142 



NA TURE 



[June 5, 1890 



from line PT to line PR, and thence through centre C upon line 

 PR'. Moreover, the point P is the point of intersection of lines 

 PT' and PR'; wherefore, by Theorem I., the lines PT' and 

 PR' are in perspective. 



In order to find the centre of perspectivity of lines PT' and 

 PR', we have the point k on line PT correlative of the point at 

 infinity on PT', k being determined by drawing B/& parallel to 

 PT'. The point k{ on PR', correlative of k on PT, is found as 

 before by projecting k first upon PR in k' and thence upon PR' 

 in k{. Thus, the required centre of perspectivity must lie some- 

 where on the indefinite line joining k{ with the point at infinity 

 upon PT'. Again, the point i on PR corresponds to the point 

 at infinity on PR', to point i on PT, and to point i-^ on PT' ; 

 hence the sought centre mu-t lie somewhere on the indefinite 

 line joining Zj to the point at infinity on PR' ; wherefore it 

 coincides with the intersection of lines /jS and /'/S. 



Similarly it can be shown that the lines PT and PR' are in 

 perspective ; for the line drawn from C, the centre of projection 

 for line PR', to S^o, the centre of projection for line PT, or, in 

 other words, the line drawn from C parallel to dd', ee' , &c., is a 

 coharmonic ray common to both lines ; therefore, according to 

 Theorem II., the lines PT and PR' are in perspective. The 

 corresponding centre of perspectivity is determined as follows. 

 When the line oo' , moving parallel to itself, passes to infinity, 

 or, in other terms, when the points o and o' pass to infinity on 

 lines PT and PR, the ray Qo' takes up the position CF, parallel 

 to PR. Hence, F is the point on line PR' corresponding to 

 infinity on PT ; wherefore the required centre must lie some- 

 where on the line through F parallel to PT. But i is the point 

 on PT corresponding to infinity on PR'; therefore the centre 

 must lie somewhere on the line through i parallel to PR'. 

 Hence we conclude that it must coincide with the point of inter- 

 section of lines FGand /G. 



In this short paper we have made an honest attempt to trace 

 one filament of the great stream of modern science to its original 

 source. The space at our service may not admit of much more. 

 Still, such a study, however limited its scope may be, is in- 

 teresting, not only on account of the novel nature of the demon- 

 strations which the proof of connection involves, but even more 

 because of the reflex light thus cast upon recent invention. 



Robert H. Graham. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 



Cambridge. — The Observatory Syndicate Report as fol- 

 lows : — 



That they have considered the proposal made in the Report 

 of the Newall Telescope Syndicate for the purchase of an acre 

 or an acre and a half of land adjoining the grounds of the 

 Observatory for the erection of the Newall telescope and its 

 appurtenances, and they are of opinion that, in view of possible 

 future requirements of the Observatory, it will be desirable to 

 secure now the larger area — namely, an acre and a half. 



They have consulted the Bursar of St. John's College, and 

 Ihave learnt that the College is willing to sell to the University 

 an acre and a half at the price of jC^So. Further, Prof. Adams 

 has offered to contribute ^loo towards expenses. 



Under these circumstances the Syndicate recommend that 

 Prof. Adams's generous offer be accepted, and that the Vice- 

 Chancellor, on behalf of the University, be empowered to enter 

 into an agreement with St. John's College for the purchase of an 

 acre and a half of land adjoining the grounds of the Ob- 

 servatory. 



SOCIETIES AND ACADEMIES. 

 London. 



Royal Society, May i.—" Photographic Determination of 

 the Time-relations of the Changes which take place in Muscle 

 during the Period of so-called 'Latent Stimulation.'" By J. 

 Burdon Sanderson, F. R.S. 



It is now forty years since Helmholtz published his funda- 

 mental experiments on the time-relations of muscular contrac- 

 tions. The purpose of this investigation was to ascertain " the 

 periods and stages in which the energy of muscle rises and sinks 

 after instantaneous stimulation " ; the word energy being defined 



NO. 1075, VOL. 42] 



as the "mechanical expression of activity"; and one of the 

 most important conclusions of the author was that, in the muscles 

 investigated by him, contraction does not begin until nearly one 

 hundredth of a second after excitation. This interval has, by 

 subsequent writers, been called the period of "latent stimula- 

 tion." 



Helmholtz subsequently (1854) showed, by experiments of 

 surpassing ingenuity, that during this period an electrical change 

 of very short duration occurs, which culminates at about one 

 two-hundredth of a second after excitation. The fact discovered 

 by Helmholtz was further investigated by Bernstein in 1S66, 

 with the aid of the repeating rheotome, and subsequently (1875) 

 by du Bois-Reymond, whose statement of the actual time-rela- 

 tions of the electrical response to an instantaneous excitation of 

 the gastrocnemius of the frog is embodied in a curve which 

 denotes that the muscular surface becomes negative to the 

 tendon about three thousandths of a second after excitation, 

 that this effect culminates at seven thousandths of a second, and 

 that it is immediately followed by a change of opposite sign, 

 which culminates at about ten thousandths. 



By a new method — that of photographing in succession the 

 mechanical and electrical responses in muscle on a rapidly 

 moving sensitive surface — the author has shown that the 

 mechanical response occurs much earlier than has been hitherto 

 supposed ; and that it is, in fact, simultaneous with the electrical 

 change above described — that is, with the so-called negative 

 variation. 



The method consists in projecting the movement to be re 

 corded, whether of the muscle or that of any instrument which 

 serves as an index of change, on a vertical slit on which the 

 vibrations of a tuning-fork and the motion of a signal are also 

 shadowed. Immediately behind the slit is a photographic plate, 

 which is carried by an equilibrated pendulum. The approxi- 

 mately uniform rate of motion of the sensitive surface which 

 receives the light-written record is about one metre per second, 

 but is determined in each experiment by reference to the rate of 

 vibration of a timing-fork. 



In the experiments on direct excitation, the muscles used were 

 the gastrocnemius and sartorius of the frog. In the former the 

 movement of contraction was communicated to a light index; 

 which was supported by a fine spring. One end of the index 

 rested on the muscle, while the other occupied the front focus of 

 a projection apparatus, the slit being in the other focus. When 

 the sartorius was used the surface of the muscle was itself 

 brought for a moment into the focus, at the seat of excitation. 

 The unavoidable exposure of the structure to the electric light, 

 which this method involved, lasted scarcely more than a second. 

 In successful experiments, the interval between excitation and 

 the beginning of the contraction was 2^ thousandths ( = -^^j) of 

 a second. 



For measurement of the delay in indirect excitation, the gas- 

 trocnemius (with the index) only was used, the exciting electrodes 

 being applied either at 12 or at 37 mm. from the muscle. The 

 results were not so constant. Corrected for loss of time by pro- 

 pagation along the nerve, the intervals between excitation and 

 beginning contraction varied from o'oo25" to 0'0035". 



In the experiments for determining the time after excitation at 

 which the electrical response begins and culminates, the capillary 

 electrometer was used, as in the author's experiments on the 

 heart and on the leaf of Dioncsa, as a signal, but with much 

 improved apparatus for recording. 



In the gastrocnemius of the frog, the electrical response to an 

 instantaneous stimulus is indicated by a sudden movement of the 

 mercurial column of so short a duration, that to most persons it 

 is invisible. Its photographic expression is that of a spike pro- 

 jecting from the dark border of the part of the plate which is 

 unprotected by the mercurial column. The electrical inter- 

 pretation of this spike is that between the contacts two electrical 

 changes of opposite sign and not more than one two-hundredth 

 of a second in duration have immediately followed each other, 

 or, more explicity, that the spot excited became, for about 

 o 0005", first negative, then for a similar period positive, to the 

 other contact. 



In the muscle (the leading off contacts being on the Achilles 

 tendon and muscular surface respectively, and the nerve excited 

 at a distance of 12 mm.) the electrical response begins at 0*004" 

 and culminates at about 0-012" after excitation. Deducting the 

 delay due to transmission along the nerve, we have, as the time 

 between excitation and response, 0"0035". It is thus seen that 

 i the electrical response, instead of preceding the mechanical, is 



