A Case of Morlus Pedicularis. 49 



mation will be useless, particularly if, in the first, we use 

 four or five well selected observations. 



We may also, in the correction of the first elements, 

 make use of the second differences in the following manner. 



Instead of calculating the values cf U, U', ^and F' in 

 the three hypotheses, we shall calculate them in five hypo- 

 theses, viz. 1. With the elements found by the first ap- 

 proximation. 2. By varying the perihelion distance by 

 a very small quantity. 3. By varying it by double this 

 small quantity. 4. By preserving the same perihelion 

 distance as in the first hypothesis, and varying by a small 

 interval the instant of the perihelion passage. 3. By vary- 

 ing the same instant double this interval. Let m, ?n', m", 

 7n"', m'"' be the values of U— F; n, n', n'', n'", n"" the values 

 of U'—V : then in order to determine the values of u and 

 t, we shall form the two equations, 



{im' — 3771 — 711") .u+ (?«'' — 9.m'-]-m) .u- + (4m'"— 3m — 771""). t 

 4- {jn"" — 2«i"' + m) J' + 2m = 0, 

 {A7i' — Sn — 7i").u + ill"— 2?j' + 7i).7/.^ + {'^7i"' — 3n—n"").t 

 -f (7^"" — 27^'"+7^). ^- + 271 = 0. 

 The values of u and of t which satisfy these equations will 

 be more precise than the foregoing. Although in most 

 cases this overmuch precision is useless, it is nevertheless 

 indispensable in forming these equations, at all times when 

 the terms depending on the second differences may be of 

 the same order with those which depend on the first dif- 

 ferences ; which will happen, for instance, when in one of 

 the observations the vector radius of the comet will be al- 

 most perpendicular to the visual ray from the earth to the 

 comet. 



[To be continued.] 



VII. A Case of Morhus Pedicularis, Communicated ly 

 John Andbee, Esq. Surgeon. 



xV. R. esq. 35 years of age, of a very healthy and strong 

 constitution, had for some years past, particularly when 

 heated by good living and in warm rooms, been often trou- 

 bled with a prickly itching on the surface of the body, 

 armpits and thighs. In the summer of last year, on coming 

 out of a warm bath at Brighton, he discovered an insect on 

 his thigh. 



This circumstance induced him to suspect that the itch- 

 ing he had so long been troubled with, might have been 

 caused by insects. From that time until he applied to me 



Vol. 39. No. 165. Ja//. 1812. D on 



