Mr. Utting on Errors in Dr. Hutton's Tables. 427 



horizon. Further researches, both mathematical and astrono- 

 mical, are therefore required for completing the solution of 

 the problem of the refractions. Theory must supply the for- 

 mulas ; and the astronomer, by numerous observations at and 

 near the horizon, must furnish the data necessary for deter- 

 mining the theoretical quantities. Even although there should 

 be little chance of attaining, near the horizon, all the accuracy 

 desired by the astronomer, yet the question is still one of 

 great interest, as it may lead to important results respecting 

 the constitution of the atmosphere. 



My chief design, gentlemen, in addressing you in this letter, 

 is to put on record nay ideas on the topics treated in it, which 

 I have frequently mentioned in conversation. I have written 

 hastily, and desire the indulgence of your readers. 



I have the honour to be, &c. 

 Junc 14 > 1824 - James Ivory. 



LXX. On some Errors in Dr. Hutton's Tables of the Pro- 

 ducts and Powers of Numbers. By Mr. James Utting. 

 Gentlemen, 

 /~\N perusing your Journal for last month, the errors men- 

 w tioned in Dr. Hutton's Tables of the Products and 

 Powers of Numbers attracted my attention. Mention is made 

 in your Journal, of 40 errata occurring in p. 20 of Dr. Hut- 

 ton's Tables. Now, Gentlemen, the number of errors in this 

 page actually amounts to about 1 700 ! which I discovered se- 

 veral years since, and of which no mention is made in the list 

 of errata : and conceiving it will be rendering an acceptable 

 service to such gentlemen as use Dr. Hutton's Tables, I take 

 this opportunity of pointing them out ; viz. The Products of 

 all numbers from 361 to 380 at the head of the Table by 15 

 to 99 at the side are all 100 too little. 



I remain, Gentlemen, yours truly, 

 Lynn Regis, 10th June, 182J. James Utting. 



LXXI. Introduction to the Sixth Section o/'Bessel's Astrono- 

 mical Observations. 

 I SHALL first give such a short description of the meri- 

 dian circle as is necessary for understanding the observa- 

 tions : a more detailed one would no doubt be very curious to 

 all those who take an interest in the great advancement of the 

 art of constructing astronomical instruments brought about 

 by Reichenbach * ; but it would require plates, and fall far 



* Wc think it right to ohserve that M. Besscl has never seen the Green- 

 wich instruments.— Edit. 



3 H 2 short 



