. Asiatic Researches. 94 ON THE FORMULA FOR CALCULATING undergoing the toil and loss of time which would attend a formal recom- putation of the whole set of observations, and it will be remarked that the second hypothesis will also enable him to compute, by means of ditFerences, a series for many nights in succession with quite as much correctness as if entire quantities had been used ; for in that case he has only to calculate the elements for the first night, and substitute for the value of d 6 the increment or decrement of polar distance, the other terms being virtually constant. It has alw
. Asiatic Researches. 94 ON THE FORMULA FOR CALCULATING undergoing the toil and loss of time which would attend a formal recom- putation of the whole set of observations, and it will be remarked that the second hypothesis will also enable him to compute, by means of ditFerences, a series for many nights in succession with quite as much correctness as if entire quantities had been used ; for in that case he has only to calculate the elements for the first night, and substitute for the value of d 6 the increment or decrement of polar distance, the other terms being virtually constant. It has always, however, been an evil complained of in operations of this kind, that by limiting the case to the actual time of maximum Azimuth, the powers of the observer are much curtailed, because he can- not take more than one observation on the same night. If observations, taken intermediately between the culmination and the time of the greatest Azimuth, were to be computed with reference to the meridian, it would be indispensable to employ large quantities, and the operose formulae of Spherical Trigonometry, which would not only be laborious, but would not give so much accuracy as the method of eliciting the correction by means of differential terms. z I shall explain this better by a reference to the diagram in the margin, wherein the two Arcs ZS, ZS' are drawn very near to each other, the angle PSZ being a right angle, and it will be seen immediately how much more easily and accurately the angle PZS' may be found by computing the partial angle SZS', and deducting it from PZS, than by direct computation of the entire angle PZS' itself. ^ I have introduced, in the first part, the ordinary rules for com- puting the elements at the time of maximum, with the view that those, for whose use these formula are intended, may not need a. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of th
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