CIRCLE. 



497 



observations, he will tken at once see afterwards which 

 of them is missing, when be comes to compare the two 

 sets together. 



Leaving the instrument clamped for altitude, and 

 screened entirely from the sun's rays, he must wait till it 

 is at the same distance from noon in the evening to re- 

 sume his task. For that, he must hold himself ready 

 against the time comes ; and, previous to it, he will do 

 well to re-examine the adjustment of his instrument, to 

 be certain that no change has happened in the stand or 

 the central cone, so as to throw its axis out of a perpen- 

 dicular. Let him then observe the same method in this 

 second set of observations as he did in those of the fore- 

 noon ; considering those wires as first, at which the sun's 

 limbs touch first ; and setting down the times of their 

 appulse to each respective horizontal wire, and bringing 

 the preceding or subsequent limb to the corresponding 

 perpendicular one, and reading off the azimuths just as 

 he did before. 



When all are passed, he may release all the clamps, and 

 replacing his shade, leave the instrument till he has re- 

 duced his observations. 



Of corresponding altitudes, if he has observed them 

 all, he will have obtained ten pair ; and of azimuths six 

 pair ; which he must now select from each other. 



In respect of corresponding altitudes, the practice is 

 so common, and the method of deducing the time from 

 them is so well known, that nothing need be said on that 

 head. Indeed, if a person wish for instruction in that, 

 he may find it in the late Mr Wales's Tract on the Me* 

 Ihod of Jinding l/ie Longitude at Sea by Time-keepers ; 

 which contains new tables of equations for equal alti- 

 tudes, and precepts for the use of them : a valuable trea- 

 tise, which may be had at a small expence, and ought to 

 be in the hands of every one who pays attention to these 

 subjects. 



But the idea of observing corresponding azimuths be- 

 ing perhaps new, or at least not very common, and 

 seemingly peculiar to this instrument, it may call for a 

 little explanation how to reduce them : and a very little 

 will suffice. 



They must be opposed to each other in pairs, just in 

 the same manner as corresponding altitudes ; the first in 

 the morning to the last in the evening, and so of the rest. 

 Then, deducting the one from the other, and applying 

 half the difference between the two to the smallest num- 

 ber in each pair, it will give a number of degrees, mi- 

 nutes, and seconds, in which, if all the observations were 

 perfect, the whole six pair would coincide ; and, if they 

 do not, the fair mean deduced from among them will ap- 

 proach nearly to the truth, i. e. the error of 180 on the 

 azimuth circle from the true meridian. 



To that mean point, deduced from theie observations, 

 the instrument must now be turned ; and fixed there till 

 the proper correction can be applied to it. Upon the 

 telescope being turned down to the horizon each way, it 

 may be observed what distinct object there may be either 

 to the north or south that coincides with one of the per- 

 pendicular wires ; or if no such object should occur, a 

 mark may be placed each way, or cither way, to which 

 to keep the instrument, till the correction can be inves- 

 tigated, which is requisite on account of the change of the 

 sun's declination during the interval between the morning 

 and evening observations : for any alteration in his de- 

 clination will affect the azimuth deduced in this way, as 

 it does the hour ; and neither of those corrections can be 

 ascertained till the latitude of the station be known. 



Yet may the latitude be now deduced, with fully suf- 

 VOL. VI. TAUT II. 



ficient accuracy for that purpose, by observing the passage Circle, 

 of any one known star over the meridian, and reading off 

 its altitude and zenith distance. The pole star, or any 

 star of the first or second magnitude, will be found vi- 

 sible in the day-time with the telescope of this instru- 

 ment ; and the latitude being, though roughly, deduced 

 from it, the correction for time may be sought in the 

 usual way. That required for azimuth may as easily be 

 investigated by this very simple formula, which the late 

 Mr Wales constructed for this purpose." 



Take the daily variation of the sun's declination from 

 the Nautical Almanac. Then say, As 24.' 1 is to half the 

 interval between the observations, so is the daily change 

 in the declination to its change in that half interval. 

 Turn the half interval into degrees, minutes, and seconds ; 

 and reduce the change in that half interval to seconds. 

 Then to the log. of the change so found add log. co- 

 secant of half intervals -f- log. secant of the latitude of 

 the station, the sum will be the log. of the correction in 

 azimuth in seconds to be applied to the middle point. 

 This will fill to the west of the true south point when the 

 tun is advancing towards the north pole, and vice versH 

 east when he is needing from it. 



" Having calculated the necessary correction, you may 

 then apply it to the azimuth before deduced, from a 

 mean of the observations ; and shift the instrument just 

 that quantity, as shewn on the azimuth circle.. Then 

 clamping it firmly there with both of the side clamps, 

 you may trust to its remaining in that position as far as 

 the instrument itself is concerned j for when once those 

 clamps are set, the tangent-screw for adjustment has no 

 power over it. 



Thus it becomes, to all intents and purposes, so far as 

 its situation and size permit, a transit circle ; placed very 

 nearly, if not quite truly, in the meridian, from one day's 

 observation alone ; and ready for making some observa- 

 tions in that first evening. 



The chronometer having been let go down, may have 

 altered its rate, which as yet will be uncertain ; though 

 if the watch be good, that rate will not be unsteady. Its 

 error at noon was known from the corresponding alti- 

 tudes ; and any observations of the evening may after- 

 wards be reduced to the real time, when the rate becomes 

 known. The passage of stars over the meridian, even in 

 this first evening, will therefore be valuable | and if the 

 moon should be among the number, an observation of 

 her passage, and a comparison of it with that of a star 

 nearly of the same declination, will already give great 

 insight into the longitude of the station. The error of 

 the instrument in collimation of altitude must be known, 

 before the exact latitude can be ascertained ; but as that 

 error is not apt to vary even by carriage, the latitude 

 may be confided in, within 10, from the observations of 

 the same evening. 



By repeating the same process, either in whole or in 

 part, as he may judge necessary, the next day, he will 

 verify his meridian, or bring it still more near to the truth. 

 He will obtain the rate of his time-keeper; and begin to 

 feel a degree of confidence. For when once he has 3 

 mark ir> the meridian to which to re-adjust his telescope, 

 he may, if he finds occasion, release the instrument, and 

 turn it in any direction for other observations, knowing 

 that he can replace it at pleasure. Yet must it be said, 

 that in all instruments, the less they are moved out of any 

 position, and their adjustments disturbed, the better they 

 will always perform what is expected from them. 



Another method there is, which has not often been 

 practised, though it was found very convenient to General 



3 R 



