TELESCOPE. 



fioiis, between no' and 218', witliin tla- accuracy of 30": 

 it is alfo cafy to conceive, that, tin- anRlc iiicrcaiuig as we 

 approach an objcd, the fame objert may be made to fill the 

 iield between the meafiiring points in a new ftation, provided 

 the dillance between the two olijcdglalTes be fo altered, by 

 trial ai\d adjuftments, that the exad power is found fuch as 

 will command this condition, and the new angle at the fecond 

 ftation will be indicated, as the old one was at the firft ; 

 and when the diihince between llie llations is meafured 

 in a right line leading directly to or from the objed, the dif- 

 ference of the angles will afford data for determining the 

 dillance of the objed from either Ration. For example, 

 fuppofing the tangents of fmall angles to be equal to the 

 angles tliemfelves, whicli they are very nearly, let us call 

 the greater angle m, the fmaller angle n, and the diftance be- 

 tween the ftations <i ; then, as the dillances of the objeft 

 from each ftation will always be inverfely as the meafured 

 angles, we have n : m (of tiie angles) for the ratio of the dif- 

 tances, and the real difference of the fame diftanccs by mea- 

 furement of the interval ; therefore, by one of the funpleil 



theorems in algebra, we have 



the greater dillance. 



and 



= the fmaller diftance : thus, if we fuppofc the 



firft, or fmaller angle = 46', and the fecond, or nearer = -68', 



120 X 68' 

 with the interval 120 feet, we mail have 



8106 

 22 



68'- 



r , j-il 120 X 46' 



370.9 tor the greater dutance, - -^ 



68' - 48' 



=: 250.9 for the fmaller, and the difference, as before, 120. 

 But it will be feen in a fubfequcnt fedion of our article, that 

 to determine diftances from fmall angles with great accuracy, 

 the value of a fingle fecond ought not to be neglefted ; and 

 that a correftion for want of parallelifm, at fliort diftances, is 

 neceffary for obtaining the true angle, whenever that is wanted. 

 The author, however, has ftiewn, that the correftion in quef- 

 tion will vary nearly with the varying length of the tele- 

 fcope, and will not affeft the ratio of the angles meafured, 

 on which the refpeftive diftances depend ; but this coinci- 

 dence of the correftion with the length or power of the 

 telefcope, does not obviate our objeftions where real mea- 

 fures of angles are required, and where extreme accuracy is 

 neceffary for the fuccefs of the operation. But we have faid 

 the conftruftion is twofold : it is extremely difficult, if .it all 

 poffible, to hold the telefcope fo fteady without a ftand, that 

 the angle, contained between the two fixed points in the 

 focus of the piece, can be meafured with precifion ; and this 

 difficulty probably led to the fubftitution of the divided 

 objeft-glafs, feen in fig. 6, and edgewife in Jig. 7, for the 

 fecond objeft-glafs I, which we have defcribed. If this 

 divided objeft-glafs, fcrewed into the fecond tube at I, had 

 precifdy the focal diftance as the entire one, and had the 

 centres of the femi-lenfes brought exaftly into contaft, the 

 fame fcale and the fame mode of taking tiie meafure of an 

 angle, would apply with it as with the one we before deno- 

 minated I ; likewife the points in the eye-piece would be 

 neceffary. But to do away the ufc of fuch points, and to 

 render the inftrument equally ufeful without as with a ftand, 

 the fecond objeft-glafs that we have now to defcribe, as con- 

 flituting the fecond conftruftion of the telefcope, was divided 

 in the centre diametrically, and had its centres removed from 

 each other, fo that each femi-lens forms a ftparate image of 

 the objeft viewed. In this conftruftion, two points may be 

 fixed on in any objeft, and when the tubes are fo drawn out, 

 that point a in one image coincides with point b in the other, 



as in DoUond's objeft-glafs micrometer, then the angle fub- 

 tended by a line connefting the points a and b will be indi- 

 cated on the fecond fcale, or fcale c J, in fig. 5. This fcale 

 in our inftrument begins with 11', and ends with 75'; fo 

 that the length of l^\ inches, being divided into 64 (75 — 

 1 1 ) fpaces, admits of tliefe minute fpaces being fubdivided 

 into three of 20" each ; and if the adjuftment for diftinft 

 vilion would allow thefe to be bifefted by eftimation, the 

 fmalleft quantity to be meafured would be 10" on this fcale, 

 which is indeed as fmall a quantity as the power of the tele 

 fcope is capable of diftinguifliing ; and therefore a longer 

 fcale would have been of no greater ufe. The peculiar ad- 

 vantage of this conftruftion is, that, as in Hadlcy's fextant, 

 a motion in the inftrument does not injure the accuracy of the 

 obfervation, or impede the operation of taking it, but 

 affords the opportunity of re-examining the exaftnefs of 

 the apparent contaft. Hence the ufe of this inftrument 

 affords a pleafing exercife, and the neceffity of a ftand is en- 

 tirely obviated. We have the authority of Tulley, the only 

 maker, to fay, that his grace the duke of Wellington had 

 one of thefe telefcopes, with filver tubes, prefented to him by 

 a friend, and there is reafon to infer, that his ufing it as a 

 coming-up glafs gave him the advantage of afcertaining, better 

 than any of his ftaff, in what direftion the enemy was 

 moving on certain critical occafions. For when it is afcer- 

 tained by obfervation, whether the angle fubtended by a 

 man in motion is increafing or dinjinifliing, it is eafy to 

 infer whether the man is approaching or receding, though 

 the exaft meafure of the angle be difregarded. And at fea 

 it is equally eafy to afcertain whether a fhip is gaining or 

 lofing ground in a chafe, when two points in a maft can be 

 diftinguillied. Wlien this patent telefcope has the divided 

 objeft-glafs as the Hiding one, the two images appear exaftly 

 finiilar to thofe in Dollond's divided objeft-glafs micrometer, 

 but the range of fcale is much greater : if Dollond's has 

 any advantage over this, it is, that the power of his telefcope 

 is ufually greater, and that the meafures taken at different 

 ftations do not depend on two adjuftments of the tubes longi- 

 tudinally, though it is neceffary always to have diftinft 

 vifion, when the edges of the images are brought into con- 

 taft. We confider that ncitlier of the conftruftions of the 

 patent telefcope, on its prefent fcale, is competent to the 

 meafurement of diftances from one ftation with fufiicient 

 accuracy ; neither has it a range of fcale fufficient to make 

 it generally ufeful for all angles. The writer of this article 

 has had the divided objeft-glafs made to have their centres 

 adjuftable to different diftances from each other, fo as to be 

 cap.ible of meafuring all fmall angles from i' up to 75', and 

 to be eftimated by the fame fcale in the different pofitions, 

 the value of the firft and laft pofitions of the tubes being 

 determined experimentally tor each pofition of the femi 

 lenfes, and the marks for the pofitions being fo made, that 

 when the fcale runs out in the firft pofition of the femi-lenfes, 

 the fame value ftiall begin the fcale at their next pofition ; 

 and thus a fucccflion of minutes is continued from unity to 

 the extreme end of the fcale at the laft pofition of the glaffes ; 

 confequently one fuch inftrument is capable of doing as much 

 as feveral inftriiments with different pairs of femi-lenfes 

 can do, when put in a fixed pofition according to the pa- 

 tent. But after all, the initial and final values of a fcale of 

 a given length muff depend on the difference of the focal 

 lengths of the principal and Aiding objeft-glaffes ; and, there- 

 fore, to obferve the nice variations in the diameter of the fun 

 or moon, it would be defirable, that the whole fcale ftiould 

 meafure only about 5', -viz. from 28' to 33' ; and then, if 

 the telefcope had power enough, the fubdivifions of the 

 fcale might afcend by fingle feconds. Indeed it is yet a 



defi- 



