[18] It is evident that many of the figures, especially those exceeding 1000°, have been determined with but little exactitude, and some, placed in Table III. with the sign (?), I have only given on the basis of rough and comparative determinations, calculated from the melting-points of silver and platinum, now established by many observers. In Table III., besides the large periods whose maxima correspond with carbon, silicon, titanium, ruthenium (?), and osmium (?), there are also small periods in the melting-points, and their maxima correspond with sulphur, arsenic, antimony. The minima correspond with the halogens and metals of the alkalis. A distinct periodicity is also seen in taking the coefficients of linear expansion (chiefly according to Fizeau); for instance, in the vertical series (according to the magnitude of the atomic weight), Fe, Co, Ni, Cu, the linear expansion in millionths of an inch = 12, 13, 17, and 29; for Rh, Pd, Ag, Cd, In, Sn, and Sb the coefficients are 8, 12, 19, 31, 46, 26, and 12, so that a maximum is reached at In. In the series Ir (7), Pt (5), Au (14), Hg (60), Tl (31), Pb (29), and Bi (14), the maximum is at Hg and the minimum at Pt. Raoul Pictet expressed this connection by the fact that he found the product [alpha](_t_ + 273)[3root](A/_d_) to be nearly constant for all elements in the free state, and nearly equal to 0·045, and being the coefficient of linear expansion, _t_ + 273, the melting-point calculated from the absolute zero (-273°), and [3root](A/_d_), the mean distance between the atoms, if A is the atomic weight and _d_ the sp. gr. of an element. Although the above product is not strictly constant, nevertheless Pictet's rule gives an idea of the bond between magnitudes which ought to have a certain connection with each other. De Heen, Nadeschdin, and others also studied this dependence, but their deductions do not give a general and exact law. [19] Carnelley found a similar dependence in comparing the melting-points of the metallic chlorides, many of which he redetermined for this purpose. The melting-points (and boiling-points, in brackets) of the following chlorides are known, and a certain regularity is seen to exist in them, although the number (and degree of accuracy) of the data is insufficient for a generalisation:-- LiCl 598° BeCl_{2} 600° BCl_{3} -20° NaCl 772° MgCl_{2} 708° AlCl_{3} 187° KCl 734° CaCl_{2} 719° ScCl_{3} ? {CuCl 434° ZnCl_{2} 262° GaCl_{3} 76° {(993°) (680°) (217°) AgCl 451° CdCl_{2} 541° InCl_{3} ? {TlCl 427° PbCl_{2} 498° BiCl_{3} 227° {(713°) (908°)