iio 



NA TURA 



[July 27, 1S93 



submitted to experiment there was a great tendency to an uni- 

 formity of figure for tlie oxygen consumed under similar physical 

 circumstances (food, temperature, &c.), so that, if the CO., ex- 

 pired fell, the oxygen alisorbed rose, and vice versa ; this was 

 accounted for by assuming that an increase of CO.. in the blood 

 in the slate of repose is produced at the expense of the O 

 absorbed. The fourth person experimented upon exhibited no 

 such tendency, the COo expire! and O absorbed rose and fell 

 together, which was ascribed to the fact that he was still 

 growing. 



2nd. Experiments were made on the influence of exercise on 

 respiration, which showed that if stepping exercise (stepping at 

 the rate of sixty-eight times per minute) is taken after a period 

 of rest, there occurs for a few minutes an accumulation of CO.j 

 in the blood ; of course the storage of CO^ after exercise must 

 be controlled by the noimal amount of COo produced in repose, 

 and the kind of exercise taken ; this storage would in the cold 

 winter weather, and between one and two hours after food, con- 

 tinue for about eighteen or twenty minutes. In my case the 

 volume of CO.^ retained in the blood amounted to a mean of 

 500 c.c. while stepping sixty-eight times per minute. The CO, 

 in store is next given out in the form of a wave, which is re- 

 newed after a certain lapse of time, .so that there does not 

 appear to l)e in respiration under exercise a fixed relation between 

 the COo expired and the COo left in the blood With practice 

 and training this relation would probably become more and more 

 uniform. 



The storage of C0._, in winter and after food was found to 

 exhibit a certain relation to the excess of CO.j expired un.ler 

 exercise over the COo expired in repose ; but eighteen or 

 twenty minutes after exercise had been commenced this relation 

 failed to show itself any longer. 



The ratio in question was the same with two different persons ; 

 but further expeiiment is required to determine whether this 

 ratio can be looked upon as general ; the mean relation found is 

 shown .by the figure o'l23 ; therefore, so far as the present 

 inquiry goes, by multiplying this figure 0123 by the excess of 

 COo given out per minute under exercise over the CO., expired 

 in repose during the same lapse of time, tire result will show the 

 volume of CO„ absorbed in the blood per minute. 



3rd. After the exercise adopted in this inquiry had been fol- 

 lowed by a coaiplete repose of ten minutes, the COo expired 

 had returned to the normal in repose, but the volume of O 

 absorbed per minute had considerably fallen, apparently owing 

 to the blood having charged itself with oxygen during exercise, 

 so that the first few minutes after rest was taken, the blood was 

 in a condition to supply oxygen for tissue-changes without taking 

 it from the air breathed at the time. After half an hour's perfect 

 rest following exercise the respiratory changes had returned to 

 their normal state of repose, or nearly so, the oxygen absorbed 

 still occasionally showing signs of being a little lower than 

 before exercise had been taken. 



June 15. — "On a Graphical Representation of the Twenty- 

 Seven Lines on a Cubic Surface." By H. M. Taylor, Fellow of 

 Trinity College, Cambridge. Communicated by A. R. Forsyth, 

 F.R.S. 



The converse of Pascal's well-known theorem may be stated 

 thus : if two triangles be in perspective, theirnon-corresponding 

 sides intersect in six points lying on a conic. An extension of 

 this theorem to three dimensions may be stated thus : if two 

 tetrahedrons be in perspective, their non-corresponding faces 

 intersect in twelve straight lines lying on a cubic surface. This 

 theorem may be deduced from the equation 



ix + aX)[y + b-X) (s -1- cT) (« -i- aT), 



pentagons, and hexagons on the surface is determined, as well 

 as the number of ways in which nine triple tangent planes can 

 be drawn to pass through all the twenty-seven lines, and the 

 number of ways in which twelve of the lines can be chosen, 

 so that they are the intersections of two tetrahedrons in 

 perspective. 



"Polarisation of Platinum Electrodes in Sulphuric Acid." 

 By James B. Henderson, B.Sc. Communicated by Lord 

 Kelvin, P.R.S. 



This investigation was begun about the beginning of Feb- 

 ruary, 1893, at the instigation of Lord Kelvin, and was con- 

 ducted in the Physical Laboratory of Glasgow University. The 

 object of the investigation was to obtain the difference of poten- 

 tial between two platinum electrodes immersed in a solution of 

 sulphuric acid immediately after the stoppage of a current which 

 had been electrolysing the solution, and to find how this differ- 

 ence varied with a variation in the intensity of the current or in 

 the strength of the solution. 



Former experiments by Buff and Fromme have given for the 

 maximum polarisation with platinum wires of very small 

 surface in the electrolysis of dilute sulphuric acid 3 "5 and 46 

 volts. 



Dr. Franz Richarz says of the above : — " In these experiments 

 the polarisation is calculated from measurements of the intensity 

 of the galvanic current during the electrolysis, tacitly assuming 

 that the resi.slance of the decomposition cell is independent of 

 the intensity of the galvanic current. The correctness of the 

 supposition has not been proved." By employing a different 

 method he found values for the polarisation never greater than 

 26 volts with small wire electrodes, and also got the same maxi- 

 mum with large platinum plates. 



The electrodes in the present investigation were rectangular 

 plates of platinum foil 7 cm. long by 5 '5 cm. broad, and were 

 immersed in the solution to a depth of 5 cm., having their planes 

 parallel, and about i cm. apart. There were thus 55 sq. cm. 

 of surface of each plate wetted. To find the polarisation one of 

 Lord Kelvin's Quadrant Electrometers was used. The method 

 used can be best understood from the diagram. By me£.ns of 



m 



\ CUADR. 



ELECTnOLYTICCELL' 

 DRAUT ELECTf^OMLTER 



I, h Jt' 

 J — ^ »c_ 



ax + fiy + yz + Su ; and a, h, c, d, o, /8, 7, S are 

 The equations of twelve lines on the surface are 



where T : 



constants, 

 evident. 



This paper shows how the remaining fifteen straight lines on 

 the surface may be obtained by means of nothing higher than 

 quadratic equations, and determines which of these lines inter- 

 sect each other. 



The paper then proceeds to give a graphical method of 

 representing all the intersections of the twenty-seven lines on a 

 cubic surface by means of a plane diagram, which admits of many 

 interesting transformations. 



By the help of such diagrams some of the known relations of 

 the twenty-seven lines to each other are deduced, and some 

 theorems with respect to the lines which it is believed are new 

 are established ; for instance, the number of closed quadrilaterals, 



NO. 1239, VOL. 48] 



BATT EflY 



the key k the breaking of the electrolysing current circuit andj 

 the switching of the electrodes on to the terminals of the electro-l 

 meter were done simultaneously. Before switching as above,! 

 however, the needle of the electrometer was deflected by keep-J 

 ing the key /!•' down, thereby making a difference of potentiaU 

 between the pairs of quadrants equal to that between the slider j 

 and the earthed end of the high resistance slide bridge, and thisi 



