REPEATING CIRCLE. 



REPEATING CIRCLE. 



14 



rent is a rent-seek. Rent-charge may be created either by deed or by 

 will. Sometimes, by the terms of the grant, the grantee of a rent- 

 charge is empowered to enter on the land and satisfy himself for all 

 arrears out of the profits of the land. When a rent-charge is created 

 under the Statute of Uses (ss. 4, 5) with a power of distress and entry 

 upon the land in case of arrear, the person to whom the rent-charge is 

 given obtains the legal estate in the rent-charge, with all the remedies 

 for its recovery, as he would by a direct grant of the rent-charge ; and 

 the same instrument (lease and release) which creates the rent-charge 

 may also make a settlement of the lands charged with the rent. In 

 this way in a marriage settlement a rent-charge may be provided for 

 the wife's jointure. 



An estate in a rent-charge may be either in fee simple, or in fee tail, 

 for lives or for years, according to the terms of the original limitation. 

 A rent-charge of inheritance is real estate, and descendible to the heir ; 

 but a payment that is due belongs to the person representative. There 

 may also be an estate in fee simple in a rent-service created before the 

 Statute of Quia Emptores. A rent-charge in fee simple is subject to 

 curtesy and dower; and also a rent-charge in tail. But if a rent- 

 charge be created and granted to a man and the heirs of his body, 

 his surviving wife will not be entitled to dower if the husband dies 

 without issue. Until the Act 3 & 4 Will. IV. c. 106, a woman was 

 not entitled to dower out of a rent-charge, unless her husband had the 

 legal estate in it. A rent-charge may be limited by way of remainder ; 

 and a new rent-charge may be created to commence at a future time. 



A rent-charge may be discharged in various ways. If a man who 

 has a rent-charge out of certain lands buys any part of them, the whole 

 rent is discharged, for it issues out of the whole of the lands ; and the 

 consequence is the same if he releases all his right in any part of the 

 land. But a man may release part of the rent-charge without affecting 

 the remainder ; and a division or apportionment of a rent by conveying 

 part of it to a stranger is a valid conveyance. If part of the lands 

 which are subject to the rent-charge descend to the grantee, the rent 

 will be apportioned according to the respective value of the two parts 

 of the land. 



A rent-seek, as already mentioned, is not, like rent-service, 

 accompanied with a right to distrain at common law ; but by the stat. 

 4 Oeo. II. c. 28, s. 5, this distinction in respect of remedy between 

 rent-service and rent-seek is abolished ; and the Act also applies to 

 rent-seek created prior to the statute which had been duly paid for 

 three years out of the last twenty years. Other rents, though they 

 belong to one of the three divisions above mentioned, are often 

 distinguished by particular names : thus the rent due from a free- 

 holder is called a chief rent (rcdditue capital!*) ; the rents of free- 

 holders and ancient copyholders of manors are sometimes called rents 

 of assise, being aaiti, or ascertained, and also quit-rents (quieti 

 reddiltu), because they are a quittance and discharge of all services. 



A fee-farm rent is properly a perpetual rent-service reserved by the 

 crown, or, before the Statute of Quia Emptores, by a subject, upon a 

 grant in fee simple. The purchaser of fee-farm rents originally 

 reserved to the crown, but sold under 22 Car. II. c. 6, has the same 

 of distress that the king had, and so may distrain on other 

 land of the tenant not subject to the rent. 



lie stat. 4'J Geo. III. c. 116, in cases where the land-tax has not 

 been redeemed in duo time by the owner of the land, it may be 

 purchased by any other person, to whom it will belong as a perpetual 

 runt-i harge (though it is called a fee-farm rent in the Act), and the 

 purchaser will have all the remedies for rent reserved on a lease. 



By the stat. 3*4 Will. IV. c. 27, g. 42, no arrears of renter of 

 interest in respect of any sum of money charged upon or payable out 

 of land <>r rent, or any damages in respect of such arrears of rent or 

 interest, shall be recovered by any distress, suit, or action, but within 

 six years next after the same res]>ectively shall have become due, or 

 some acknowledgment in writing given to the person entitled thereto 

 by the person by whom the same was payable ; except where there has 

 been a prior mortgagee or other incumbrancer in possession of any 

 land or receipt of the profits thereof within one year next before an 

 action or suit shall be brought by a subsequent mortgagee, Sic. ; and 

 then the arrears of interest may be recovered for the whole time such 

 prior mortgagee, Ac., was in such possession or receipt. 



Ul'.l'KATlXU CIRCLE. The principle of repetition from which 



this circle has its name was first explained by Tobias Mayer, professor 



of the university of Oottingen, in ' Commentarii Societatis lieguc 



Scientiaruui Gottingensis,' torn, ii., p. 325, for the year 1752. Mayer 



found that the common surveying instruments were often inaccurate 



to 5', while the quadrant, then used in all great scientific surveys, was, 



from ite weight and price, and the trouble required for verifying and 



adjusting it, scarcely to be considered a portable instrument, but only 



fit for the observatory. The substitute which he proposed for geo- 



desic.il purposes may be described briefly as follows : Suppose a 



hollow tube fitting upon an axis, to which it can be clamped, when 



nfl, by a screw; the axis itself is fixed on the top of a staff. 



irt of the instrument is exactly similar to a common mounting 



rveying compasses, Ac., where greater stability is wanted than a 



ball and wicket will give. On the top of the tube a flat bar is screwed, 



i f \\liii-li i.-. horizontal whm the- tube and axis arc vertical; 



ri !> pifce, which has tin' .sl> ;- u of a T. A 



I bar of the same length is placed exactly above the former. 



This latter bar moves easily, and without shake, on a pin concentric 

 with the tube and axis, and thus can be placed at any angle with the 

 fixed rule, and. as it is supposed, without at all disturbing it. Two 

 fine dots are pricked towards the ends of each bar; the lines joining 

 the dots in each should pass exactly through the axis of motion of the 

 upper bar, and the dots must be equidistant from the centre. When 

 this is so, the four dots will, in every position of the bars, be the 

 angular points of a rectangle, and the equality of the opposite sides 

 can be ascertained by measuring the distance with compasses. Finally, 

 on the top of the upper bar a telescope with cross wires is fixed, the' 

 telescope being a little shorter than the bar, that it may, not interfere 

 with measurements between the dots. 



The mode of measuring an angle with this instrument is as 

 follows : Let the two objects be R (that to the right) and i, (that 

 to the left). Set the fixed bar to some angle from 10 to 20 degrees 

 to the right of K by the motion of the tube on the axis, and clauip the 

 axis-screw firmly ; then, by the motion of the upper bar alone, bisect 

 K with the telescope. Take, with a pair of compasses, the distance 

 between the dots, apply the distance to a scale of chords, and you have 

 the angle between the fixed bar and the object R. Call this angle 0. 

 Now, by the motion of the upper bar alone, bisect the object L. It is 

 clear that, if the distance between the dots were again measured, and 

 the angle deduced, as before, from the scale, we should have a measure 

 of the angle required + 9. But instead of measuring at present, let 

 the telescope be brought back on K, by unclamping the axis-screw and 

 moriuy the whole instrument on. its a~cis ; when this is satisfactorily per- 

 formed, clamp the axis, and bisect L exactly as before, by moving the 

 upper bar and telescope alone. The angle between the bars as deduced 

 from measuring the chord between the dots will now clearly be twice 

 the angle required + 8. Let the operation be performed HO many 

 times eight, for instance that the bars are nearly in their original 

 position with regard to each other, and let the distance between the 

 dots be measured and the corresponding angle be deduced from the 

 scale of chords, which suppose to be <f>, <t> being larger than 6. If this 

 last- mentioned angle had been 8 exactly, it is clear that the bar would 

 have come round exactly to its original position after having moved 

 through 360 ; but as it has besides moved over an angle = </> 9, the 

 whole angle moved through is 360 + <J> fl, which is also eight times 

 the angle to be measured : hence the angle subtended at the spectator 

 by R and L is J(360 c + ^> 6). By continuing this process of stepping 

 several times round, there seems to be no limit to the accuracy with 

 which an angle can be measured, except that which depends on the 

 imperfection of the telescope, the indistinctness of the objects, or the 

 uncertain lateral effect of terrestrial refraction. Mayer used a scale of 

 chords, probably because he was thus able to construct the instrument 

 himself, and could dispense with any circular arc or divisions. We do 

 not see that he has noticed one slight inaccuracy, namely, that as the 

 dots lie in different planes, the distance between them is not the actual 

 chord of the angle required, but is the hypothenuse of a right-angled 

 triangle, the altitude of which is the thickness of the upper bar, while 

 the base is the chord required ; but this error is easily allowed for, 

 and, when the angle to be measured by the compasses is of a tolerable 

 size, is scarcely worth considering. If we conceive the plane of the 

 lower bar extended and changed into a divided circle, while the upper 

 bar becomes a vernier at each end, we should probably have the instru- 

 ment Mayer would have proposed, had it been in his power to employ 

 a tolerable mathematical -instrument maker. Mayer says that he 

 invented this instrument eight years before the publication of his 

 memoir. 



The reward proposed by the English parliament for any means by 

 which the longitude at sea could be determined, stimulated Mayer to 

 perfect the method of lunar distances. For the successful solution of 

 this problem two things are required tables correct enough to predict 

 the true place of the moon at any future time, and an instrument for 

 measuring the distance between the moon and star with sufficient 

 accuracy. Mayer fulfilled the first condition by his celebrated Lunar 

 Tatik'H, one copy of which was sent to the Lords of the Admiralty in 

 1 755, and a later, improved up to his death (1762), forwarded by his 

 widow in 1763. For measuring the distance between the moon and 

 star he proposed an instrument similar to Hadley's sextant, but in 

 which the angle can be repeated or multiplied without intermediate 

 readings off, similar hi principle to the instrument just described. 



Mr. Troughton says (article ' Circle," Brewster's ' Cyclopiedia ') that 

 Bird was employed to make reflecting circles after Mayer's idea, but his 

 dividing was so excellent, that the entire circle was thought useless, 

 and the sextant preferred, as having a larger radius, and being lighter 

 and handier. 



In 1787 the Chevalier de Borda published his ' Description et Usage 

 du Circle de Rc'flexion,' in which he proposed a modification Of Mayer's 

 circle, so slight that at first sight it would almost seem trivial, but 

 which gives an unquestionable superiority to this above every other 

 form of reflecting instrument when well made and skilfully and per- 

 lereringly used. We shall return to Mayer and Borda's construction of 

 the repeating reflecting circle in the article SEXTANT, as those instru- 

 ments cannot be understood until the principle of reflecting instru- 

 ments has been explained. 



The date of the invention of the repeating circle which is the proper 

 subject of this article, is somewhat uncertain : it is later than that of 



