230 The Astronomer Royal's Experiments on 



ties to be integrated are : — 



Longitudinal 



■x[x — a) 



Transversal 



bx 



{{x-df + tfY 



and the results of integration are :- 

 Longitudinal force 



I 



+ 



I 



+ hyp.log{(/ + fl )a + j8^-/_a}-hyp.log{(/-. fl )« + 62li + /-a}, 

 J ransversal force =- = + r« 



I have computed these numbers for each of the eighteen 

 stations. For comparison with observation, I have taken the 

 experiments with the flat side towards the small magnets, 

 which represents most nearly the case of a linear large magnet ; 

 and, for facility of comparison, I have multiplied the experi- 

 mental numbers by 6. The following is the comparison : — 



Experimental. 



Theoretical. 



Longitudinal. 



Transversal. 



Longitudinal. 



Transversal. 



-1500 







- 1 849 







-1560 



4- 822 



-1750 



-1089 



-1416 



+ 1656 



-1441 



-2112 



-1092 



+2664 



- 827 



-2928 



- 216 



+3240 



+ 355 



-3180 



+ 948 



+2706 



+ 3126 



-2283 



+ 1950 



+ 1890 



+ 1589 



-1389 



+3312 



+ 1104 



. +2395 



- 622 



- 960 







-3029 







- 894 



+ 432 



- 971 



+ 517 



- 738 



+ 816 



- 776 



+ 960 



- 474 



+ 1110 



- 428 



+ 1267 



- 72 



+ 1302 



- 2 



+ 1319 



+ 306 



+ 1140 



+ 335 



+ 1066 



+ 552 



+ 924 



+ 409 



+ 801 



4- 720 



+ 708 



+ 668 



+ 633 



+ 942 



+ 492 



+ 805 



+ 380 



4- 1140 



+ 240 



+ 984 



+ 251 



The agreement is not satisfactory; but I am unable to 

 suggest the nature of the change that ought to be made in the 

 assumed law. 



I shall add only one remark, of a somewhat practical charac- 

 ter. In a paper published originally by Dr. Lamont in Pog- 

 gendorfPs Annalen, vol. cxiii. p. 239 &c, and of which a 

 translation, by W. T. Lynn, Esq., of the Royal Observatory, is 

 printed in the Philosophical Magazine, 1861, November, 



