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employing a large number of divisions, and by occasionally shifting the zero point of the instrument to another set of divisions : the employment of several divisions at each observation is objectionable only as far as regards fatigue, and loss of time to the observer ; but to the shifting of the zero point there are objections to be urged of a much more serious nature ; it is true, in the determination of fixed angles, such as the altitude, or north polar distance of the fixed stars, the plan of shifting the zero point of an instrument is applied with some advantage, but in the determination of the ever-changing places of the sun, moon, and planets, the shifting of the zero point is of no avail whatever; and in the determination of parallax, of the coefficients of aberration, nutation, &c. to which a good set of observations are applicable, the plan cannot be employed at all. With this view of the subject, since the erection of the Madras Mural Circle, in January 1831, I have employed the circle without shifting the zero point: and this circumstance, added to the fact of the division of this instrument having been effected upon an entirely new plan, rendered it very desirable that some knowledge of the amount of error of division should be obtained ; accordingly I set to work as follows.

It is well understood that parallel rays of light after passing through an object glass, converge and meet eventually at a point which is called the principal focus: the converse of this is, that rays of light which diverge from the focal point after passing through the object glass will pursue a parallel course, and hence will appear distinct when viewed through an astronomical telescope adjusted to the solar focus. To be better understood in what follows, I must here refer to the description of the Madras Mural Circle given in volume I. of the Results of the Madras Observations for 1831 : it is there stated, that “ the telescope is furnished with an axis of its own, which works into the axis of the circle ;” hence it will appear plain that the telescope being unclamped at the two ends from the circle, it moves on its own axis independently of the circle, or on being clamped to the circle, it moves with it at pleasure. Thus much being premised, I clamped the circle, so that O corresponded with the zero of the reading microscope A, and read of B, the opposite microscope ; I then directed the telescope to

the object glass of a DoL1.oNn’s five feet achromatic, in the focus of

which I had previously fixed a pair of lines crossing one another at an angle of about 30° ; these lines which were distinctly seen, were bisected by the movable wire of the telescope, the telescope being first firmly clamped to the circle ; the circle was now loosed, and moved with the attached telescope to the object glass of another telescope, (a 12 inch theodolite telescope for want of a better,) the cross wires of which bad been previously adjusted to subtend as nearly as possible an angle of 90° with the former ; the difference betwen the reading now obtained, and the first reading, gives the exact angle between the two,+ or—error of division. The telescope being now released from the circle was again directed to the first-named telescope ; again clamped to the circle; and, by means of the movable wire, a bisection again made ; releasing the circle, it was with the attached telescope again turned till the telescope bisected the wires of the smaller telescope, when 180° nearly, or double the angle subtended by the pairs of cross wires, was read off ; pursuing this course after five readings we arrived at the point of departure : now the difference between the first and last divided by four, or the true value of the angle, being added to the first reading gives the second ; being again added gives the third, &c. these compared with the actual reading give the error of division of the points 0°, 90°, 1800, 8:0. thus :—-

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A B Mean of Mean Au- Interpolat.- Error of ' ' A and B. gle. ed. division. 0 I II I! II ‘I II I! II 3 0 0.0 1.1 0.55 2l.90—0.55 0.55 0.00 90 0 5.2 5.2 5.20 4 5.89 —0.69 180 0 10.7 12.2 11.45 11.23 +0.22 270 0 15.4 17.4 16.40 " 16.57 --0.17 360 0 22.9 20.9 21.90 =+5.34 21,90 000 From the mean of ten repetitions in this way the errors came out, II For 0 and 180 = 0.00 90 and 270 -0.45 180 and 360 -0.03

For the error of divisions intermediate between the above, I placed DoL1.o1~1D’s 5-feet Telescope as before, and by means of two wooden supports, A. B., a42-inch Achromatic, by DOLLOND, was supported immediately above, so that apair of cross lines fixed in the focus, subtended an angle of 30° with the cross-lines fixed in the other Telescope. I then made the following measures :

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In this case to find the true angle subtended by the pairs of cross lines, it is necessary to apply to the mean of A and B the errors already found above for 0° and 180° and for 90°, and 270° and then to interpolate between these corrected readings: from the mean of ten

measures in this way the errors come out as follows:

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To ascertain the error of division at the points intermediate between 0° and 30° and between 30° and 60°, &c. I placed the 42-inch telescope by Douonn (already spoken of as the upper telescope) so near to the lower telescope, that the images of the pairs of cross-wires subtended an angle of five degrees nearly, and in a manner similar to that explained above, made the following measures of the angle:

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Mean of Mean of Interpo1at- Error of

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Microscope A. B. A and B‘ Pairs. True angle. ed. division_ 0 I II II I! I! I) /I I! /I 0 0 0.0 1.0 0.50 1.10 15.ll—-1.10 1.10 0.00 5 0 1.3 1.2 1.25 2,42 6 3.44 -1.02 10 0 3.0 3.0 3.00 4,85 5.78 -0.93 15 0 6.9 7.1 7.00 8,12 8,11 -I-0.01 20 0 8.2 11.0 9.60 10,32 /1 10.45 ——0.13 25 0 10.8 14.0 12.40 12.47 _2.335 12.78 -0.32 30 0 15.1 14.6 14.85 14.85 _ 15.11 -0.26 25 0 11.9 13.2 12.55 20 0 9.8 12.3 11.05 15 0 9.1 9.4 9.25 10 0 6.1 7.3 6.70 5 0 3.5 3.7 3.60 0 0 1.1 2.3 1.70

The above difi'ers from the preceding only that I have here returned back to the point of departure in an inverse order, instead of again beginning at 0° 0'.

In a similar manner the following five series were obtained.

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0.15 2.05 4.80 7.55

10.65

13.55

15.20

13.15

11.45 9.85 8.10 5,15 2.70

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18.65

1.42 3.60 6.45 8.70 11.05 13.35 15.20

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60 0 18.2 55 0 13.2 50 0 12.0 45 0 9.6 40 0 6.4 35 0 2.5 30 0 0.6 60 0 0.0 65 0 1.5 70 0 4.5 75 0 7.9 80 0 10.2 85 0 13.8 90 0 15.1 85 0 12.8 80 0 10 7 75 0 10.0 70 0 7.3 65 0 4.6 60 0 2.7 90 0 0.0 95 0 59.4 99 59 56.1 104 59 54.8 109 59 53.5 114 59 53.0 119 59 52.0 114 59 53.0 109 59 53.2 104 59 55.8 99 59 54.2 94 59 57.2 89 59 59.0 120 0 0.0 125 0 1.5 130 0 3.9 135 0 5.0 140 0 7.7 145 0 8.4 150 0 8.9 145 0 7.3 140 0 9.9 135 0 8.0 130 0 5.7 125 0 5.6 120 0 2.1 150 0 0.0 154 59 58.8 159 59 51.0 164 59 48.0 169 59 44.0 174 59 42.2 179 59 38.2 174 59 41.8 169 59 44.2 164 59 50.2 159 59 50.8 154 59 55.0 150 0 1.3

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18.65
14.80
13.40
10.00
7.65
4.10
0.45

0.45
58.70
55.55
54.15
52.75
52.00
51.10
52.35
53.10
55 40
54.75
57.35
59.35

58.50
0.50
2.30
4.00
6.50
7.75
8.50

59.50
58.15
51.65
48.25
44.35
42.60
38.95
41.75
45.00
50.85
51.40
55.00

0.50

59.85 2.52 3.42 5.50 7.32 7.45 8.50

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From themean of 10 sets, similar to the above, the errors of division for two opposite divisions are as follows :

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I am not prepared at present to furnish the error of the divisions intermediate between the above, but I may remark that out of a great many which I have examined, the largest error I have found does not

Y exceed that above found for 150° and 330°.

VII.-—Table of the Times qf high water at the principal places between - Calcutta and Point Palmiras, prepared by Mr. P. G. Smenam.

We have much pleasure in giving insertion to the accompanying table, which will be extremely useful not only to navigators here, but also to the philosophers in Europe, who are now engaged in investigating the course of the tidal waves over the entire globe. We published in vol. ii. p. 151, a list of Professor Wnuwnmls desiderata regarding the co-tides of the Indian ocean. His memoir on the cotidal lines is published in the Trans. Roy. Society 1833, Pt. 1, and we there find that the coasts of India present nearly a blank : the time of high water at Point Palmiras differs two hours from the time given by Mr.- SrNcLAm’s observations. We hope to be furnished from our correspondents at other places, such as Masulipatam, Madras, Chittagong, Kyook Phyoo, Penang and Singapfn with tables similar to the present, but we would suggest that the other desiderata, of the lift of the tide—the establishment of the place,——the correction for other days of the semi-lunar period, 810. should also receive the attention of observers.

The present table must not be understood as rigidly correct, but rather as an useful practical approximation ; for the intervals of retar

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