222 Final Remarks by Mr. Edward Riddle on finding 



traction of that semidiaineter applied to the distance. This, as 

 we shall afterwards see, is only an elaborate nay of creating new 

 errors." This is the main object of his letter, and he subsequently 

 demonstrated a properly of the ellipse with which all mathemati- 

 cal men were very well acquainted, and referred to that property as 

 a demonstrative proof that an augmeutation ought to be applied, 

 not a deductioyi made from the semidiameter applied to the di- 

 stance. How, in the face of these circumstances, Mr. M. has had 

 the courage to lay before the public the assertions contained in 

 the above extracts from his letter of December 3, 1 am totally at; 

 a loss to conjecture. 



He says I " cannot produce the appearance" of his not know- 

 ing that the distance of the centres is the object of the compu- 

 tation. He is here again wrong, for the task is very easy. I 

 showed that by the method practised by careful computers in cor- 

 recting the semidiameters applied to the observed altitudes and 

 distance, the true altitude of the centres and their apparent al- 

 titudes and distance would be correctly obtained, and that hence 

 the tiiie distance of the centres might be computed ; and further, 

 that the true distance of the centres was what was wanted. What 

 Mr. M. kneiu on this subject may be gathered from what he said. 

 Take the following extracts from his letter already referred to in 

 vour July Magazine. " The centre is not necessarily the appa- 

 rent place of the angular point of the triangle." " The centre is 

 seldom the point from which the apparent distance should be 

 reckoned." "^ The mistake has no doubt arisen from the old 

 established habit of estimating the apparent distance from the 

 centre." The " appearance" of his not knowing that the distance 

 of the centres is the object of the computation is therefore pretty 

 clearly made out. 



How I could insinuate that Mr. M. has " inculcated the ob- 

 servance of such nicety at sea" will appear strange enough to 

 those who consider that the principal object of his letter was to 

 show that the application of these corrections, under any circuia- 

 gtances, was productive of error; and that my object was to de- 

 fend them from this imputation. 



On the subject of " trifles" to which we have seen he has ad- 

 verted, let us take his former estimate of their value. He has 

 told us " that in the common method the reduction of the semi- 

 diameter is neglected altogether." And in page 36, July Ma- 

 gazine, In " the method for correcting the altitude for the dis- 

 tortion of the disk, by a table answering to the diminution of the 

 vertical semidiameter, what is gained in getting the true altitude 

 of the centre is lost in departing from the point from which the 

 distance should be taken, and to which the common way of 

 working often makes a much nearer approacJu" And further, 



«Ido 



