bably equally affected by the sun's rays: the apparent excess of corrections for No. 3 level being due to the observer, who had a habit of not relevelling his instrument during observations; his results therefore give the fairest measure of the sun's influence. They give an average dislevelment of 092 second of arc per station, if supposed to act only during the hottest part of the day; this, though small in amount, has a serious cumulative effect.

This is now cancelled in the practice of the G. T. S., at least as far as possible, by watching the corrections, adding them together algebraically as the work proceeds, and tilting the instrument by its foot-screws slightly upwards to the north away from the sun, whenever necessary to counteract the tendency to droop in that direction; otherwise, any error in the value of the run of the level would affect the final results by the same fraction of the accumulated corrections that it is of the run.

In ordinary levelling operations, the action of the sun is more liable to produce error than in those of the G. T. Survey, where the bubble-reading is noted and recorded immediately after the staff has been observed; because, in ordinary cases, the bubble is first adjusted and the staves read afterwards, leaving an interval for the sun to act on the instrument: the amount of error resulting will depend on the length of time of this interval, and with the direction of line of operations. Change of weather and time would probably cancel or affect this error, but there are no means of entirely removing it; and no method of working in a circuit or otherwise would indicate the amount of error. As long as the cause remains constant, these errors re-enter with

out attracting notice to an equal extent in the up and down lines; thus the opposite extremes of a circuit, which closes without apparent error, may be yet considerably erroneous.

4th. Atmospheric influence.-Different results may be obtained from levelling at different times of the day, especially when the rays of light graze the ground in passing from the staff to the observer; this occurs in cloudless weather, when the sun shines brightly, but never in the cloudy. The following result of experiments on two following days, January 10 and 11, 1859, at Hatedara, in Sind, by surveyors of the G. T. Survey, shows a tendency to a diurnal law of variation.

Such atmospheric influences would tend to cancel each other in a long line of operations, excepting under the following circumstances:-First, when operations are carried on more before than after noon, they are more under a sinking than under a rising refraction; hence the first pair of staff-readings will have a tendency to be more refracted than the second, thus introducing cumulative error, unless the precaution is taken to alternate the order of observations. Secondly, when operations are carried over a line of country which slopes uniformly in one direction, when the rays of light from the upper staff to the observer are usually nearer the ground than those from the down staff, and are there

fore more subject to extremes of refraction. In India there are fewer working hours before than after the ground has been heated by the sun in the practice of the G. T. Survey; consequently, the rays from the up staff must have an excess of negative refraction, compared with those from the down staff, and the result on an ascent would be to make it too small. The amount of this error will vary with the season, and is evidently beyond control.

With regard to the extremes of refraction, the following has been observed by the G. T. S. in the plains of the Punjab. A station or object seen from another station ten miles off, appears at a minimum height between I P.M. and 3 P.M.; it then rises gradually, and afterwards rapidly as the sun sinks and the dew falls, to its maxinium at night; on the following morning this occurs in the reverse order, the extreme height through which it appears to rise and fall in 24 hours being 100 to 150 feet. A few feet of difference in the absolute height of the observed station has a considerable effect on these phenomena, which vary with the heights at which the rays from the object pass above the ground level, also with the atmospheric moisture, the soil, and the heat of the sun's rays.

The following experiment was also made:-A pair of signals was placed 10 miles off, the one signal being 16 feet above the other vertically, and truly subtending a vertical angle of 60 seconds; during different times of the day, the subtenses varied as follows:

From this it appears that it is absolutely necessary to take vertical angles reciprocally and simultaneously if possible, and that they should be taken at the period of minimum refraction.

5th. The settlement of the instrument on its axis.This was shown to the observers on the G. T. Survey by examination of the recorded bubble-readings of operations made, which indicated that the index error of the level had a tendency to alter always in the same direction during the observations at each station. Thus in one instance taken at random out of many, the index error in the second pair of observations at forty-seven consecutive stations was found, when compared with its value for the first year of observations, to have decreased 39 times, increased 5 times, and remained unchanged 3 times, the algebraical mean decrease being 12 seconds of arc. This indicates a constant deviation in the adjustment of the level to the axis of rotation during the settlement of the instrument on its axis, on being taken out of its box and set up on the stand, which has to be done at every station, when a large heavy level is employed. It is of no importance by itself, save as indicating that a similar alteration may take place simultaneously in the adjustment of the usual axis of the telescope to the level. Were the forward staff to be invariably read after the back staff, as is the usual custom, the error mentioned, 12 second per station, would amount to feet per 100 miles. To cancel this, therefore, the back staff and the fore staff should be alternately read first in a series of levels.

6th. Personal errors.-Among practised observers, those in connection with the manipulation of the instrument are mostly not great; those in connection with the

staff-reading are again likely to cancel themselves, except perhaps in working in a meridional direction, when, one staff being invariably more illuminated than the other, these errors become cumulative.

The most probable source of personal error is in reading the bubble. The observer generally gets a side view of the bubble refracted obliquely through the thickness of the glass tube, which is not so clear as the view from above. The rim round the bubble caused by the adhesion of the liquid to the sides of the tube becomes so prominent, that its extremities may be read, instead of the actual ends of the bubble. When light falls obliquely on the instrument, the outer edge of the rim, towards the light, is more clearly defined than the inner, while at the opposite end of the bubble, the inner edge of the rim is most clearly defined; hence there is a tendency to bring the bubble too much towards the light, and to give the readings an erroneous bias by an amount equal to half the breadth of the rim, which might have a considerable effect on a long line of levels.

7th. General remarks.-Generally, to prevent bias or accumulation of error, changes of observers, changes of instrument, change of weather, change in the putting up of the instrument at each station-at one time putting one side foremost, the next time the other-and change in the manner of carrying the instrument from one station to another, all have a decided effect.

The Instruments, Appliances, and Methods employed by the Great Trigonometrical Surveyors in Levelling. The levels were standard levels, by Messrs. Troughton and Simms, of 20 or 21 inch focal length, and powers