92 



SCIENCE 



[N. S. Vol. XXXVI. No. 916 



tracting cells can be grown not only from the 

 pieces of hearts of young embryos, but from 

 the heart muscle of a fourteen-day chick 

 embryo. 



These experiments, therefore, give direct 

 evidence for the myogenic theory of the heart 

 beat. 



MojVtrose T. Burrows, M.D. 

 Anatomical Laboratory, 

 Cornell "University Medical College, 

 New Yoek City 



ON molecular cohesion, a preliminary 



statement 

 There is much uncertainty both about the 

 laws and nature of molecular cohesion. The 

 attraction has been supposed to vary inversely 

 with the square, the fourth, fifth, seventh, or 

 even the ninth power of the distance between 

 molecular centers; and whether cohesion is of 

 the nature of magnetic, electric, or gravita- 

 tional attraction, or ^whether it is of a kind 

 of its own, is uncertain. Its relation to 

 gravitation, on the one side, and to atomic 

 aiSnity, on the other, is unknown. 



1. The Derivation of the Value a/V^ in Van 

 der Waals's Equation. — The value of a/V^ in 

 Van der Waals's equation represents molecu- 

 lar cohesion. If each molecule has a mass of 

 cohesion, M, and if the molecules attract each 

 other inversely as the fourth power of the dis- 

 tance, as Sutherland suggests, then the at- 

 traction between two molecules is M'^K/v*/^, 

 V being the volume of one molecule. If there 

 are 1/v^/^ molecules in a surface of one sq. 

 cm. of a gas or liquid, the pressure per sq. cm. 

 will be 2PK/V-. If each molecule attracts 

 only its neighbors, owing to the fact that the 

 cohesion does not penetrate matter, then the 

 internal pressure will be the same as the at- 

 traction of each double layer of molecules and 

 instead of M^E/v^ we may multiply numera- 

 tor and denominator by N-, where N is the 

 number of molecules in the volume V. This 

 makes N-M-E/V-, which is the value a/V- 

 of Van der Waals's equation. It has the ad- 

 vantage over the usual form, a/V-, in that the 

 various constituents of " o " appear at once. 



2. The Latent Heat of Vaporization. — 



Mills discovered the empirical relationship 

 that the internal latent heat of vaporization 

 divided by the difference of the cube roots of 

 the densities of the liquid and vapor was a 

 constant, except near the critical tempera- 

 ture. His equation was: L — Ee = E(d^/^ — 

 P^/^). He assumed that the internal latent 

 heat of vaporization, or i — E„, where L is 

 the total latent heat and E^ that part of it 

 consumed in doing external work, represented 

 only the energy consumed in separating the 

 molecules. He was struck by the resemblance 

 of this equation, when transformed into 

 L — Ee = E'(l/v^/^ — l/V^/^), to that of 

 Helmholtz representing the heat given out 

 from the sun on contraction from the radius 

 CR to the radius B, or 3M'-E(1/R —l/0R)/5. 

 The latter equation is derived by the gravita- 

 tional law. Mills, therefore, concluded that 

 the attraction of molecules must also follow 

 the gravitational law and vary inversely as 

 the square of the distance. The error in 

 Mills's reasoning is the assumption that 

 L — Eg represents only the work of overcom- 

 ing molecular cohesion. It represents not only 

 this but also the heat consumed by the ex- 

 pansion of the molecules from their volume 

 in the liquid to their volume in the vapor, for 

 the molecules certainly expand on passing 

 from the liquid to the vapor. If the heat thus 

 consumed by molecular expansion is E^y then 

 since the difference in molecular cohesive 

 energy in the vapor and liquid is N-M^K(l/v 



— 1/7), L—Ee = N^M"-K(l/v — l/V)—E^. 

 Near the critical temperature E„t becomes 

 nearly zero, and at the critical temperature 

 this goes into the form L — Ec = N^M^E(l/v 



— 1/V). Since the heat rendered latent by 

 the expansion of the molecules increases as 

 we go dovsmward from the critical tempera- 

 ture, the value L — E^ must become con- 

 stantly greater than N-M^K(l/v — 1/V), by 

 the amount E^- This is found to be the 

 case. For example in methyl propionate 

 (L — Ee)/(d — D) has the following values 

 in absolute units taking gram mol quantities : 



