CIRCLE. 



491 



Circle, our best makers, was, in point of exactness, nearly on 

 "*"Y*~ > '' a level with its columns : but the Tables of Gauss, com- 

 puted from the theorems of La Place, left both far be- 

 These now, however, form the basis of our Al- 

 manack, and an instrument of commensurate exactness 

 is to be found in the British circle. 



With the reflecting circle so constructed, the Alma- 

 . 30 improved, and with Captain Mendoza's excel- 

 lent Tables, which far surpass every thing of the kind 

 teen before, finding the longitude, either at sea or land, 

 i> no longer either a doubtful or a difficult operation. 



\Ve shall close our observations on the reflecting circle 

 v.ith some account of the laudable endeavours of the 

 rcntleman, whose name has just been mentioned, to im- 

 prove it, and to render it a companion worthy of his 

 other nautical labours. 



SECT. IV. Description of Mendoza's Reflecting Circle. 



In a pap?r published in the Phil. Trans, for 1800, 

 Captain Mendoza has described, at considerable length, 

 one construction, and briefly mentioned others, all of 

 which, however, lead only to extend the repeating prin- 

 ciple. We shall confine our account to that which, to 

 ourselves, appears to be the best, and we refer to the pa- 

 per itself for farther information. It is offered as an 

 apology for not having given a figure of this circle, that 

 it is easy to describe its peculiarities in words, but ex- 

 tremely difficult to make them appear in a drawing. 



The general fabric of thii circle is, respecting the 

 frame, position of the glasses, and handles, exactly as in 

 Troughton'n construction, to which the repeating pro- 

 perty has been restored in a very ingenious manner, and 

 so as to produce double the effect that is done in Bor- 

 da's, by collecting the sum of backward and forward 

 motion of the index into one reading. For this purpose, 

 there have been added two very light circles, one of 

 which he calls a flying circle, and the other a flying no- 

 nius. They are both centred upon the upper end of 

 the socket, which receives the axis of the proper index, 

 and of the great mirror. The motions of these two cir- 

 cles are free and independent of each other : they are si- 

 tuated one above the other clo.e to the limb of the fixed 

 frame, having no connection whatever with it, except at 

 the centre. It will be remembered, that, in the former 

 construction, the indi-x with three branches had back- 

 ward and forward motion ; it is precisely so in this, on- 

 ly this index has but one branch, namely that with the 

 screws for quick and ilow motion. This index carries 

 no vernier, nor are there any divisions upon the limb of 

 the fixed frame to which it applies. The graduation is 

 made upon the flying circles, the lower of which is di- 

 vided into degrees, and every 20 7 ; the upper one carries 

 opposite verniers, subdividing the lower down to 20". 

 There is a clamp attached to the index, which lays 

 hold of the flying nonius, and in an observation forwards 

 carries it along over the face of the flying circle ; and 

 there is a similar clamp, which, laying hold of the flying 

 circle in an observation backwards, carries it back under 

 the flying nonius. The flyng- circle is, in the former 

 case, clamped to the limb of the fixed frame, and in the 

 latter, the nonius is secured in the same manner. 



Now, a* in the observation forwards, the nonius ad- 

 ranceg upon the circle, and in the one backwards, the 

 circle recedes upon the nonius, it in evident, that the bum 

 of the two motions will be given at one reading off. In- 

 stead, however, of reading here, forward and backward 

 observations are to be repeated, until a sufficient set has 

 been procured, and then the whole space that the circle 



3 



and nonius have been moved respecting each other may 

 be read off, and on being divided by twice the number 

 of forward and backward motions together, will give the 

 required angle. There are two sextants of coarse divi- 

 sions made upon the fixed limb, whose zeros are distant 

 from each other by the breadth of the index of the in- 

 dex glass ; contiguous to these divisions slide two pieces, 

 which, being set right and left to the angle about to be 

 measured, will stop that index in the requisite positions 

 for finding the objects nearly together in the field of the 

 telescope. This useful contrivance enables an observer 

 to take a set of sights of any number without looking 

 at the divisions, the first and last excepted. 



Mr Trougluon first applied this neat contrivance to 

 the circle of Borda, which, without it, is extremely 

 inconvenient to use. It ought to have been mentioned 

 in the account of that instrument, that a previous rough 

 observation must be made for computing at what points 

 upon the limb the two indices must be set, in order that 

 the objects may be found together in the field of view ; 

 and it requires the observer, at every successive sight, 

 to set the indices alternately to the computed angle ; 

 but, with this apparatus, a set may be taken in the 

 dark. 



Notwithstanding the great ingenuity displayed in these 

 contrivances, we think that the rtflecting circle last de- 

 scribed, can neither be very accurate nor very pleasant 

 in its use : the management of five clamps, which are to 

 be made fast and loose in regular succession ten distinct 

 operations to every pair of observations, any of which 

 being mistaken or neglected would spoil a whole set, re- 

 quires a degree of attention not to be found in every ob- 

 scrter. And the liability which there must be, even in 

 the best work, to force the flying circles from their pla- 

 ces in clamping, and thereby to cau.-e errors, without 

 any means of detecting them, is a most forbidding cir- 

 cumstance. And should the index of the central mirror 

 have a motion eccentric t those of the flying circles, the 

 latter at every step will feel the effect, and in consequence, 

 the result will be charged with the full error belonging 

 to a single observation. 



Circle. 



SECT. 



V. Professor Hassl-er's Method of restoring the- 

 Reflecting property to Trotigltton't Circle. 



Since the above was written, we understand that there P 

 has been suggested to Troughton an unexceptionable - 

 method of restoring the repeating property to his reflect- method of 

 ing circles, without in the least diminishing the advanta- restoring 

 ges of the fixed frame. In this the circular border of the ?' ie re "t- 

 frame is not employed ; it has one flying circle, (which "^To 

 was probably borrowed from the instrument last descri- Trough*, 

 bed,) and it is divided in the usual manner. Two indices ton's ciide.. 

 are employed ; one of them, below the circle, is screwed 

 fast 'o the frame, the other is above, having, like the cir- 

 cle itstlf, free and independent motion round the centre; 

 the latter carries at the luwcr end of the axis the index- 

 glass. B )th of the indices have screws for quick and 

 6low motion, which act upon the flying circle; and they 

 are bo'h furnished with opposite verniers, those of the 

 lower index being brought round from below, in order 

 to count upon the divisions of the circle. When the in- 

 dex and horizon glasses are parallel, the two indices cross 

 each other at right angles ; therefore the upper one has 

 a range of backward and forward motion through the 

 full hextantal angle, without interfering with the lower 

 one. 



The effect produced by this arrangement is as follows. . 

 In an observatioa forwards, the circle being clamped by, 



