SCIENCE. 



[Vol. XX. No. 497 



' flatheads ' are more particularly found in the piae-wood 

 regions, where game is obliged to subsist solely upon heather 

 forage (sweet broom), and where food is to be found only in 

 occasional places. 



"As transitory forms, there are also in such districts, in 

 addition to the few flatheads found at all times, deer having 

 one 'scurr' or stunted horn, while the other horn is well 

 developed, bearing perhaps ten to twelve branches, and the 

 majority of the rest of the deer have only small, smooth 

 antlers of light color, some curiously bent or spirally 

 twisted. Deer which instead of antlers bear a long, straight, 

 spear-like horn on one side were formerly called ' provincial 

 murderers,' as they were considered a very dangerous enemy 

 of other deer during the rutting season, and on which ac- 

 count their destruction was sought. 



"In the main, these so-called deformities, and even the 

 total absence of antlers on the flatheads, can in no way be 

 considered an indication of the lack of procreative power, nor 

 can they be classed with the abnormal forms or the total loss 

 of antlers, which results from injuries, and which reappear 

 in their young. The flathead deer are seldom unequal in 

 strength or weight to the others of the same age and the 

 same district, but occasionally excel the latter in these re- 

 spects. They also early enter the rutting season, and show 

 themselves equally ready for the conflict. Their art and 

 manner of fighting are singular enough ; like the female, 

 they rise up high on their hind feet, and with their fore-feet 

 they, from above, mercilessly strike their antagonist. It is 

 remarkable how the antler-bearing antagonist intuitively 

 enters such conflict by rising on his hind feet, making no 

 use of his terrible weapons. On such occasions the flathead, 

 having developed superior skill in his movements, almost 

 always puts to flight in a few rounds much larger deer with 

 immense forked horns. Also at other seasons the contests 

 may be observed in regions where the flatheads are found, 

 and where at times a troop of such game is run together into 

 a narrow space, as is the case occasionally during the prepa- 

 rations of a suspended hunt; yet those encounters are less 

 fierce and soon ended, as they are brought on by the momen- 

 tary invitations and accidental meeting of the deer in the 

 press." 



Have there been any cases of deer, bisons, etc. , with ' flat ' 

 or hornless heads noticed in America ? A. 



SOME ANALOGIES BETWEEN MOLECULES AND 

 CEYSTALS. 



BY JOHN W. CALDWELL. 



Chemistry and crystallography are closely related 

 branches; they are, indeed, but parts of one great whole. The 

 special design of chemical laws is to present the methods 

 and conditions of the re-arrangement of atoms, which re-ar- 

 rangements we generally denominate chemical reactions. 

 The laws of crystallography, on the other hand, primarily 

 relate to the element of form. While the first series of laws 

 concerns the arrangements of atoms, the second takes cog- 

 nizance of the arrangements of molecules: while the one 

 considers the influence of the chemical force of affinity, the 

 other is concerned with the physical force of crystalliza- 

 tion. 



A consideration and comparison of the most important 

 laws of the two series will develop, I think, a most interesting 

 parallelism and correspondence. Thus, the Srst great law 

 of cheinistry is that of definite proportions, in which is stated 

 the principle of the fixed and unchanging composition of 



every compound. It finds its satisfactory analogue in the 

 crystallographic law of the constancy of the interfacial 

 angles, first propounded by Steno in 1669, and re-enunciated 

 by Eome de I'lsle in 1783. It affirms that for a certain 

 crystal species, under conditions of absolute identity of chem- 

 ical constitution and equality of temperature, the correspond- 

 ing interfacial angles in different individuals will be found 

 always to be equal and constant; and this holds in imperfect 

 as well as perfect crystals. It is evident then, that what 

 the law of definite proportions is, in regard to chemical con- 

 stitution, the law of constancy of the interfacial angles is, in 

 respect to crystalline form. 



Another equally perfect and beautiful correspondency 

 obtains between the law of multiple proportions and that of 

 the rationality of the indices. The former emphasizes the 

 simple multiple ratio of one element as it unites with some 

 other element to form two or more compounds; whereas 

 the latter, an important crystallographic law, attributed to 

 Haily, articulates the remarkable fact that the modifications 

 of specific crystalline form always take place by a multipli- 

 cation of one or more of the index values (or the reciprocals 

 of these, the parameter values), by small and simple numbers 

 or fractions, by rational and not by irrational quantities. 

 The analogy here existing is easily appreciated: in the one 

 case we have presented the method (namely, by simple mul- 

 tiple ratio) of the formation by weight of chemical com- 

 pounds containing the same elements; in the other, the 

 method, also by simple multiple ratio, by which is deter- 

 mined the modification of fundamental form of a crystalline 

 species. 



A third analogy is found in the comparison of the law of 

 valency or equivalence in the chemical domain, and the 

 law of replacement or substitution in the crystallographic. 

 The first of these, of course, refers to the relation by weight 

 in which the various elements react; potassium beina: ex- 

 changed for sodium m the proportion of 39 of the former to 

 23 of the latter; and, in like manner, chlorine (35.5) for 

 bromine (80). The chemical type or idea is continued in 

 such reactions, although one of the original constituents may 

 have been substituted by another element. Correspondingly, 

 the law of replacement allows the crystallographic type or 

 idea to be continued, though by altered agents. Thus, the 

 recognized substitution-power of magnesium and calcium 

 allows, in compounds of the latter, a greater or less substitu- 

 tion of the former, without change of crystalline form ; cal- 

 cite and dolomite are both rhombohedral in crystallization, 

 the angles of the two differing slightly. 



A fourth analogy is expressed in the allotropisms and 

 isomerisms of chemistry, and the dimorphisms and poly- 

 morphisms of crystallography. The allotropism of elements 

 is probably to be explained upon the basis of different 

 atomicities of the elemental molecule; but, however ex- 

 plained, like atoms are able in many cases to build up struc- 

 tures sometimes as variant in physical characters as are the 

 diamond and ordinary charcoal, having chemical dispositions 

 as different as common phosphorus and red phosphorus. 

 Similar suggestions apply to the subject of isomerism. Now, 

 to this, crystallography presents an analogue in the di- 

 morphism so often to be seen in minerals; one and the same 

 substance showing itself in nature in two (sometimes more) 

 crystalline forms, i.e., belonging to distinct crystalline sys- 

 tems; take, as illustration, calcite (rhombohedral) and arra- 

 gonite (orthorhombic). Here again diversity of form is set 

 over against diversity of physical and chemical characters. 



A fifth analogy (the last that I shall venture) bases upon 



