H 



NATURE 



[July i, igog 



biana zoologiae professor, qui saltationes illas karyokinesis 

 nomine nuncupatas doscripsit, quas ovorum in cellulis 

 dividendis nuclcorum fragmenta certatim exercent. In 

 insectis autem nonnullis, docente doctore nostro novo, 

 detcrminatur sexus, prout nuclcorum fragmentum unum 

 aut adest aut abest. Genus femininum tot fragmenta 

 efKciunt ; fragmenta uiio tantum minora raasculinum. 

 Videtis, Academici, discrimine quam tenui genus mascu- 

 linum a genere feminino separetur, ne dicam superctur. 



Charles Ren^ Zeillek, Professor of Pal.iobotany in 

 P.IIRIS. — E tot docloribus supremus adest Francogallorum 

 Instituti celeberrimi socius, palaeobotanicae professor prae- 

 clarus Parisiensis, qui iam per annos triginta plantas 

 fossiles (ut aiunt) accuratissime examinavit ; Africae, 

 Americae, Indiac, Asiae Minoris flores extinctos non sine 

 summo iudicio, non sine summo ingenio, investigavit. 

 Viri huius auxilio. Florae antiquae e monumentis non iam 

 unum alterumve capitulum perbreve, non iam paginae 

 cuiusque lineae paucissimae, sed novae paginae plurimac, 

 orbis terrarum quasi vitae perpetuae ad catenam continuam 

 anulos novos addiderunt. 



" Sic umimquicquid paulatim protrahit aetas 

 in medium, ratioque in luminis erigit oras. 

 namqne alid ex alio clarescere et ordine debet_ 

 ommius, ad summum donee venere cacumen."' 1 



Rerum naturae seriem aeternam claudit Homo sapiens : 

 honorum nostrorum seriem hodiernam claudit vir in Flora 

 antiqua sapientissimus, Carolus Renatuf Zeiller. 



A NEW ANALYTICAL ENGINE. 



THE April number of the Scientific Proceedings of 

 the Royal Dublin Society contains an interesting 

 and very original paper by Mr. Percy E. Ludgate 

 on a proposed analytical machine. Of all calculating 

 machines, the analytical machine or engine is the 

 most comprehensive in its powers. Cash till reckoners 

 and adding machines merely add or add and print 

 results. Arithmometers are used for multiplying and 

 dividing, which they really only accomplish by rapidly 

 repeated addition or subtraction, with the exception 

 alone, perhaps, of the arithmometer of Bollee, which, 

 in a way, works by means of a mechanical multi- 

 plication table. DifTerence engines originated by 

 Babbage produce and print tables of figures of 

 almost any variety, but the process is one of addition 

 of successive differences. The analytical engine pro- 

 posed by Babbage was intended to have powers of 

 calculation so extensive as to seem a long way outside 

 the capacity of mere mechanism, but this was to be 

 brought about by the use of operation cards supplied 

 by the director or user, which, like the cards deter- 

 mining the pattern in a Jacquard loom, should direct 

 the successive operations of the machine, much as 

 the timing cam of an automatic lathe directs the 

 successive movements of the different tools and feed- 

 ing and chucking devices. However elaborate the 

 mechanism of Babbage, if completed, might have 

 been, the individual elements of operation would, so 

 far as the writer has been able to understand it, have 

 been actually operations of addition or subtraction 

 only, and, with the exception of the method of multi- 

 plication created by Bolide, the writer does not recall 

 any case in which mechanism has been used to com- 

 pute numerical results except by the use of the pro- 

 cesses of addition or subtraction, simple or cumula- 

 tive. Of course, harmonic analysers and other instru- 

 ments depending on geometry are not included in the 

 category of machines which operate on numbers. 



The simplicity of the logarithmic method of multi- 

 plying must have made many inventors regret the 

 inherent incommensurability of the function to any 

 simple base, or, if commensurability is attained for 

 any particular number and its powers by the use of 



^ Lucretius, v. ad/incin. 



NO. 2070, VOL. 81] 



an incommensurable base, the incommensurability of 

 the corresponding logarithms of numbers prime to 

 those first selected. On this account the writer has 

 always imagined that the logarithmic method was 

 unsuitcd to mechanism, or, if applied at all, could 

 only be so applied at the expense of complication, 

 which would more than compensate for the directness 

 of the process of logarithmic multiplication. 



Mr. Ludgate, however, in effect, uses for each of 

 the prime numbers below ten a logarithmic system 

 with a different incommensurable base, which as a 

 fact never appears, and is able to take advantage of 

 the additive principle, or, rather, it is so applied that 

 the machine may use it. These mixed or Irish log- 

 arithms, or index numbers, as the author calls them, 

 are- very surprising at first, but, if the index numbers 

 of zero be excepted, it is not diflicult to follow the 

 mode by which they have been selected. The index 

 numbers of the ten digits are as follows : — 



Digit 01234 56 78 9 



Index number. 50 o 1 7 2 23 8 33 3 14 



When two numbers are to be multiplied, the index 

 numbers of the several digits are mechanically added 

 to the index numbers of each of the digits of the 

 other, and, the process of carrying the tens being 

 carried on simultaneously, the time required is very 

 small. For instance, the author gives as an example 

 the multiplication of two numbers of 20 digits each, 

 which will require 40 of these additions, which he 

 shows will require gj time units if a time unit is 

 one-tenth of the time of revolution of a figure wheel. 



Unfortunately, while the principle on which the 

 proposed machine is to work is described, only the 

 barest idea of the mechanical construction is given, 

 so that it is difficult to judge of the practicability of 

 the intended construction. Whatever this may be, the 

 originality of the method of mixed commensurable 

 logarithms to incommensurable bases seems to the 

 writer so great and the conception so bold as to be 

 worthy of special attention. 



Division has hitherto always been effected by the 

 process of rapid but repeated subtraction, following in 

 this respect the method practised with pencil and 

 paper. Having discovered how to harness the 

 logarithm to mechanism, Mr. Ludgate would, it would 

 be expected, have managed to effect division by a 

 logarithmic method, and possibly he could have done 

 so, but here again he has left the beaten track, and 

 by his ingenuity has made division a direct, and not, 

 as hitherto, an indirect or trial-and-error process. 

 Starting with a table of reciprocals of all numbers 

 from 100 to 999, which in a mechanical form is 

 intended to be stored in the machine, he imagines 

 both numerator and denominator of the required frac- 

 tion piq to be multiplied by the reciprocal A of the 

 first three digits of q so as to become .\p I \q. Aq 

 must, then, in every case begin with the digits 100, 

 and it may be written i + x, where x is a small frac- 

 tion. Then plq=Ap{i-x)(i+x'-)(i+x<')(i + x') . ._ . 

 a highly convergent series of which five terms will 

 give a result correct to twenty figures at least, and so 

 division is intended to be effected by a process of direct 

 multiplication. 



Until more detail as to the proposed construction 

 and drawings are available it is not possible to form 

 any opinion as to the practicability or utility of the 

 machine as a whole, but it is to be hoped that if the 

 author receives, as he deserves, encouragement to 

 proceed with his task, he will not allow himself 

 to become swamped in the complexity which must be 

 necessary if he aims at the wide generality of a com- 

 plete analytical engine. If he will, in the first in- 

 stance, produce his design for a machine of restricted 



