630 PHILOSOPHICAL TRANSACTIONS. [aNNO 1723. 



these three angles, is double tiie complement to a right one of the angle under 

 AKL, the angle under kml, or the refracted angle, being equal to half the sum 

 of this angle under akl and the angle under cky : as in the last place the angle 

 under klv, that is the angle of incidence, equal to the sum of the angles under 

 KML and under mkl. 



I need not observe, that the geometrical methods of deducing these angles 

 of incidence and refraction from the angle measuring the distance of each rain- 

 bow from the point opposite to the sun, afford very expeditious mechanical 

 constructions. 



On the Method of procuring the Small Pojc, in South fVales. By Perrot 

 Williams, M. D. N^ 375, p. 262. 



However new the method of communicating the small pox may appear in 

 this kingdom ; yet it has been commonly practised by the inhabitants of Pem- 

 brokeshire in Wales, time out of mind, though by another name, viz. that of 

 buying the disease, as I have been long since informed by several who pro- 

 cured the distemper by that means. There is a married woman in the neigh 

 bourhood of this place, who practised it on her daughter, about a year and a 

 half since, by which means she had the small pox favourably, and is now in 

 perfect health, though she has ever since, without reserve, conversed with 

 such as have had that distemper. 



To procure the distemper, they either rub the matter taken from the pustules 

 when ripe, on several parts of the skin of the arms, &c. or prick those parts 

 with pins, or the like, first infected with the same matter. And though they 

 omit the necessary evacuations, such as purging, &c. yet I am informed they 

 generally come off well enough ; and I cannot hear of one instance of their 

 having the small pox a second time. 



One Mr. Owen, a gentleman of this country told me, that above 20 years 

 since when at school, he and several of his schoolfellows, infected themselves 

 at the same time, from the same person, and that not one of them miscarried. 

 The method he used was this : having rubbed the skin off his left hand with 

 the back of his penknife, till the blood began to appear, he applied the variol- 

 ous matter to that part; which by degrees growing inflamed, about a week 

 afterwards he fell into the snriall pox. I have since conversed with several others, 

 who made the like experiments on themselves, 20 years since : who all posi- 

 tively affirm, that they never had the small pox a second time. 



Haverford West, Sept. 28, 1722. 



