Jtdy 4, 1872] 



NATURE 



179 



The passage from the one rule to the next is very gradual, 

 but never tedious ; there is copious explanation, but yet 

 we think no supe'rfluous verbiage. Every page is to the 

 point, and marks the writer as one who has had practi- 

 cally to deal with the sort of young minds for whom his 

 work is primarily if not solely intended. The book is a 

 thoroughly rational one, though at first sight the reader 

 may think he has stumbled by mistake upon an elaborate 

 treatise on the subject of dominoes, for the method of 

 teaching is based on a combination of what has been 

 called "palpable" with written arithmetic. In actual 

 teaching the palpable method is the one adopted. Mr. 

 Orme's own words are, " Teachers are strongly recom- 

 mended to take every available opportunity of using suit- 

 able blocks of wood to represent units, tens, hundreds, 

 and thousands, and I should wish it to bo distinctly 

 understood that, without these blocks or some substitute 

 for them, the subject will become too abstract to be com- 

 prehended by those for whose sole benefit this book has 

 been compiled" (Preface, p. 4); and on p. 7 the resemb- 

 lance of each diagram to a domino suggests the remark, 

 " Learn to play at the game called dominoes ; this will 

 teach you how to tell the number of dots in a figure very 

 quickly." 



The main divisions are occupied with units, or single 

 unpacked things ; tens, or single unpacked deca-units ; 

 hundreds, or single unpacked hecto-units ; and thousands, 

 or single unpacked kilo-units. I'"roni some of the terms 

 here employed, it might be supposed that the work treats 

 principally of questions concerned with metres, decimetres, 

 and other quantities, which require an acquaintance with 

 the metric system ; but this is not the case, though it is 

 well fitted to serve as an introduction to the use of such 

 a system. Special reference to this system is confined to 

 two pages of " Directions," where the dimensions of a 

 square centimetre are represented in a figure. 



The following extract from the Preface will serve to 

 show the spirit by which the writer is actuated: — "If 

 the teacher proceeds in this way {i.e., by the palpable 

 method of using blocks) he will be amply rewarded by 

 finding that children, not so stupid as they are often 

 said to be, will frequently make out processes of their 

 own for arriving at trutlts, having been taught to rely not 

 on rules, but on reason ; and occasionally the youngest 

 pupil will unconsciously show his teacher how to teach. . 

 . . . More good will arise from the introduction of a 

 scientific method into the teaching of the ordinary sub- 

 jects of education than will accrue from object lessons, 

 or the freely-accepted dicta of men of science." hi thus 

 letting Mr. Orme speak for himself, we shall best put be- 

 fore our readers the object aimed at in his boolc — an ob- 

 ject which he seems to us to have compassed ; and as we 

 think it is a right one, it is on this ground we venture to 

 recommend the work to all who may be in search of a 

 good elementary introduction to arithmetic. If they care- 

 fully follow out the advice given, and pursue the plan 

 laid down, they will convey a sound and accurate view of 

 the subject, and that without wearying the young student. 

 There is good store of simple and varied exercises in 

 this handy volume, which may readily be curtailed or 

 enlarged, according to each individual case. The only 

 typographical faults we have to point out occur on pp. 

 30, 104, and 105, and are readily corrected. We com- 



mend the book as the work of a " cunning " arithme- 

 tician. " It is pitie that commonlie more care is had, 

 yea, and that emongcs verie wise men, to finde out 

 rather a cunnynge man for their horse, than a cunnyng 

 man for their children."' 



OUR BOOK SHELF 



Contribution to the Biology and History of the Dcvclop- 

 iiit'iit of the Ustilagincce. By Dr. A. Fischer von 

 Waldheim. Translated for the Transactions of the 

 iN'ew York State Agricultural Society for 1S70. From 

 '■ Pringsheim's Jahrbiicher," vol. ii. part i, 2, 1869. 

 (Albany, New York : 1S72.) 



The section of Fungi to which the Ustilagines belong 

 has occupied cofisiderable attention from mycologists 

 during the past quarter of a century. Old notions of the 

 autonomy of species have been dispersed, and at the 

 present time all the old genera are suspected, some are 

 condemned, and not a few amalgamated. The present 

 condition of the classification of the Uredinous Conio- 

 mycetes is eminently transitional ; so much has been 

 written, so many observations made that await confirma- 

 tion, or require further researches to render the work com- 

 plete, that no one would be rash enough to predict what 

 another twenty years may accomplish towards settling the 

 relations of tlie genera in this group to each other. From 

 the vague notions and doubts of Unger's " Exantheme " in 

 1S33, Leveille's researches in 1839, Tulasne's first memoir 

 in 1847, De Bary's " Brandpilze" in 1S53, Tulasne's second 

 memoir in 1854, there has been a regular advance in the 

 accumulation of observations and the record of facts up 

 to the publication of Fischer von Waldheim's communi- 

 cation in 1869. The relations of Tricliobasis\.o Puccinia, 

 of some species of LccytSica to Mclainpsora, of others to 

 Phragmidium, are admitted on every hand ; but whether 

 Tridwbasis, Puccinia, Uroniyces, and ^-Ecidium, shall all 

 give way to an amalgamated genus, in which the four 

 forms shall be recognised as four conditions of the same 

 plant, though accepted by some, cannot yet be considered 

 as settled beyond a doubt. The more sceptical of myco- 

 logists suspend their judgment, and await the confirmation 

 of certain observations. Whatever the result may be, 

 there can be but one opinion that such men as Tulasne, 

 LeveiUe, De Bary, and others, deserve all commendation 

 for the work they have accomplished. Whilst the Uredines 

 Proper have suffered greatly in tlie stability of their 

 generic distinctions, the Ustilaginous group has at present 

 maintained its character for the autonomy of its species. 

 Up to the present Tilletia, Ustiia^o, Thccaphora, and 

 Urocystis, seem to represent comparatively stable genera. 

 It is not impossible that this is more seeming than real, 

 and that future workers may reveal affinities more close 

 than as yet are suspected. The "contribution" of 

 Fischer von Waldheim dates as far back as 1S69, although 

 now presented for the first time in an English dress, and 

 we have to thank our Transatlantic cousins for having 

 accomplished this fact. The New York State Agricul- 

 tural Society is wise to diffuse this and all similar infor- 

 mation amongst its members. None are more deeply in- 

 terested in the development, conditions of growth, and 

 metamorphisms (if any) of the " Smuts " than agricul- 

 turists, and to no societies should we look with more 

 confidence for the publication of such memoirs as the 

 present. How far they have accomplished this belongs 

 to the past, and has become history ; what they may do in 

 the future lies within their own power. The memoir now 

 published commences with a very good digest of the 

 literature of the subject, after which follow the personal 

 observations of the author on the mycelium and spore 



* Ascham, " The Schoolnuister," Book 1. 



