101 [ 237 J 



measured at points of the third order, where \vc had made a more or loss 

 protracted stay; and, finally, to confirm the levelling of these transient 

 stations, which may be termed of the fourth order, we had the control from 

 two extreme and limiting stations of the third order, together with the 

 lights derived from our continuous sketches of the route, and the descrip- 

 tive journal of what we saw. 



I ask pardon ior entering into details, tedious and useless even for 

 those who are familinr with the subject of wiiich 1 have been treating. 

 But I believed that I ought not to dispense with a candid exposition of 

 the methods of observation which, in this particular, were left for me to 

 follow. 



II. The best method of determining lime, in exploring expeditions, when 

 one is not provided with a transit instrument, is to measure the absohite 

 altitudes of the sun, or of some principal stars, taken both east and west of 

 the meridian of the spot where the observation is to be made. 



The method of equal aliiindes, which appears still generally adhered 

 to, exposes such an expedition to loss of time, without offering any deci- 

 ded advantages over the observation of absolute altitudes. In order to ef- 

 fect the utmost possible, the whole day-tiiTie has to be occupied in gaining 

 ground and distaijce, in reconnoitring and sketching the features of the 

 country ; while a portion of the night must be devoted to astronomical ob- 

 servations, however strong might be otherwise the desire for repose. The 

 health of the observer, too, requires that he should not expose himself, with- 

 out absolute necessity, to make a long stand under the direct heat of the sun ; 

 and, more than all, the method of equal altitudes, while it causes a halt 

 for several hours, exposes, also, to the regret of seeing the sun passing the 

 meridian without avail : for it must be remembered that the season lor such 

 expeditions (the finest part of the year) is also the season during which the 

 sun, with his high northern declination, cannot be reached at noon with 

 the divisions of the sextant. 



But, with the method of absolute allitudes, two or three series of obser- 

 vations to the east, and two or three series to the west of the m.eridian, 

 taken in the course of the same night, upon some of the principal stars, 

 (which must be selected, as much as possible, to fulfil the theoretical con- 

 ditions required for good hour-angles,) are enough to supply the absence of 

 a transit instrument, which is not always within the means of a private 

 traveller to be procured, or to be carried. 



The calculations which have to be made out in both cases, (absolute 

 altitudes and meridian transits,) do not diffei: in amount enough to offer 

 advantage in the employment of either one above the other ; for if, on the 

 one hand, there are no hour-angles to deduce from absolute altitudes, there 

 is not less the necessity of observing stars differing much in declination, 

 in order to determine the deviation oF the instrument from the plane of thte 

 meridian. 



Now, to make a judicious application of the method of absolute alti- 

 tudes, it must be remembered that the formukc for the calculation of the 

 hour-angle are derived with the assumption that the changes of altitude 

 in the heavenly bodies, above the horizon, are proportional to the times: 

 but this can be taken as strictly true only for short intervals of time — say 

 four or five minutes. To prolong, therefore, a series of observations be- 

 yond a term like this, is to introduce a case wherein must be used 



