VOL. TLVIII.] PHILOSOPHrCAL TRANSACTIONS. 475 



(u — 2au + a* + b') X («' — lau + a* + c»), &c. = (2 + 2y) X ( u* — 2ciu 

 + (3") X ("' — 2au -f y") X (?i — 2rtw + i*), &c. if instead of Vq' + 6% 

 t/a* + t'j ^f^- (tlie secants of the arcs of which b, c, d, &c. are tangents) we 

 put p, y, S, &c. 



And, by a like substitution in the equations in art. 1 1 and 14 it appears, that 

 (2a — w)" — u" is = 2an X {a — u) X (u' — 2au + y'') X (u' — 2au + ^), &c. 

 or 2 (a — w) X («' — 2au + y') X (?«' — 2au -^ i''), &c. according as n is an 

 even or an odd number: and that (2a — u)" + m" is = 2a« X (m' — 2au + (3*) 

 X («' — 2aM + y"), &c. or 2 X (n' — 2au + (3*) X (m' — 2aM + y ), &c. ac- 

 cording as n is an odd or an even number. 



LXXFII. An Extraordinary Disease of the Shin, and its Cure. Extracted 

 from the Italian of Carlo Crusio. By Rob. Watson, M.D., F.R.S. p. 579. 



A young woman of 17, the daughter of a citizen of Naples, was brought to 

 the royal hospital June 22, 1732, and was placed in one of the wards assigned 

 to the care of Dr. Crusio; who was informed by her, that her complaint was an 

 excessive tension and hardness of the skin over all her body, by which she found 

 herself so bound and straitened, that she could hardly move her limbs. He 

 found her skin hard to the touch, like wood, or a dry hide; however, he ob- 

 served some difference in the degrees of the hardness; for in some places it was 

 greater; as in the neck, forehead, and particularly in the eye-lids; so that she 

 could neither raise nor entirely shut them. It was also very great in the lips, 

 tongue, and on each side of her body ; but the muscles under the skin seemed 

 not to be affected, because the joints could be bent; and if in any place there 

 was any difficulty in moving the limbs, this arose not from any defect in the 

 muscles, but from the hardness and tension of the skin and cellular membrane, 

 which did not yield to their contraction and relaxation. Her skin had lost its 

 natural warmth, but was sensible, when it was pressed by the nails, or a pin; 

 the patient then saying, that she felt a pain, as if the skin were tearing. Her 

 pulse was deep, and obscure; but equal, and regular. Her respiration was free, 

 and uninterrupted; her digestion good, and she found no inconvenience after eat- 

 ing, except a greater constriction round the belly. The alvine excretions were 

 easy and proper; but the urinary sometimes exceeded the quantity of what she 

 drank, and appeared loaded with salts ; both which circumstances perhaps pro- 

 ceeded from the sensible and insensible perspiration being entirely wanting. For ' 

 she never sweated, though ever so much exercised. Her sleep was natural; she 

 had never had the menstrual evacuation. Her disorder began first in her neck, 

 when she could not move it as usual ; then she found the skin of her face and 

 forehead grow hard ; and so successively, she found all the external parts of her 



3p2 



