Feb. 21, 1878] 



NATURE 



321 



than any other body excepting hydrogen. E. Lecker has shown 

 to the Vienna Academy that mixtures of methylic alcohol and 

 water have a specific heat higher than that of water, and accord- 

 ingly take the second place,"' &c. Can you spare me a corner 

 to point out that in 1869 the specific heats of some mixtures of 

 ethyl ic alcohol and water were proved by Dr. A. Dupre and 

 myself to be considerably higher than that of water, e.g. a mix- 

 ture containing 20 per cent, alcohol, has a specific heat of 104 3, 

 water = 100 i^Phil. Trans., 1869, 591 ; Walts's Diet., 2nd Sup- 

 plement, 475). Moreover, we especially mentioned "that our 

 experiments furnished the first example of a liquid having a 

 specific heat higher than that of water." Since 1869 Dr. Dupre 

 has estimated (/V-iJc. Roy. .Soc, xx. 336) the specific heats of 

 mixtures of methylic alcohol and water without finding any such 

 mixture to possess a specific heat above that of water. 



University College, London F. J. M. Page 



Age of the Sun in Relation to Evolution 



I HAVE read Mr. Plummer's letter along with his article in 

 the Popular Sciettce Review, and am surprised at his objections 

 to my paper on the " Age of the Sun's Heat." 



It matters not whether the sun's heat was derived from the 

 contraction of his mass or from the falling in of meteorites, or of 

 comets, as advocated by Mr. Plummer in the article referred to, 

 we could only have had a supply of heat sufficient for twenty or 

 thirty million years, at the present rate of radiation. Probably 

 not much more than half of this would be available for the for- 

 mation of the stratified rocks, and the development of lite on the 

 globe ; a length of time irreconcilable alike with geology and 

 evolution. We are therefore compelled to look for some other 

 source than gravity as the origin ot the sun's heat. It will not 

 do to lengthen this period by assuming that the rate of radiation 

 was less during past ages than at present, because we should have 

 to assume that the temperature in the past was also less, a conclu- 

 sion at variance with the known facts of geology and of palaeon- 

 tology. I never supposed that the rate of radiation in the past 

 may not have been greater than now. Nor did I ever sup- 

 pose that there is any antecedent improbabiiity whatever in 

 the collision of stellar masses. What I maintained [Quart. 

 Journ. of Science for July, 1877) was that the formation of 

 a sun is an event which, on an average, can only be witnessed 

 once in about 15,000 years, or the number of visible stars 

 would be greater than it actually is. And this, I think, is a 

 sufficient reason why we should not expect any historical record 

 of such an event. Further, it does not necessarily follow that 

 the two bodies coining into collision should possess equal mass 

 or velocity in order to have their motion of translation converted 

 into heat. If it be true that the stars derived their heat from 

 loss of motion then this may quite well explain why their motions 

 are so small. In a word, the energy which the sun has been 

 dissipating into space through past ages, always existed in the 

 form of motion. Collision only changed it from one form to 

 another, viz., from the motion of translation to molecular motion. 



James Croll 



The "Phantom" Force 1 



It might be supposed that permanent and entirely local or 

 " internal" force-pairs of this kind acting on innumerable material 

 couplets in a system would so disturb the individual energies of 

 their motions that no general conclusion as to the total change 

 of energy during the progress of such a system's motion 

 could be drawn ; but the simple law that impulses act indepen- 

 dently of each other and of existing motions soon shows that the 

 whole gain of energy in the system is the sum of the separate 

 gains in the several mass-couplets due to their absolute or several 

 actions and reactions at . every instant of the motion, and that 

 when these abstract force-pairs are all permanent, the above 

 constancy of the sum of their actual and potential energies is 

 possessed by the whole system as perfectly as would be the case 

 by one only of its couplets, or component pairs. That this is 

 not merely an abridged expression for the resulting actual energy 

 in all the possible different phases that such a system may go 

 through, briefly stated for any initial and final configurations and 

 initial motion of the system by means of the negative scale or 

 potential function of all the several component force-pairs sup- 

 posed known ; not merely, that is to say, a logical consequence 

 of arbitrary and fanciful definitions, but a conclusion lull of 

 importance and of real natural signification depends, firstly, upon 

 ' Continued from p. 303. 



the fact that the thing defined as " impulse," or the gradient of 

 the scale, which is here independent of the time and depends 

 only on the mutual configuration, is not permanent by a very rare 

 occurrence, but that it is often so, and under very various circum- 

 stances ; and again that this impulse, or flux of momentum, or 

 gradient of energy, occurs in many other motions with conditions 

 of equal simplicity ; and lastly, and above all, on the fact pointed 

 out at the beginning of these reflections, that while we are able 

 to use, and of our free will to call into existence force in innu- 

 merable ways, we learn from our experience that this impulse i-; 

 invariably caused or dictated by a certain special efficacy or com- 

 pulsion, which our power of exercising it as we please so as 

 either to annul, to modify, or to increase it at will with the 

 consequence of obtaining with it any effective impulses that we 

 desire, shows us to be a different kind of quantity from the 

 impulses that we either thus obtain, or that we see it producing 

 in surrounding nature. Newton's second law of motion in fact 

 recognises this specific difference between the magnitudes of a 

 force and of its effect, when it asserts that forces produce their 

 ■whole effects (that is to say, remain unaffected in their efficacies) 

 whatever may be the state of rest or of motion of the bodies upon 

 which they act. As it is found that forces or compulsions 

 (measured as they are in statics by additions, subtractions, and 

 oppositions to a standard force) are always proportional to the 

 free impulse, or undisturbed acceleration of a mass-unit which 

 they can produce, so that by taking the impulsive effect and 

 the active compulsion of any one standard force as the units 

 for measuring these quantities respectively, they are then said 

 to be numerically equal to '^ach other in every force ; it yet 

 follows from their specific independence that they are not iden- 

 tical in kind as they are in measure. The same is true of the 

 products obtained by multiplying them separately by any small 

 space through which a force acts ; and it would be an obvious 

 misstatement to assert that the sum of the works of a compul- 

 sion, and of the free impulse which it produces taken negatively, 

 is constant when a force acts freely ; because this would be 

 confusing in one sum two different quantities ; a result which 

 it seems must arise from the simple fact that our part in 

 mechanical "compulsions" distinguislies and removes them 

 from the category of impulses to which they would otherwise 

 belong, and leads us to regard them as the causes of the im- 

 pulses which we observe. The language adopted by Newton 

 (and used also by D'Alembert) in the proposition quoted at the 

 beginning of this letter is that in a proper mechanical system, 

 compulsions equal to the observed impulses reversed, will (as is 

 obvious) arrest in their origin all changes of motion in the 

 system, and will (with the immutable force conditions proper 

 to the system) hold in balance, or give a complete account of 

 all the forces (other than those immutable ones) acting upon it. 

 Using the principle of virtual velocities in ihis case of equilibrium 

 of balancing forces, Newton expresses the rule for exploring all 

 the mechanical efficacies (superadded to the immutable ones) 

 acting in the system by concluding that the sum of all the similar 

 *' works of compulsion," or of all the "actions " in a short time 

 corresponding to a small motion of the system, when the reversed 

 ones have been introduced, will be a constant quantity. Thus 

 both Newton and D'Alembert agree in this, that they recognise 

 in forces causes which differ from the effects which they produce. 

 By what similar laws of work found to hold true in a proper 

 conservative system the modern science of energy (which deals 

 with the phenomena of causation in a wider and more diversified 

 form) seeks to extend the method of cancelling the counteracting 

 causes, or the principle of energy conservation here laid down by 

 Newton for a mechanical one, to the far larger, but less thoroughly 

 explored and exhausted field of all the onward flowing streams 

 of physical agencies which we perceive following their natural 

 bents or inclinations around us, I will presently endeavour to 

 explain. It should be noticed in connection with this general 

 extension of the principle, that the ' ' work " of a force in a short 

 time, however fixed its eflicacy, or its rate of doing work in a 

 short space (or of producing momentum, in the short time) may be, 

 is incidental, and not a fixed quality of the agent force like its 

 faculty of tension, since a force as often diminishes as increases 

 actual energy by a momentary action, and thus no fixed rule is 

 drawn from the natural tendency of force to impart momentum, 

 that potential energy necessarily becomes, or even necessarily tends 

 to become, actual energy in every mechanical energy-transforma- 

 tion. The mechanical stress of friction is an example of the 

 opposite tendency ; and it also furnishes us with an example of 

 a force whose zvorking poiuer only, and not its motive tendency, 

 is a mechanical " agent " which we can summon up at will ; but 



