May i, 1884] 



NA TV RE 



5 



the radius of curvature of a bath of mercury, and in taking stil' 

 greater pains it will be possible to go further and to reach an 

 exactitude such that the radius of curvature might be twice as 

 great. Under these conditions it is not possible, as one can 

 readily see, that there can be any appreciable imperfection. 

 The problem is therefore solved, as I said above. 



(2) The impossibility of finding glass-works capable of furnish- 

 ing large disks for mirrors, pointed out by Mr. Grubb, does not 

 exist. We have in reserve at the Observatory a disk for a plane 

 mirror of 1 - 22 m. diameter, weighing 650 kilos. The mirror 

 just finished by the brothers Henry has a diameter of 40 

 inches, with a thickness of '17 m. ; this weighs 380 kilos. 

 The glass-works of St. Gobain are prepared to furnish blocks 

 weighing a ton, the diameter 58 inches, to anybody who will 

 order them. 



(3) The third point in Mr. Grubb's criticism has arisen from 

 some eiTor in calculation. Mr. Grubb makes me say that 

 it is necessary to give the mirror a thickness equal to 1/5 of 

 the diameter, and then making some calculations with this 

 false datum, he finds that the mirror necessary for an equatorial 

 coudeof 27 inches would weigh 8A tonnes, and it is this result that 

 misleads him. Here are the facts. I have never said that the 

 thickness should be - i8 of the diameter. I have given - i8 as a 

 maximum. Allow me to quote textually what I have said 

 (Journal de Physique, August 1883) : " Des recherches effectuees 

 avec des miroirs de o'o8 m. m'ont demontre que pour prevenir 

 dans un miroir toute deformation causee par la flexion ou un 

 leger serrage, il faut que 1'epaisseur du verre soit <ri8 du 

 diametre. Peut etre avec des miroirs plus grands sera-t-il possible 

 de reduire notablement cette epaisseur ; en tout cas, la fraction 

 o'l8 doit etre considered comme un maximum." 



In my equatorial coude for example, the mirror has a thickness 

 equivalent to 1/6 of the diameter. In taking 1/7 for a mirror of 

 38 inches destined for an object-glass of 27 inches, one has still 

 nothing to fear, for its weight would scarcely reach 250 kilos., 

 that is to say, the half of the weight indicated by Mr. Grubb. 

 For an instrument which weighs already between 8 and 9 tonnes, 

 this addition of 250 kilos., or of 280 kilos, if we adopt the propor- 

 tion of 1/6, is so small as not to be worth mentioning. From a 

 mechanical point of view the displacement of the cylinder carrying 

 mirrors of 250 kilos., or even a tonne, considering both the move- 

 ment and the stability of the installation, does not offer the least 

 difficulty. It is a mechanical problem so elementary that not 

 only the first-class artists of all countries but even ordinary 

 constructors would be able to solve it without any great effort of 

 intelligence. I am only astonished that a man of Mr. Grubb's 

 reputation should have stopped to consider such a detail. 



(4) We now come to the question of expense. I am curious to 

 know whence Mr. Grubb could have got his information, because 

 it differs so absolutely from the facts. In spite of the addition of 

 two supplementary mirrors, the price of the new instrument is 

 less, or at all events not greater, than an ordinary one. The 

 simplicity of the construction is such that the saving in the 

 mechanical part covers the expense of the optical one. As I 

 have already pointed out in the Comptes Rendusm 1871 and 1873, 

 and in the Journal de Physique already quoted, the considerable 

 expense of rotating domes, &c, is entirely avoided. I am greatly 

 astonished, therefore, that Mr. Grubb makes on this point, so 

 thoroughly studied, an objection so little founded. If he had, 

 moreover, looked at the drawing which I published in the Jour- 

 nal de Physique of last year, he would have seen that it is almost 

 identical with that which he has communicated to the Dublin 

 Society, so far as the general arrangements for sheltering the 

 observer and instrument are concerned. M. Gautier has been 

 good enough to furnish me with the prices. 



Dimensions Ordinary Ejuvtorial Equatorial CoudcJ 



Inches Francs Francs 



12 48,000 44,000 



iS 81,000 79,000 



27 183,000 183,000 



These prices are for instruments of the most complete kind. 



The objects which I wished to attain were (1) to realise an in- 

 strument more stable than the ordinary ones, and to render 

 possible the measurement of large angular distances ; (2) to 

 establish an arrangement which permits the astronomer to explore 

 the whole sky and to regulate himself, with the most perfect 

 convenience, all the movements of his apparatus ; (3) to 

 avoid the necessity of those monumental domes, of which 

 both the building and the movement are always so costly ; 

 (4) to realise an instrument which, in spite of the introduc- 



tion of two supplementary mirrors, would be optically more 

 perfect. Indeed, being able to give the telescope a much greater 

 focal distance than in the common large instruments, the achro- 

 matism may be rendered more perfect. I believe that I have 

 succeeded in satisfying these various conditions, and that I can 

 appeal to the judgment of several of the most eminent astrono- 

 mers who have studied the instrument. Mr. Grubb makes a last 

 reproach rather curiously. He is astonished that I have not as 

 once applied the new system to the construction of a large instru- 

 ment, for he adds, " No one finds any difficulty in working an 

 equatorial of 11 inches." I do not know whether this opinion 

 of Mr. Grubb is based on his personal experience, but I do 

 know that all astronomers do not share his optimism on this 

 point. To cite only one instance. In all the observatories 

 where the discovery of comets or small planets is in question, 

 telescopes of 6 or 7 inches aperture at the outside are employed. 

 Continued work of this kind with a larger instrument is accom- 

 panied with fatigue. Now in my instrument, whatever be the 

 nature of the research, a precious economy of time and energy 

 is secured. If we have not in Paris a larger telescope on my 

 plan, I must say that my regret is greater than that of Mr. 

 Grubb, and that the lack of it does not depend on me. 



In a subsequent letter I propose to discuss Mr. Grubb's counter 

 proposal. M. L<EWY 



Paris Observatory, April 10 



On the Motion of Projectiles 

 Experiments made in 1866 showed that the resistance of the 

 air to the motion of projectiles varied only slightly for such forms 

 of heads as were likely to be used in practice, and that it was of 

 no importance whether the apex of the shot was pointed or 

 rounded off. 



From what I have said (Nature, vol. xxix. p. 527) it is evi- 

 dent that before we can calculate the trajectory of shot we must 

 know something of the quality of the gun from which the shot is 

 supposed to be fired. For if trajectories of shot fired from the ex- 

 perimental guns were calculated by the use of the tabular values 

 of K;, it is plain that the calculated ranges would err in excess 

 for the 3-, 7-, and 9-inch guns, and in dject for the 5-inch gun. 

 As Mr. Ristori, using tabular coefficients, finds his calculated 

 less than his experimental range, it may be that his gun gave a 

 degree of steadiness above the average, as the 5-inch gun did. 

 It is also necessary to be correctly informed of the exact initial 

 direction taken by the shot, because, owing to the recoil of the 

 gun, there is a "jump," which gives a greater elevation to the 

 direction taken by the shot than the elevation of the axis of the 

 gun. It is also a difficult matter to obtain the correct initial 

 velocity of a small-arm bullet. For I am assured on the highest 

 authority that the cotton threads of which my screens are com- 

 posed, would be likely to cause unsteadiness in the motion of a 

 small bullet, and if so, the measured velocity would be lower 

 than the velocity of the undisturbed bullet. And if wire screens 

 were used, the evil would be increased. From the excellent 

 work done by Robins with a small ballistic pendulum, I am dis- 

 posed to think that that instrument might be advantageously used 

 in experiments with small-arm bullets. 



As my tabular values of K T . were determined from the average 

 results given by 3- to 9-inch shot, I did not venture to put them 

 forward as being applicable to the calculation of the motion of 

 small bullets. But recently Major McClintock, R.A., Assistant 

 Superintendent Royal Small-Arms Factory, has used them for 

 that purpose. He says :— " The accuracy of rifle-bullet trajec- 

 tories calculated by means of Prof. Bashforth's tables, has been 

 tested by firing a large number of rounds through paper screens 

 placed at different points along the range. The rifle used in the 

 experiment was the Martini-Henry, and the screens were erected 

 at intervals along a 500 yards and a 1000-yards range. The result 

 of the experiment was most satisfactory, the mean heights of the 

 bullet-holes in the screens agreeing closely with the heights 

 found by calculation." 



As is well known, guns vary greatly in the degree of steadiness 

 they impart to elongated shot, and this often changes with the 

 initial velocity of the shot. It is important, therefore, to have 

 a ready way of changing the tabular coefficients K,. in the ratio 

 of 1 : k, when the coefficients will become k K r , where k is a 

 constant for that round. In the calculation of the general tables, 

 ami in using the tables of values of integrals denoted by X, Y, 



and T, we have to deal with the product — x(«K ] = 



