4 EINAK LÖNNBERG, STUDIES ON EUMINANTS. 



for use, otherwise they \voukl l)t' brokeii ;it thc iirst trial niid coii8e(|uenlly witliout value. 

 The niecliaiiical structuve of the cow of each species can thus be i-e^vivded ns tlie siiuiniod 

 iip and inherited result of the characteristics aqui]'ed durinii' the phylogcnetical develop- 

 ment of this organ. We can therefore with Zschokke talk about a »iimewohnendo Ver- 

 (•i'l)ungs- und Bihlungskraft». »Nur so wird es erklärlich», says the author quoted, »wanini 

 Forniou und Constructionen veverbt und gebihlet wevden, welehe nicht bloss den jewci- 

 ligen Entwicklungsötadien, resp. dessen physiologischeu Anforderungen angepasst sind, 

 sondern von vornehereiu eine gewisse Maximafleistuiig des Organisnius beriicksichtigen, 

 wie man es na-raentlich bei jenen Organen beobachtet, welche sicli an (^inc plötzlich verlaugte 

 Mehrleistung uicht rasch genug anpassen können.» This was said about the skeletal bones, 

 but niay very well be applied to the structures of the horns. 



It is ho\vever, not only the spongious bony tissue of the horn-core that ^v•ill be 

 considered in the following pages, but I shall endeaxour to gi\e a brief sketch of the 

 general structure of the whole organ of different types of Cncicoriiia. 



If not solely ornaments, and that seems hardly ever to be the case, the horns are 

 used in butting a.nd hooking rivals and foes. They have then to withstand bending 

 and breaking po^vers as well as torsion. To endure these kinds of violent forces they 

 ought to be strengthened in such a way as to answer to the purpose and, at the 

 same time, it is well if mateiial can be saved and the weight of the horn diminished 

 without lesseniug the eftective power. We can here in advance make the follo\\ing genei'al 

 statements applicable in the coming discourse. Most horns can be compared with a lever 

 iixed at one end, the base of the horn, and wlien the hoiTi is used a force is applied to 

 the free end. In such a case the greatest risk of breakage is at the rtxed end, the base. 

 The horn must therefore be most strongly built there. The power of resistance can be 

 increased by adding material to the thickness of the horn, especially in the plane of 

 attaek so that the dimensions of the horn in this direction become g]'eater than in the 

 o[)posite one. That is what the (lerman authors call the »Verlängerung des Quer- 

 schnittes» or »Verlängerung der in der Biegungsebene liegenden Querschnittsdimensionen». 

 A similar result can also be obtained by the development of bracing ridges or ribs placed 

 iu or near this plane. The resisting power gains, too, by a peripherical arrangement of 

 the elements as far as possible from the neutral axis. A tube is less easily broken th:in 

 a^ solid stick nuide of the same amount of material and the strcngth of the tube is in- 

 creased continually with the cnlargement of its lumen or the lengthening of its diameter. 

 That is, as far as there is no danger of cori-ugation of the wall. Finally we have to 

 bring to mind Culmann's law which is especially applicable -with regard to the struc- 

 tureof the s])ongious bony tissue and also in other cases. According to this law it is 

 known that if a bcani or some other object comparable to such a one is fixed hori- 

 zontally with one end and then chai'ged ^vith a Aveight at the free end this tends to 

 eftect a stretching of the u]jper and a compression of the lower side of the beani on each 

 side of the central neutral axis. The lines along which these powers work are called 

 the trajectories of tension. The trajectories of stretching originate on the upper, the 

 strained, side and extend at tirst longitudina.lly parallel to this side, then curve evenlj^ 

 t(jwa.rds the middle, crossing the neutral axis at an anglc of 45°, and reach the o)jposite 



