246 On finding the Longitude 



ference between the apparent and true altitudes inay generally 

 be determined to a second ; and under such circumstances the 

 resulting distance will not be affected to an extent worth caring 

 for by any such small errors in the altitudes themselves. 



. But if the case were otherwise, such errors could not always be 

 avoided in observations taken at sea. For the observations which 

 have been made with Dr. Wollaston's Dip -sector show that from 

 the variableness of the horizontal refraction, the apparent de- 

 pression of the horizon will sometimes differ more than three 

 minutes from its mean quantity. 



In the apparent altitudes, therefore, greater errors are generally 

 unavoidable than the imaginary ones which drew from Mr. Mei- 

 kle this querulous exclamation — " It is in vain that we expect ac- 

 curacy even from the best observers and instruments, if such 

 needless errors are persevered in." 



It is however evidently pushing the calculation to a nicety in- 

 consistent with the data, to compute the apparent altitude of the 

 centre to a second, when that of the limb may pdssibly be af- 

 fected by an error of two or three minutes ; and in altitudes for 

 clearing the distance, it is fortunate that such precision is not 

 necessary. 



In the apparent distance we have seen that much greater ac- 

 curacy is requisite ; and it is one of the advantages of the lunar 

 method of finding the longitude, that this element, the distance 

 on the correctness of which the precision of the result so mate- 

 rially depends, can generally be measured with very considerable 

 exactness. 



But supposing the elements determined from observation to be 

 correctly obtainedjit is certainly desirable that we should not in any 

 degree vitiate the result of a good observation by mistakes in the 

 theory on which our computation from it is founded. What the 

 theoretical principles are which must guide us in the preparatory 

 steps of the operation, I hope the reader of the preceding remarks 

 will not need to be informed. And if he have already been in- 

 structed in the method of finding the longitude by lunar obser- 

 vations " according to the old established method," it may af- 

 ford him some satisfaction to perceive that the cavils which 

 Mr. Meikle has raised agahist that method are entirely without 

 foundation. 



Dismissing this subject, I come to his remarks on the princi- 

 ples of the quadrant. Though it is true that if a ray of light be 

 reflected from a revolving mirror, the angle described by the re- 

 flected ray will be double that described by the mirror ; and 

 though it is an obvious consequence of this property that the an- 

 gle measured by the revolution of the index in the quadrant is 

 half that described by the reflected image of the object observed j 



yet. 



