and after 

 conjunction, by reason of the overpowering effulgence of the sun's rays. 

 By means of the altitude and azimuth-circle, or the altazimuth as it 

 hu been called, this inconvenience has been effectually obviated, the 

 number of extra-meridional observations being about twice as great as 

 the number of observations made when the moon is on the meridian. 

 The altazimuth was designed by Mr. Airy, and constructed by Messrs. 

 ft"*"""' and May of Ipswich, and Mr. Sinims of London. The verti- 

 cal and azimuths! circles are each 3 feet in diameter. The telescope 

 is furnished with on object-glass of 3] inches aperture. The observa- 

 tions with this instrument were commenced on the 16th of May, 1847. 

 A remarkable illustration of their utility in contributing towards the 

 improvement of the lunar theory, has been recently afforded by a 

 comparison of the meridional and extra-meridional observations of the 

 moon made at the Royal Observatory, Greenwich, in the year 1852, 

 with the corresponding results of ' Burckhardt's and Hausen's Lunar 

 Tables.' (' Monthly Notices, R. Ast. Soc.' voL xix. p. 211, et teq.) 

 The agreement of the observed places of the moon with Hansen'a 

 Tables ' (in the preparation of which the extra-meridional observation* 

 of the moon were used) leaves nothing to be desired. 



Besides the works we have already referred to, the astronomical 

 reader may consult, as to the mural circle, Pond's ' Observations,' 1812, 

 p. 236, and 1S25 (where on example is fully worked out), for on 

 account of his two methods, and his memoirs in the ' Phil. Trans.' and 

 'Memoirs of the Astronomical Society;' 'Cambridge Observations,' 

 vols. vL and vii., and Johnson's ' Catalogue of Southern Stars,' 1835. 

 For the transit circle, Wollaston's ' Fasciculus,' preface and appendix. 

 For the altitude and azimuth circle, a paper by Mr. Troughton, 

 'Memoirs of the Astron. Society,' vul. i. |>. 33; and generally, the 

 article ' Circle ' of the Edinburgh Cyclopaedia,' by Mr. Troughton, and 

 Dr. Pearson's ' Practical Astronomy.' Oil the mode of dividing cities 

 and the errors to which their divisions are liable, see GRADUATION, and 

 Troughton ' Memoir, Phil. Trans.,' 1808, p. 105 ; Dr. Robinson's Paper, 

 already cited, and another by the same author, ' Memoirs of the Irish 

 Academy,' 1825 ; two Papers in the ' Memoirs of the Astron. Society,' 

 on the ' Errors of the Cape Circle,' one by Mr. Sheepshanks and Pro- 

 fessor Airy, vol. v. y. 320; the other by Mr. Henderson, vol. viii. 

 p. 141. 



CIRCLE, MURAL. [CIBCLE, ASTRONOMICAL.] 



CIRCLE, QUADRATURE OF THE. [QUADRATURE] 



CIRCLE, REKLECTIXU. [SEXTANT.] 



CIRCLE, REPEATIXU. [Kti'KATi.vu CiBOLE.] 



CIRCLE, TRAXSIT. [C'mcLE, ASTRONOMICAL.] 



CIRCLES OK DECLINATION, ALTITUDE, Ac. The useof these 

 terms is not very well settled. According to some, a circle of decli- 

 nation would mean the parallel of any declination, or the small circle 

 all whose points have the same declination ; that is, a parallel to the 

 equator. According to others, it would mean the circle on which 

 declination is measured, that is, an horary circle passing through the 

 poles. And the same of the other circles. Perhaps the latter sense is 

 the more generally used ; but in all oases the student must bo aware 

 of the difference when he consults a book on the doctrine of the 



. 



CIRCUITS, in English law, denote the periodical progresses of the 

 judges of the superior courts of common law through the several 

 counties of KngUn.1 and Wales, for the purpose of administering civil 

 and criminal justice. The ordinary circuits take place in the spring 

 and summer of each year ; and for several yean past the judges have 

 made winter circuits through the principal counties in the month ..i 

 December, for the trial of criminals. In 1858, the experiment of a 

 Winter Aasise for civil business was tried at Liverpool. All the 

 circuit* take place under the authority of several commissions under 

 the great seal, issued to the judge* and others associated with them on 

 each occasion. [ ASSIZE.] Most barristers practising in the common U 

 courts in London are attached to one or other of the circuits ; and each 

 circuit is constantly attended by a numerous bar. The transaction of 

 judicial business in the prssenco of a professional audience of thin 

 kind, has been justly considered as one of the best securities for the 

 due administration of justice; and in consequence of the system i 

 circuits, this advantage is not confined to the metropolis, but is com- 

 municated to the most remote part* of the kingdom. 



Sine* the statute 11 Geo. IV. and 1 Will IV. c. 70, by which the 

 aneisat system of Welsh judicature was abolished, the circuits of the 

 judges ar* eight in number, and the counties of England and Wale* 



are distributed among them in the following iuanu< !>. >u 



Circuit comprehends the couir N.nthuml 



Cumberland, Westmoreland, and Lancast. 



((hands the counties of Southampton, W . I 



and Somerset, and Bristol; the Oxford Circuit L ,,|,,|, 



counties of Berks, Oxford, Worcester, Stafford, Salop , M..H- 



mouth, and Gloucester ; the Midland Circuit couipreh 



li.uiiptoii, Rutland, Lincoln, Nottingham, Derby, Leicester, and 

 Warwick ; the Home Circuit comprehends the counties of Hertionl, 

 Essex, Kent, Sussex, and Surrey ; the Norfolk Circuit comprehends 

 the counties of Buckingham, Bedford, Huntingdon, Cambridp 

 the Isle of Ely, Norfolk, and Suffolk ; the South Wales Circuit 

 prehends the counties of Glamorgan, Carmarthen, Pembroke, Cardigan, 



Radnor, and Chester ; the North Wales Circuit compn 

 the counties of Montgomery, Merioneth, Carnarvon, Anglesey, Denbigh, 

 Flint, and Chester. 



CIRCULAR PARTS (NAI-IEB'S). A proposition which generalise* 

 the relations between the parts of a spherical right-angled triangle into 

 two only ; first given (with a demonstration) by Napier in his ' .V 

 Logorithmorum Cauouia Descriptio' (ch. iv. 1-8). It is as follows: 

 Let a and 6 be the sides, c the hypotenuse, and A and B the angles 

 opposite a and b, in a right-angled spherical triangle. Then take the 

 complements of the hypotenuse and of the two angles, and the two 

 sides, and write them in order in a perpetually recurring svi i 

 round a circle, as follows : 



Then taking any three parts, one may be made the Middle part, aiid 

 the other two either adjacent extremes, or opposite extremes. Thus 

 80 B being the middle part, a and 90 C ore its adjacent c.v 

 and b and 90 A its opposite extremes. Napier's rules are 



1. Sine of middle^ product of tangents of adjacentt. 



2. Sine of middle = product of cosines of tjctremcs. 



Thus sin. 4 = tan. o tan. (90* A) 



= cos. (90 B) cos. (90 c). 



But we should strongly recommend the student to have nothing to 

 do with this artificial memory, for it involves a process upon every 

 occasion ; and while one person is learning which are the ports, w hich 

 have complements taken, and the rules, another will master the six 

 results, and will have no occasion f.ir any future process. These 

 results ore 



1. Cosine of hyp. = product of cosines of sides. 



2. Cosine of hyp. = product of cotangents of angles. 



3. Sine of Wi=ine of hyp. x sin. ojijKHttt angle. 



4. Tang. of iide = tang, of hyp. x cos. adjacent angle. 



/ 



5. Tang, of i!de = tu\g. oppotite angle x sine of othei 



6. Cos. of j/fc = co8. of oppotite side x sin other angle. 



These pain present analogies which will help tin 

 should recommend them in i . the rules o! irte. 



CIKCCI.AK I'nl.AIM/.ATIoX. (ROTATORY I'OI.AKI/ATIOS.] 

 MKITI.ATlNi; HKCIMAI.S. When a i ..... mioii fr.irt ion cannot 

 bo expressed exactly as a decimal, (lie attempt leads to a never-ending 

 series of figures, any number of which, with the decimal point properly 

 placed, is on approximation to the common fraction, and the more 

 near the greater the number of figures taken. Thus 1 with ciphers 

 affixed and divided by 7, leads to the recurring or circulating series 



142857142857142857 . 



and -1428 is nearly j, but -14286714 much more nearly. Hence it is 

 said that f is a circulating decimal whose period is 142857, and is 



denoted by -142857. Similarly -12:'i denotes '128999 and -0538 



denotes -053636 .... As a part of fractional arithmetic, the rules for 

 converting these fractions into common fractions are useless, though 

 found in most elementary works. One example will be sufficient 

 here. 



14362 = '14302362, 4c. = '1 4 + , fe x '362302. . . . 



