Feb. 4, 1875J 



NATURE 



275 



that the value of the distance of these two points is beyond the 

 pale of all discussion. In fact, their position has been deter- 

 mined or verified by the most eminent observers, especially on 

 the occasion of great geodesic works and of the measure of the 

 velocity of sound undertaken by the Academy in the last century, 

 at the time of the meridian operations, of the determination of 

 the metre, of the map of France, and of the new measure of the 

 velocity of sound made by the Bureau des Longitudes. These 

 two stations are thus in a manner classic, and are bound up with 

 the most glorious memories in the history of French science. 



The experiment was installed in conditions worthy of the im- 

 portance of the problem to be solved. The emission telescope 

 has not less than S'S5 metres focal distance, and o'37m. aper- 

 ture. The mechanism of the toothed wheel permits a velocity 

 of the latter exceeding 1,600 revolutions per second ; the chrono- 

 graph and electric recorder ensure the measurement of time to 

 the thousandth of a second. M. Breguet, to whom the construc- 

 tion of these pieces of mechanism had been confided, has brought 

 to bear upon their e.xeculion that devoted co-operation which he 

 has always given to all the operations with which his name is 

 associated. 



All the apparatus is firmly fixed on the superior terrace of the 

 Observatory ; an electric communication, establishing the corre- 

 spondence of the chronograph with the beatings of the pendulum 

 ol the meridian chamber, fi.\es the unit of time with the greatest 

 precision. At the opposite station, on the summit of the Mont- 

 ihery tower, there is but a reflecting collimator, of which the 

 objective is o'i5 m. in aperture and 2 m. focal distance; it is 

 surrounded by a large cast-iron pipe, fixed into the wall, in order 

 to secure it from the curiosity of visitors. 



The description of the apparatus and of the method of observa- 

 tion will form the subjects of a detailed memoir. I will only 

 recall now the principle of the method. A beam of light is sent 

 across the teeth of the moving wheel, which beam is reflected 

 from the opposite station. The luminous point which results 

 from the return of the rays appears fixed, notn'rthstanding the 

 interruptions of the beam, owing to the per.sistence of the impres- 

 sions upon the retina. The exper.ment consists in ascertaining 

 the velocity of the toothed wheel, which extinguishes this 

 iuininons alio. Extinction occurs when, in the time necessary for 

 the light to traverse double the distance of the stations, the wheel 

 has substituted a tooth for the iiilcrval between two teeth which 

 permitted the passage of the light at starting, so that the extinc- 

 tion of the order 11 corresponds to the passage of 2 « — i semi- 

 teeth during this short space of lime. The law of the motion of 

 the mechanism which moves the toothed wheel inscribes itself on 

 a smoked cylinder, and the observer, by an electric signal, 

 records the precise moment when the necessary velocity is 

 attained. 



The observations are thus preserved as tracings, which I have 

 the honour to submit to the inspection of the Academy. 



The following is a summary of the results obtained from 504 

 experiments, which I have sought to vary by diversity of wheels, 

 by the number and form of the teeth, as well as by the magni- 

 tude and direction of the rotation. These results represent the 

 velocity of light in air expressed in kilometres per second of 

 mean lime ; they are arranged according to the order n of the 

 extinction which determined them ; the number accompanying 

 them represents their relative weights, that is, the product of 

 the number of observations into the factor 2« — i. 



H=4 « = s ?! = 6 « = 7 K = S 



V 300.130 300,530 300,750 300,820 299,940 



/'X(2«-i).,. 15x7 33X9 20X11 10X13 7X15 



« = 9 n-io «=ii n—\2 n = i^ 



'■' 300,550 300,640 300,350 300,500 300,340 



^■X(2«-I)... 94X17 69X19 72X21 3X23 4X25 



U-14 « = i5 «=i6 «=:i7 «=iS 



^ 300,350 300,290 300,620 300,000 300,150 



/•X(2«-l)... 9X27 65X29 4X31 22X33 35X35 

 «=I9 « = 20 « = 2I 



^ 299,550 ,, 300,060 



^X(2«-l)... 6X37 „ 36X41 



The agreement of these numbers is as close as can be desired 

 in experiments of such difficulty, and which the least undulation 

 of the atmosphere can hinder ; it is true that I always awaited a 

 purity and exceptional calmness of the atmosphere to make 

 these measurements, my patience being thereat much tried, but 

 owing to this precaution the series have always been very regular. 

 It is necessary to add, that in no case can atmospheric disturb- 



ances be the cause or systematic errors, for their occurrence is 

 always fortuitous, and on the mean of a large number of observa- 

 tions their influence is nil. 



The experiments were made at night by means of the Drum- 

 mond light, with the exception of the series of the fifteenth 

 order, which, by an exceptionally favourable meteorological cir- 

 cumstance, were able to be performed by day with sunlight. 

 Notwithstandmg the ditTerence in the nature of the luminous 

 source, the result does not deviate from the mean. 



The mean of all these va'ues, having regard to the importance 

 of each group, is equal lo 300.330, whfch, multiplied by the 

 mean refractive index of air (10003), gives as definite result the 

 velocity of light in vacuo, V = 300,400 kilometres per second of 

 mean time,* with a probable error below one-thousandth in rela- 

 tive va'ue. 



From this the solar parallax is deduced in two different 

 manners. 



1. From the e,]uaiion of liohf. — It is thus that was desi^nited 

 in the last century the time 6 which the sun's light takes to tra- 

 verse the mean radius R of the terrestrial orbit. The reduction 

 of more than a thousand eclipses of Jupiter's satellites gave 

 Delambre 9 = 473-2 mean seconds. Calling € the parallax of 

 the sun and p the equatorial radius of the earth (p = 637S'233 

 km.), we have obviously R = VO, p = A' tang ;•, whence tang e = 

 ^-andc = 8'-S7S. 



2. From the aberration of light.— V.iAiXn'^, who discovered this 

 phenomenon, found for the annual semi-elongaiion a of an ideal 

 star situated at the pole of the ecliptic (elongation due to the 

 composition of the mean velocity u of the earth in its orbit with 

 the velocity of light V), the value a = 20" -25. According to 

 W. Struve this number ought to be increased to 20' -445. The 

 equation of condition, designating by T the duration in mean 

 seconds of the sidereal year {T = 365 '26 x 86400), will be : 



tang « = if = ^'^-'^ = _ ._^JLL 

 V VT K7'tange 

 whence 



^ rytanga 



By substituting a = 2o"-25 we deduce e = 8"-88l ; with 2o"-445 

 we get 8"797. The agreement of the two methods is complete 

 if we adopt Bradley's number. 



I will recall the fact that Foucault had, by the method of a 

 revolving mirror, found for the velocity of light the number 

 298,000 km., but with an indeterminate approximation, and by 

 combining this value with Struve's constant he concluded 8" 86 

 to be the value of the solar parallax. 



The study of the planetary perturbations leads to a value for 

 the solar parallax which still further increases the interest of this 

 agreernent. I will specially cite the profound study of the per- 

 turbations of the motions of Venus and Mars made by W. Le 

 Verrier, and which has led to the following numbers : e = 

 S"-853 by the consideration of the latitudes of Venus at the 

 moments of the transits of 1761 and 1769; e = S"-859 by the 

 discussion of the meridian observations of Venus in an interval 

 of 106 years; finally, € = 8' -866 deduced from the occultation of 

 i/ Aquarii, observed by Richer, Picard, and Roemer on the 1st 

 of October, 1672 ; the mean of these values gives 8"S6. 



To summarise, the methods which serve in astronomy to 

 determine the parallax of the sun can be classed into three 

 groups -.-^ 



1. Physical methods, founded on the observation ot an optical 

 phenomenon ; they comprise the observation of the eclipses of 

 Jupiter's satellites, or the aberration of the fixed stars, combined 

 with the value for the velocity of light deduced without the in- 

 tervention of other astronomical phenomena ; the present work 

 permits us to profit by the observations which are the basis of 

 the method: the results are, e = 8"-SS, 8"'8S, 8"-So. Mean, 

 S"-8s. ■ 



2. Analytical methods, which depend on the comparison of 

 astronomical observations with theoretical laws founded on the 

 principle of universal gravitation : they give, as we have just 

 seen, values near 8"-86. 



3. Purely geometrical methods, depending on the parallactic 

 displacements of the planets near the earth : the oppositions of 

 Mars furnished, in 1862, e = 8"-84. But the transit of Venus 

 across the sun is the phenomenon in which the geometrical 

 method can attain the greatest precision. 



* The velocity in English miles per mean second will be 186,700. 



