NOTES AND MEMORANDA. 323 



sacrifico of definition, and, as the better the image the more notice- 

 able do errors resulting from this plan of overlapping several of them 

 become, wide-angled glasses show the defects of this jilan more mark- 

 edly than narrow-angled lenses, whence has arisen the fallacy that 

 narrow-angled lenses are possessed of an inherent property of " pene- 

 tration " and a residual error has been lauded as a virtue.* 



Process for Measuring the Solid Angles of Microscopic Crys- 

 tals. — In the ' Bulletin de la Societe Mineralogique de France ' 

 (1878, No. 4, p. 68) M. Thoulet gives the following method for 

 measuring the solid angles of microscopic crystals: — 



If, in a tetrahedron, we know the lengths of the six edges, we can 

 ascertain the angles of the faces surrounding the same summit, and 

 can consequently resolve the spherical triangle whose sides are respec- 

 tively the angles of the faces of the tetrahedron, and whose angles are 

 the dihedral angles of the edges of this same tetrahedron. 



We place the crystal (which may be isolated or contained in a thin 

 plate of rock) in any given position Tinder the Microscoi>e, and choose 

 four special points, two on the edge, and the others respectively on 

 one and the other of the two planes whose angle is to be measured. 

 By means of the fine adjustment of the microscope, we successively 

 bring into focus each of these summits, and note the vertical displace- 

 ment in each case by the milled head. 



Without moving the crystal, we replace the eye-piece by a camera 

 lucida, and make a drawing of the crystal, marking very accurately by 

 pricks the position of the four j^oints ; then the crystal is replaced by 

 a stage micrometer, which will make a scale of the drawing to be 

 made. 



We now possess all the data necessary to calculate the solid angle. 

 Each of the sides of the tetrahedi-on is determined : 1st, by its hori- 

 zontal projection on the drawing ; 2nd, by the difierence in the vertical 

 height of its two extremities, as indicated by the fine adjustment. 



The rest of the work is only a trigonometrical calculation of three 

 rectilinear triangles, whose three sides are known, and of which one 

 of the angles has to be found, and, finally, the calculation of a sphe- 

 rical triangle whose three sides are known, and one of the angles of 

 which is to be found. 



Instead of drawing the whole crystal, it is evident that it would 

 suffice to note the four essential points ; the complete drawing, how- 

 ever, allows a subsequent verification, which is often necessary, and, 

 besides, enables us to decide as to the crystallographic notations to be 

 given to the crystalline face. 



The solid angles of crystals having dimensions less than y-^^ of a 

 millimetre can be measured to less than a degree by this method.f 



Method of Isolating the Connective-Tissue Bundles of the Skin. 

 — Dr. George Thin, in a paper communicated to the Eoyal Society,;]: 

 describes the method he has made use of for this object. 



* From a paper read by Dr. Blackham before the Indianapolis Congress. 

 Cf. a French translation m ' Journal de Microgranhie,' iii. (1879). 

 t ' Bull. Soe. Belg. de Micr ,' v. (1878) 6. 

 i ' Proc E. Soe.,' xxviii. (1879) 251. 



Y 2 



