489 



SEXAGESIMA. 



SEXTANT. 



490 



per head of the population of the towns. The average sewers-rates 

 of well-drained towns seem also to be about 2i per cent on the rental of 

 the houses. 



It may be added that in the London sewerage there appears to be 

 present about 1 ton of solid matters to every 266 tons of water ; but 

 in very unfavourable cases the proportions of solid to liquid may 

 increase to 1 in 96, or even to 1 in 36 ; the proportion of 1 in 66 is 

 considered to be the largest which is consistent with the safe working 

 of pipe sewers, in which the fluid can move with a velocity of 3 feet 

 per second. 



(Consult ' Reports of Health of Towns Commission," and the various 

 Blue Books on the London Sewers ; ' Transactions of Civil Engineers ;' 

 ' Annales des Fonts et Chausse'es,' &c.) 



SEXAGESIMA, the second Sunday before Lent, or the next to 

 Shrove Tuesday; so named, as being, not exactly, but about the 

 sixtieth day before Easter. Brady, in his ' Clavis Calendaria,' vol. i., 

 p. 175, says, "The name of the first Sunday in Lent having been 

 distinguished by the appellation of Quadragesima, and the three weeks 

 preceding having been appropriated to the gradual introduction of the 

 Lent fast, it was consistent with propriety to call the three Sundays of 

 these weeks by names significant of their situation ; and reckoning by 

 Decades, the Sunday preceding Quadragesima received its present title 

 of Quinr/ua-:eimtt, the second Sexagcsima, and the third Septuar/ciima. 



SEXAGESIMAL, a name given to the system of reckoning in which 

 each unit is the sixtieth part of the preceding, to which, in our day, 

 we are only accustomed by the method of measuring angles and time. 

 The Greeks, and Ptolemy in particular, brought this method into use in 

 astronomical matters, and their successors seem to have attempted to 

 make it a general mode of reckoning. There exist treatises of arithmetic 

 fashioned on this system ; one, for instance by BARLAA.M. [Bioo. Div.] 



In the sexagesimal arithmetic, 17 26' 48" 53"' 9 1 ' stands for 17 

 units + 26-sixtieths of a unit, or 26 minutes or fcrupula prima 

 [SCRUPLE] + 48-sixtietha of a minute, or 48 seconds or tcrupula 

 Kcttnda + 53-sixtieths of a second, or 53 thirds or tcrupula ttrtia + 

 9-sixtieths of a third, or 9 fourths or tcrupula quarta. 



Addition and subtraction are easy enough in this system ; multipli- 

 cation, division, and the extraction of roots are more complicated. If 

 we had, for example, to multiply 7 26' 43" 51'" by 11 47' 18" 56'", 

 each term of one factor must be multiplied by every term of the other, 

 and the denomination of each product must be as high as those of both 

 factors put together. Thus when we come to 43" x 56'", the result 

 must be in fifths (2 + 3 = 5); and 43 x 56 being 2408, we have 2408', 

 or 40" 8". This process was aided by a large sexagesimal multiplication 

 table, which may be seen in Delambre, ' Astronomic Ancienne,' vol. ii. 

 There is also a large sexcentenary table, constructed by John Bernoulli 

 (III.), and published (or republished) by the British Board of Longi- 

 tude. There is little need to give any further account of sexagesimal 

 pro 



SEXTANS (the sextant), a constellation which Hevelius had the 

 singular bad taste to place on the bock of the Hydra and at the feet of 

 the Lion. It comes directly between the bright stars a Leonis 

 (Regulus), and a (or Cor) Hydra;. There are no (tars of conspicuous 

 magnitude in this constellation. 



. 'I' A NT. The history of the sextant was involved in some doubt 

 until the late Professor Rigaud undertook to investigate the subject. 

 The result will be found in the ' Nautical Magazine,' vol. i., p. 351, and 

 No. xxi. The following account is a brief outline of his inquiry. 



The early modern navigators used the crou-ttaff; this was afterwards 

 exchanged for Daris's bact-ttaff, called by the French quartier auylnii. 

 Hooke proposed an instrument for the purpose of taking altitudes at 

 sea, which is very ingenious ; the sun was seen reflected from a plane 

 glass, while the horizon was viewed directly.* Hooke does not seem 

 to have esteemed his invention so highly as it deserved ; for in a sub- 

 sequent lecture on astronomy and navigation, in 1694, he makes no 

 mention of this, but describes a quadrant of a different construction. 

 In 1699, Newton exhibited an instrument to the Royal Society, which 

 is described as " the old instrument mended of some faults ; " and at 

 some later time he communicated to Dr. Halley a scheme for an instru- 

 ment which was probably never executed, but of which a drawing and 

 description were found among Dr. Halley 's papers after his death in 

 1742. (' Phil. Trans.,' voL xliL, p. 155.) 



The date of the invention of Hadley's quadrant wag proved, on 

 examination by the Royal Society, to have been cot later than the 

 summer of 1730. A notice of it was given at a meeting of the society, 

 May 13, 1731 ; and the instrument exhibited May 27. The memoir is 

 published, voL xxxvii., p. 147. 



At the meeting of the society. May 20, Dr. Halley expressed an 

 opinion that the principle of Hadley's new instrument had been dis- 

 covered and proposed by Newton, and a search was made into the 

 minutes of the society to ascertain the fact. The only notice which 

 could be found was that already mentioned, namely, in 1699, and 

 this was clearly an improvement of an old instrument, and not the 

 proposal of one new in principle. Halley, at a meeting on the 16th of 



* Thu in described in II oke's ' Posthumous Works,' p. 903, and was pro- 

 bably prFwnti d to the Royal Society in 1666. In practice, beside* some other 

 objection*, it wuuld have been troublesome to ascertain the ii.dtx error in this 

 construction. 



the following December, expressed himself satisfied that Hadley's 

 instrument was much different from that formerly invented by Sir 

 Isaac Newton. It seems not unlikely that Halley's recollections'were 

 of the instrument which Newton had proposed to him, and the 

 description of which was found among his papers, but that he had 

 forgotten the manner of the communication, and confounded the latter 

 instrument with that which Newton had exhibited to the Royal 

 Society. This is, we think, a very probable failure in the memory of 

 a man of seventy-six, and what many younger persons experience 

 daily. That Halley did not immediately see the advantages of 

 Newton's latter proposal may appear a little strange ; but Halley's 

 forte clearly did not lie in mechanical construction or astronomical 

 observation. 



A little after Hadley's invention, namely, about October or Novem- 

 ber, 1730, Thomas Godfrey of Philadelphia, a glazier by trade, 

 proposed and had executed an instrument which he called a bow, very 

 much resembling Hadley's earlier construction. This was described 

 in a letter to Dr. Halley from James Logan, Esq., dated 25th May, 

 1732. Mr. Logan had put off writing more than twelve months after 

 the instrument was placed in his hands, and this neglect threw some 

 doubt on the originality of the invention, which could only be satis- 

 factorily established by additional evidence. After examination, the 

 Royal Society came to the conclusion that Godfrey's discovery was also 

 original. We think it is clearly proved that the priority is due to 

 Hadley.and that there is no pretence for doubting Godfrey's originality. 

 Some hasty writers, adopting mere hearsay for their guide, have 

 attempted to give the subject a national and patriotic colour, which, 

 unphiloeophical at all times, is a simple absurdity when the contending 

 parties are, as in this instance, of the same race. \Ve have thus tried 

 to give a hasty summary of Professor Rigaud's statements and con- 

 clusions, which we entirely adopt. The perusal of ' the original 

 memoirs will gratify the lover of exact and discriminating research. 

 Hadley's second construction, which is incomparably superior to his 

 first and to Godfrey's bow, scarcely differs from the present sextant. 



The sextant is figured and described in almost every book of 

 navigation, and is so commonly to be met with that we shall be very 

 brief. A is a plane glass, called the index glass, silvered behind, and 

 perpendicular to the face of the instrument. It is fixed on a centre 

 perpendicular to the instrument, and moves with the index bar A B, 

 the end of which, B, slides over the graduated arc. c is a plane glass, 

 the lower half of which, next the instrument, is silvered, and the 

 upper half left clear. It is called the horizon-glass, and should be 

 parallel to the index-glass when the index points to at the beginning 

 of the arc. D is a telescope for viewing the objects observed. This 



should be of good quality and with an inverting eye-piece. In the 

 common quadrants there is merely a plate with a small hole for 

 directing the tight. Suppose a ray of light to proceed from the eye, it 

 will proceed in the direction of the telescope ; and if it falls on the 

 upper or unsilvered part of the horizon-glass, it will pass forward in a 

 continued straight line until it falls upon some exterior object. But if 

 the ray falls upon the silvered part of the horizon-glass it will be 

 reflected to the index-glass (the horizon-glass is so placed as to make 

 equal angles with lines from the eye and index-glass), and again 

 reflected from the index-glass, outwards (that is, from the observer), 

 until it meets some external object. Now instead of supposing the 

 rays to pass from the eye, suppose them to come from external objects 

 to the eye ; then there will be two images presented at the same time, 

 one formed by the rays which pass through the unsilvered part of the 

 horizon-glass, and another formed by the rays which have been pre- 

 viously reflected by the two glasses ; and it is easily shown from the 

 elementary principles ,of optics, that when two objects are thus appa- 



