78 



NA TURE 



{Nov. 24, 1887 



than these, Prof. Nipher's experience is totally at variance with 

 my own. 



During the last four years, Dr. Thorpe and I, assisted at some 

 Scotch stations by Mr. A. P. Laurie, have made about three 

 hundred independent determinations of the dip. The observations 

 have been made in the course of a magnelicsurvey of the United 

 Kingdom at various stations, in all weathers, and without any 

 delay after magnetization. We have used two sets of 32-inch 

 needjes, and have made determinations with two needles at nearly 

 all the stations. In no single case does the difference between 

 the results obtained with two needles amount to 4'. In 

 three or four cases only does it exceed 3', while differences 

 of 2' are relatively rare. Thus in forty-six ^scotch stations (for 

 which alone the results are fully tabulated) the differenc-s ex- 

 ceeded 2' in nine cases only. Mr. Welsh, in the survey of 

 Scotia id, recorded in the Report of the British Association for 

 1859, and the Rev. S. Perry obtained results in which the 

 discordance between the two needles was of the same order of 

 magnitude as in our own work. 



If, therefore, Prof. Nipher refers to differences comparable 

 with those exhibited by his published observations, they are con- 

 trary to the experience of observers working with better constructed 

 instruments. If he refers to errors smaller but observed with an 

 instrument with which a discordance bet\\een the two needles of 

 from 10' to 24' can be tolerated, I should doubt if his apparatus 

 is suitable for the elucidation of the point. If he is in possession 

 of good evidence that, in the case of needles for wh'ch the maxi- 

 mum difference between observations made without delay 

 after magnetization is not greater than 4', the accord between 

 them is improved by delay, the matter is no doubt of 

 interest for observatory work. My own experience has been 

 chiefly gained in the field, and I can only say that I have never 

 noticed anything which led me to suspect such a cause of error. 



It is, however, capable of proof that the improvement can be 

 but small, as results obtained in a laboratory and without the 

 precaution Prof. Nipher insists on agree nearly to the limit 

 to which the instrument can be read. 



This can be illustrated from the observations made by Dr. 

 Thorpe and myself at Kew for the purpose of testing our survey 

 instruments. At first we employed only a circle by Dover, No. 74- 

 The following observati ms were made with it in the magnetic 

 house by Mr. Baker, the Chief Assistant, and ourselves : — 



Mean. 



(>1 366 

 67 36-0 

 67 36-3 



These results were about 2' lower than those obtained by Mr. 

 Baker with the Kew instrument about the same time, but what- 

 ever the cause of this may have been they certainly do not convey 

 the idea of instability. 



Lately we have again compared No. 74 with the Kew instru- 

 ment and with Dover No. 83, which belongs to the Science and 

 Art Department. Thus six needles (two belonging to each 

 instrument) were used. I quote (he results, not as in any way 

 extraordinary, but as types of the accuracy usually obtained by 

 competent observers with good ins'ruments : — 



Mr. Baker's observations with the Kew instrument are again 

 (as is shown below) a little higher than those obtained with 

 Dover's circles. 



Judging then from these results and from our own field obser- 

 vations, I do not believe that, apart from small instrumental 

 errors, the error of the determination of the dip with a single 

 needle, and without any delay after magnetization, will in general 

 exceed ± i'. Under unfavourable circumstances it may reach 

 ± i'"5. These estimates embrace not only the assumed insta- 

 bility of the magnetic axis, but that and all other causes of error 

 combined. That some effect of the kind referred to by Prof. 

 Nipher, which only affects the re.sult below these limits, may 

 exist even in good needles is perhaps possible. As the verniers 

 of the circles only read to minutes it could not be detected except 

 by making a number of observations for the purpose. 



In conclusion I may add that for good dip observations good 

 instruments are es-ential. In a preliminary survey in the 

 neighbourhood of Mull, made in 1883, we employed an older 

 instrument which had been a good deal used in a laboratory. 

 The measurements made with it were less satisfactory than those 

 above described, but the largest difference between the two 

 needles did ujt exceed 6'. For survey purposes ir^mall needles 

 and circles seem on all accounts better than the large ones used 

 by Prof. Nipher. Arthur W. Rucker. 



South Kensington, November 2. 



Greek Geometry. 



In the notice of the last part of "Greek Geometry from 

 Thales to Euclid" (Nature, vol. xxxiv. p. 548) I was 

 uncertain whether Dr. Allman intended it to be Part vii. or not ; 

 I observe from the extract before me {Hentiathena, No. xiii., 

 1887, vol. vi. pp. 269-78) that the present part is so entitled. 

 The author's plan led him to the temporary omi-^sion of 

 Thesetetus of Athens, a pupil of Theodorus of Cyre.ie, and also a 

 disciple of Socrates, who greatly advanced the science of 

 geometry. How his gifts and genius impressed both Socrates 

 and Plato is well known from the dialogue which bears his 

 name. From an analysis which our author makes of part of this 

 dialogue it appears that Thefetetus, in addition to Eudoxus and 

 the Pythagoreans, was one of the original thinkers to whom 

 Euclid was most indebted in the composition of the " Elements." 

 Dr. Allman thus recapitulates : — "In the former parts of this 

 paper we have seen that we owe to the Pythagoreans the sub- 

 stance of the first, second, and fourth books, also the doctrine of 

 proportion and of the similarity of figures, together with the 

 discoveries respecting the application, excess, and defect of areas, 

 the subject-matter of the sixth book. The theorems arrived at, 

 however, were proved for commensurable magnitudes only, and 

 assumed to hold good for all. We have seen, further, that the 

 doctrine of proportion, treated in a general manner, so as to 

 include incommensurables (Book v.), and consequently the re- 

 casting of Book vi. and also the method of exhaustions 

 (Book xii.) were the work of Eudoxus. If we are asked now : 

 In what portion of the ' Elements ' does the work of Thea:tetus 

 survive? we answer: Since Books vii., viii., and ix. treat of 

 numbers, and our question concerns geometry ; and since the 

 substance of Book xi., containing, as it does, the basis -of the 

 geometry of volumes, is probably of ancient date, we are led to 

 seek for the work of Theeetetus in Books x. and xii. ; and it is 

 precisely with the subjects of these books that the extracts (rt'), 

 \e), and (/) are concerned." 



The extract {d) states that Euclid, x. 9, is attributed to 

 ■ Theastetus by an anonymous scholiast, probably Proclus ; extract 

 {e) translates, discusses, and illustrates fully the passage (147 D- 

 148 B) of the iJialogue ; and extract (/) me itions the statement 

 by Suidas, thit our geometer taught at Heraclea, and that he 

 first wrote on " the five solids," as they are called. Attention is 



