160 



SCIENCE. 



[Vol. I., No. 6. 



far to seek. We would submit that many easy 

 waj's suggest themselves of awakening a slug- 

 gard without need of molesting the sleep of 

 his just, and presumably virtuous, neighbor. 

 There be, in manifold variety, clock-alarums, 

 clepsj'dras, sand-glasses, and galvanic appli- 

 ances, which are full}- competent to privately 

 admonish a slumberer, without any public scan- 

 dal ; not to speak of the old English method, 

 by which an active lad gained a weekly wage 

 by ringing the house-bells of his heavier-sleep- 

 ing comrades. In one word, there is a right 

 and a wrong in this matter of the bell-ringing, 

 as science has made plain. It is not in the 

 least a question to be determined to-day or to- 

 morrow by the votes of interested parties ; for 

 the correct and the final solution of it was 

 written long ago, in the name of eternal jus- 

 tice and the immutable fitness of things. 



ON AN ALLEGED EXC'EPTION TO THE 

 SECOND LAW OF THERMODYNAMICS. 



According to the received doctrine of radia- 

 tion, heat is transmitted with the same inten- 

 sity in all directions and at all points within 

 any space which is void of ponderable matter 

 and entirely' surrounded by stationarj' bodies 

 of the same temperature. We may apply this 

 principle to the arrangement recentlj' proposed 

 by Prof. H. T. Eddy ^ for transferring heat 

 from a colder body A to a warmer B without 

 expenditure of work. 



In its simplest form the arrangement con- 

 sists of parallel screens, which are placed be- 

 tween the bodies A and B, and have the form 

 of very thin disks with certain apertures, and 

 the propertj' of totally refiecting heat. These 

 disks, or screens, are supposed to be fixed on 

 a common axis, and to revolve with a constant 

 velocit3\ For the purposes of theoretical dis- 

 cussion, we may allow this velocity to be kept 

 up without expenditure of work, since we may 

 suppose the experiment to be made in vacuo. 

 If the dimensions and velocity of the appara- 

 tus are such that the screens receive a consid- 

 erable change of position during the time in 

 which radiant heat traverses the distances be- 

 tween them, the apertures in the screens may 

 be so placed that radiations can pass from A 

 to B, but not from B to A. It is inferred that 

 it is possible, by such means, to make heat 



1 Journ. Frankl. inst., March, 1883. 



pass from a colder to a warmer body without 

 compensation. 



In order to judge of the validitj^ of this in- 

 ference, let us suppose thermal equilibrium to 

 subsist initialljr in the system, and inquire 

 whether the motion of the screens will have 

 an}' teudencj- to disturb that equilibrium. We 

 suppose, then, that the screens, the bodies A 

 and B, and the walls enclosing the space in 

 which the experiment is made, have all the 

 same temperature, and that the spaces between 

 and around the screens and the bodies A and 

 B are filled with the radiations which belong 

 to that temperature, according to the princi- 

 ple cited above. Under such circumstances, 

 it is evident that the presence of the screens, 

 whether at rest or in motion, will not have any 

 influence upon the intensity of the radiations 

 passing through the spaces between and around 

 them ; since the heat reflected bj' a screen in 

 any direction is the exact equivalent of that 

 which would proceed in the same direction 

 (without reflection) if the screen were not 

 there. So, also, the heat passing through any 

 aperture in a screen is the exact equivalent of 

 that which would be reflected in the same direc- 

 tion if there were no aperture. The quantities 

 of radiant heat which fall upon the bodies A 

 and B are therefore entirelj' unchanged by the 

 presence and the motion of the screens, and 

 their temperature cannot be affected. 



We may conclude a fortiori that B will not 

 grow warmer if A is colder than B, and none 

 of the other bodies present are warmer than B. 



Since the bodj' A, for example, when the 

 screens are in motion, does not receive radia- 

 tions from every body to which it sends them, 

 it is not without interest to inquire from what 

 bodies it will receive its share of heat. This 

 problem maj^ be solved most readily by sup- 

 posing the screens to move in the opposite - 

 direction, with the same velocity as before. 

 One may easilj' convince himself that every 

 bod}' which receives radiant heat from A when 

 the apparatus moves backward, will impart heat 

 to A when the apparatus moves forward, and 

 to exactly the same amount, if its temperature 

 is the same as that of A. J. W. Gibbs. 



PHOTOGRAPHIC FOCUSING. 

 Considerable discussion has arisen of late 

 as to the propriety of focusing with a large 

 stop, and then using a much smaller one with 

 which to make the exposure. Most of those 

 who have written upon the subject have as- 

 sumed that it was merely a question of spheri- 

 cal aberration. It seems to the writer, how- 



