2 THOMAS DWIGHT OX THE 



Dr. Julius WolfT' aj)i)lic'(l tlie principles of matliomaties more rigidly than bad been 

 heretofore done to the study of the bony jilates. ^Vt his request Prolessor Cuhnanu 

 caused to be di-awn the stress lines of a ci-ane of the general shape of the ui)per end 

 of the femur and found a sui'prising resemblance betAveen the stress lines and the tra- 

 beculae. Dr. AVoltt" concluded that from our laiowledge of the needs of a bone we 

 can predict its internal structure and also that the converse of the pro])osition is true. 

 He writes: 'xVud thus we come to the view which, when we have once gi-asped it, seems 

 so natural and self-evident, that the plan on which the bone is built is the only possible 

 one." I make no comment on these conclusions as the discussion of this and allied (jues- 

 tions is the puri)ose of the present paper. 



Wolfermann'" wrote shortly after in the same sense and included in his observations 

 the bones of many animals. !N^ot content with admitting the relation between the me- 

 chanical needs of the bone and its structure, he went so far as to assert that the fornu'r 

 are actually the cause of the latter. 



Aeby' maintained that the arrangement of the laminae of a bone depends on its move- 

 ments. The laminae, according to this theory, are parallel when the axes of two Cjou- 

 nected bones remain so, but if one of these bones is flexed on the other by turning on one 

 axis, the plates converge in the planes perpendicular to the axis. If the bones move on 

 more than one axis there is a general convergence. Moreover, all these types show near 

 joints a system of slightly developed transverse plates. At points of muscular insertion 

 the muscle represents the axis of a bone. 



Merkel,' in a [)aper on the fenuir, expressed some doubt as to the teleological arrange- 

 ment of the plates, basing his objection on the striking similarity of the plan in the 

 human heel bone" which rests on the groinid and that of the quadruped which ]irojects 

 in the air. 



Bardeleben^ published a monograph on the spinal colunm in man and animals which he 

 argued is to l)e regarded as a trestle-work. 



Langferhans" and Wao^stafte' made many sections of human l)ones and each conciu'red 

 in the prevailing vicAV. 



Ogston'^ started the theory that plates develo])ed fi-om articular cartilage are ])erpen- 

 dicnlar to the surface of the bone, and those from the periosteum parallel to it. 



Professor Humplny' conti-averted this, maintaining that the arrangement is nf)t due 

 to development, but rather has "relation to the line of Aveight and the direction of the 

 forces to be resisted." 



In 1882, V. Meyer'" classified more accurately than lie had done the different kinds of 

 cancellated tissue. He recognized a round-meshed sti-iicture fitted to resist pressure 

 ill all directions. This generally presents in the middle Avhat he calls an intermediate 

 spongy portion, made of thicker plates and larger spaces, Avhich adds to the strength. 

 Then there are the short bones that receive pressure in two opjjosed directions and cou- 



'Vircliow's Arcliiv, Tlntitl i,, ISTfl. ^Vircliow's Arcliiv, P.iinrl i.xi, 1874. 



-IJou-liert mid Dii Bois Hpyinoiul's Arcliiv, 1R72. "St,. Tlioiiias' Hospital Kepovt.*, 187.5. 



■'Ci'iilralblatt fiir incd. Wi.ssoiiscli , lt<7;5. Moiinial of Aiiat. and Pliys., Vol. xn, 187S. 



'Virchow's Arcliiv, Bami i.ix. 1874. "J)itU), Vol. Xlii, 1878. 



^Bcitnigc ziir .Vnatoiuie dcr Wirbclsiiulc, .Tcna, 1874. '"Beitriige zu Biologic. (BischofT's Jiibilauiii.) 



