NATURE 



\Nov. 4, 1875 



OUR BOOK SHELF 



Further Researches in Mathematical Science, embracing 

 the Appendix of '^'' The Two Discoveries^ By the author 

 of " The Two Discoveries." (Clement Pine, Taunton 

 Road, Bridgwater, 1875.) 



Our readers may ask, who is the author of ''The 

 Two Discoveries," and what are the Discoveries ? An 

 advertisement informs us that Mr. Clement Pine him- 

 self is the former, and that the subjects of " The 

 Two Discoveries" are "The Mathematical Discovery, 

 the Spiritual Telegraph, Astronomy, Cause of the Changes 

 of the Seasons, Botany, Capillary Attraction, or the 

 Principle of Growth ; Religion, Progression, Scenery 

 in the Spirit Realm, &c., and a variety of other topics." 

 A suggestive list ! We shall extract a niorceau here and 

 there which will indicate the nature of the present 

 pamphlet. There are " important discoveries in a science 

 in which very slight advances have been made since its 

 foundation was laid by Euclid." We commend this to 

 the " Improvement of Geometrical Teaching Associa- 

 tion." To his scholastic ignorance and to his loss of sight, 

 Mr. Pine attributes the fact of his attention having been 

 turned ^to these subjects and of his having hit upon 

 shorter, simpler, and more effectual modes of obtaining 

 certain results. 



After a personal narrative, he tells us he bought a 

 guitar. " The guitar having only six strings to perform a 

 melody which may require sixteen whole tones, besides 

 semi-tones, to be effected by shortening the strings by 

 fingering, I had now a fair field open for my calculations. 

 So I conceived a musical instrument of sixteen strings 

 similar to the guitar, which would require no shortening 

 of the strings by fingering, but which could be played 

 straight ahead, each string representing a different note, 

 like the harp. Now, all my stock-in-trade in mathematical 

 science was a knowledge of the properties of the right- 

 angled triangle, which, connected with the rule of propor- 

 tion known as the Rule of Three in arithmetic, seemed like a 

 magic key to unlock the mysteries connected with geometry 

 and trigonometry." He then dwells on the properties of the 

 right-angled triangle. The especial property is the dis- 

 covery imputed to Pythagoras. This he expects is of 

 ''greater value than any other axiom in mathematics." 

 He simplifies " this simple axiom, and if you want it any 

 plainer, the only way is to set your own brains to work." 

 With his Minstrel (the musical instrument) he has plenty 

 of amusement. " I would be so absorbed in calculating 

 and committing the numbers arrived at to memory as to 

 be quite unconscious I had lost my sight. The outer 

 world was invisible, but the inner world of the spirit was 

 transparent." He then comes to his main point, viz., the 

 true mode of obtaining the distances of remote objects 

 by observation. " My mind must have been occupied on 

 this theorem for five or six years, and it was not until a 

 year after the recovery of the sight of one eye that I dis- 

 covered the principle. At length it came to my mind 

 like a flash of lightning, first to find the correspondence of 

 the circle to the square ; and then to obtain the distance 

 by the proportion of the paralax {sic) to the length of the 

 square for a divisor, and the length of the base line mea- 

 sured or obtained as the multiplier. . . . The principle 

 itself is perfect, and the approximation to perfection in its 

 application depends altogether on the comparative per- 

 fection of the instrument used and of the observations 

 made." 



There are two diagrams and long descriptions. We 

 have preferred to let our author speak for himself, and so 

 to show that if he is not affected with the morbus cyclo- 

 metricus, the diagnosis points to a disease nearly allied 

 to it. Further, we have hardly dared to discuss the 

 pamphlet in other fashion on account of the para- 

 graphs on p. 12, prefaced with the remark, " But what is 

 to come will startle you." " I have been receiving from 



my honoured father in the Spirit Realm, John Pine, senior, 

 some two dozen essays on philosophical subjects. He 

 was giving his views on religion in very forcible language, 

 and thinking I was becoming too excited, he made a 

 sudden change to trigonometry, and then referred to my 

 diagrams, and the importance of my discovery in mathe- 

 matics ; and that it was my duty to lay it before the 

 world. I said it seemed to me very complete for terres- 

 trial observations, but I was not aware that it would apply 

 to astronomy. He remarked that it was equally applicable 

 to astronomical as terrestrial observations ; and he in- 

 sisted that I should continue my researches on the subject. 

 I have taken his advice, and have continued my mental 

 researches ; and shall now present them for public 

 scrutiny." His father further states : " Two years ago, or 



more, when you used to be showing them to , I was 



with you all the time when you were studying on the 

 subject, and am better acquainted with the diagrams than 

 you are yourself." With the announcement of this " Im- 

 primatur " we close our notice of this singular farrago. 



Notes 071 Forestry. By C. F. Amery, Deputy Conser- 

 vator, N.W. Provinces, India. Pp. 119. (London : 

 Triibner and Co.) 



This is a little book written by a forest officer for the 

 benefit of those Englishmen who, having been trained in 

 the schools of forestry in France and Germany, require a 

 convenient handbook written in their mother tongue to 

 guide them in their future operations in forest work. 

 Bulky books in the languages of the two countries just 

 alluded to already exist, but these, as the author says, 

 deal so largely in details that the student has frequently 

 to wade through a great mass of matter before he can get 

 a clear view of the individual facts he is specially in 

 search of, or of the broad general principles which govern 

 forest administration. Considering the number of edu- 

 cated and intelligent men now employed in the Forest 

 Department of India, we might suppose that some would 

 be tempted to record their experience for the benefit of 

 those who may be working in the same cause. Dr. 

 Brandis's " Forest Flora " is the first trustworthy work 

 devoted to the scientific and economic aspects of the 

 Indian forests, but besides a knowledge of the trees them- 

 selves the practical forester requires to know more than a 

 little about the planting and thinning of trees, the trans- 

 port and measurement of timber, &c., and it is upon these 

 matters that Mr. Amery's "Notes" deal. He points 

 out that Nature's method to foster the growth of the 

 young seedlings is to allow the admission of sufficient 

 light and air. The practice prevailing in Germany is to 

 thin out the young plants at first only lightly to assist 

 germination, then to admit more light to encourage 

 healthy development. " The period between the first 

 thinning and final clearing varies from ten to thirty years. 

 On the plains of India, such is the rapid growth of some 

 of the trees in their earlier stages as compared with the 

 rate of growth in Europe, that it will probably not be 

 desirable to extend the period beyond two or three years ; 

 but this difference of conditions does not affect the prin- 

 ciple, which is the admission of as much light and no 

 more than is necessary to the well-being of the young 

 crop at every stage." The seedlings of some of the finest 

 timber trees are of so delicate a nature that they have not 

 power to struggle through any kind of undergrowth, even 

 through rank grass : to overcome these difficulties it is 

 recommended that in ordinary grass land the sods should 

 be removed and inverted grass to grass, and the seeds 

 sown on the inverted sod, which should be from five to 

 six inches thick. The advantages of this system are, that 

 the seedling plants are elevated a few inches above the 

 surrounding soil, so that they have no foes to contend 

 with in the early stages of their growth. From these 

 remarks it will be seen that the book is entirely practical, 

 and will, we have no doubt, be consulted by young 

 foresters. J. R. J. 



