56 PHILOSOPHICAL TRANSACTIONS. [aNNO 1736. 



the point c of the lens cg, where it is refracted towards the point d of the lens 

 DF, and there again refracted into the line de, cutting the axis in k. The angle 

 AOP contained between this last line de, continued backward, and the first line 

 of incidence of the ray ab, will be very nearly equal to double the angle of in- 

 clination of the axis of the lenses el, to the plane of the speculum bn ; i. e. 

 double the angle ghn. 



Demonslr. — Produce the lines of incidence and reflection of the ray ab and 

 BC, till they meet the axis of the two lenses in i and l ; and through the point 

 B draw BK perpendicular to the plane of the speculum, and cutting the same 

 axis in k; then the angles kbl and kbi are equal. The angle klb is the differ- 

 ence of the angles ikb and kbl ; and the angle hib is the sum of the angles ikb 

 and KBI = to KBL : therefore the angle ikb is equal to half the sum of the angles 

 hib and klb. But by the foregoing lemma, the angles klb and fed are very 

 nearly equal. Therefore the angle ikb is nearly equal to half the sum of the 

 angles hib and fed ; that is, to half the angle pob ; and its complement bhi or 

 GHN is nearly equal to half the angle aop, the complement of pob to a semi- 

 circle, a. E. D. 



If the first incidence of the ray be supposed to be in the line ed, it will pro- 

 ceed in the same track as before, but with the contrary directions ; so that the 

 angle eob made between the first incident ray, and the last reflected, will still 

 be equal to the double of ghn, as before. 



It is evident that on this principle an instrument might be constructed, the 

 effects of which would in a great measure resemble those of that before-men- 

 tioned (N° 420) : but it would be liable to the errors arising both from the 

 spherical figure of the lenses, and also the different refrangibility of the rays of 

 light, when the object is seen at a distance from the axis of the telescope ; 

 though those errors, by a proper disposition of the parts of the instrument, may 

 be reduced to a very small quantity. However, for this reason, and also be 

 cause the instrument seemed to be attended with greater inconveniencies, both 

 in its construction and use, than the other, Mr. Hadley did not think it neces- 

 sary to give any more particular description of it. 



Of a large Bony Substance found in the fVomb. By Edward Hody, M. D., 



F.R.S. N°440, p. 189. 



In examining the pelvis of a woman, 57 years of age. Dr. H. found a large 

 bony substance, contained in the womb, and so strictly united to it, that they 

 seemed to be one and the same body. On cutting the substance asunder, he 

 observed, that the ossification went no farther than the thickness of a shilling; 



