262 Oti the Latitude, Sfc. of the Observatory on the Gallon Hill. 



account for the excess of 11" in that derived from the Trigo- 

 nometrical Survey, after making all due allowance for the in- 

 feriority of my instruments and mode of applying them. I 

 never lost sight of the subject whenever an opportunity pre- 

 sented itself; and at last found that the same discordances 

 had occurred of nearly the same amount to a very distinguished 

 practical astronomer, whose observatory is situated about 23' 

 S. of Edinburgh. I was most unwilling to admit that an 

 en'or of that amount could possibly be committed in that great 

 national undertaking, conducted by such eminent observers 

 with such fine instruments. But what other conclusion was 

 it possible to draw ? No doubt the latitudes are only given 

 to the nearest second in this part of the island ; and conse- 

 quently an error of half a second, amounting to about fifty feet 

 in the relative position of the places observed, may have oc- 

 curred by the method I have employed to derive the latitude 

 of the Calton Hill from the Trigonometrical Survey ; and this 

 may have vitiated my conclusions in some degree, though 

 I believe it to be small. It is true that the latitudes to the 

 nearest second are as much, generally speaking, as can be de- 

 pended on even by the best instruments, and sufficient for the 

 nicest purposes ; but for my purpose in this particular pro- 

 blem, it would have been better to have had the latitudes to 

 fractions of a second, in order to keep up a consistency between 

 the measured angles and their relative positions. It would, 

 perhaps, seem impertinent in me to suggest any cause for this 

 anomaly if my observations are correct, which, to a consider- 

 able extent, I am persuaded they are ; and I sincerely hope 

 that offence will be taken in no quarter, by merely attempting 

 to clear up a difficulty that has occurred to others besides my- 

 self: more especially, if I am mistaken, I am most anxious to 

 be put right. I have, indeed, attempted to account for it by 

 the deflection of the plumb-line by the action of the dense 

 strata at ArburyHill, and by the consequent shortening of the 

 length of a degree by that means deduced. The length of a de- 

 gree a little south of this station, in latitude 52° 2' 20", is stated 

 at 60820 fathoms, or about six fathoms less than would be 

 derived from a spheroid of .0'00324 of compression at that la- 

 titude. Arbury Hill is only about 10' 35" N. of that latitude, 

 or in 52= 12' 55" N. 



Now if the latitude, for the reason assigned above, be sup- 

 posed too great by about 5" ; and since the latitude of Edin- 

 burgh is nearly 55° 57' 20", the difference is 3'' 34' 25" N. 

 = 3-573. Whence 3*573 x 6 = 21-438 fathoms at the Calton 

 Hill. Now at the mean latitude between these places, or at 

 54° 6' S5" N. the length of a degree is about 60850 fathoms, 



and 



