Aug. 29, 1872J 



NATURE 



351 



system consists in utilising tlie kitchen fire, wliicli is 

 almost constantly kept alight in summer and in winter. 

 " Endeavour is made to pre\ent the air from enter- 

 ing the house at all except by the inlet provided in 

 the lowest story of the house, with conditions available 

 for the warming, cleaning, disinfecting, or otherwise im- 

 proving the quality of the incoming fresh air, and regu- 

 lating its quantity ; the fresh air is then conducted into 

 the central private hall, which is protected from smells, 

 and all other means of pollution : it is from this private 

 hall that the rooms draw their supply, even when the 

 doors are shut. Having served its purpose in the rooms, 

 the air is drawn off through the ceiling into the foul air 

 chamber, and thence down and behind the kitchen fire, 

 up the chimney-stack, and discharged high up in the 

 open air, all possibility of back draught being prevented 

 by the length and heat of the exhausting-syphon." It 

 is a work which can be highly recommended to the 

 officer of public health, the architect, and the householder, 

 as a guide to the true principles of healthy ventilation. 

 In "Sewer Gas; a Handbook on House-drainage," we 

 hr.ve a very simple and original plan suggested for pre- 

 venting noxious gases and exhalations from drains enter- 

 ing our houses. It is shown that these gases, being speci- 

 fically lighter than atmospheric air, frequently ascend in 

 pipes, and that they are also occasionally drawn in 

 by the suction caused by the warmth of a house through 

 accidental crevices in the drain pipes. It is proposed to 

 remedy these evils by doing away with all traps except 

 those connected with the pans of closets, and by placing 

 a large trap in the pipe which connects the house drains 

 with the sewer. A plan of this trap is given, showing 

 that it is easily accessible, and can be cleaned at any time 

 by even an inexperienced workman. The subject is one 

 of even more importance than good ventilation. When 

 we recollect that one of the most valued lives in Great 

 Britain has been so recently imperilled from a mere defect 

 in a system of drainage, we cannot too highly estimate 

 the eft'orts of those who suggest, both by precept and ex- 

 periment, the adoption of such measures as will ensure 

 the safety of all sensible householders. 



LETTERS TO THE EDITOR 



[ The Editor does nol hold himself responsible for opinions expressed 

 by his eorrespondenis. No notice is take7i of anonymoits 

 eommunications, ] 



Hindrances to Students of Mathematics 

 It was the opiniuti of Dr. Samuel Johnson that everything 

 ouglit to be persecuted in order that we may know whetlier 

 it is worthy to live or not. There is, doubtless, a good deal of 

 truth in this opinion, and the idea or the man that cannot endure 

 and overcome a considerable amount of difficulty is of but little 

 value. Still there must be a reasonable limit to persecutions and 

 difficulties, and hence I hope that the praiseworthy efforts of the 

 KngUsh mathematicians to improve their text-books of geometry 

 will be successful. In considering such a matter as the improve- 

 ment of tcit-books, an extensive knowledge of the experience of 

 all classe. of students will be valuable, and as many of the 

 mathematical books profess to be written for those who are not 

 fortunate enough to have a teacher, an account of the difficulties 

 whicli such a one has experienced may be of some interest. 



I. I place first among these difficulties the practice common to 

 nearly all mathematical writers, of restricting the number of 

 axioms or fundamental assumptions, making them fewer than 

 they naturally are. It is worse than useless to attempt to prove 

 something that is self-evident, or which is so nearly so that it is 

 impossible to make any proof illustrate it. In all such cases it 

 would be better to state frankly and clearly that we make an 

 assumption, depending on observation to justify it. An example 

 of this superfluous proof may be found in many of the books on 

 rational mechanics, where sve are told that a body cannot move 

 out of the place of the force.*;, because we know of no reason 

 why it should move to one side rather than the other ; therefore, 

 cJcc. Of useless definitions wc have an e.\ample in a popular 



work on arithmetic, where we are told that ' ' time is the measure- 

 ment of duration," and a few pages further on that "duration is 

 a portion of time." Allied to this is the contemptible habit of 

 those who explain, with kind condescension and with great detail, 

 all insignificant matters, while at the same time they cover up or 

 dodge by some such phrase as "it is evident " the really difficult 

 points. 



2. I do not object to a frequent and thorough application of 

 the differential calculus in a text-book, and such an application 

 seems to me better than the coarse processes under which this 

 calcidus is sometimes coucealed ; but there is a habit, common 

 to young writers, of introducing forced and difficult demonstra- 

 tions where more simple ones would be better. An illustration 

 may be found in one of our best books on astronomy. In the 

 first edition of this book the author gave a long and difficult 

 demonstration of the well-known formuhc for the transformation 

 of rectangular co-ordinates in a plane. The demonstration was 

 made to depend on the solution of functional equations by means 

 of the dilferential calculus, and is an awkward thing to place at 

 the beginning of a text-book. In the second edition, having 

 removed this demonstration and supplied its place by a simple 

 one, the author has made the first chapter of his book the best 

 synopsis of spherical trigonometry that I know of 



3. An error of the English text-books written by Cambridge 

 men is, I think, the great number of examples given at the close 

 of each chapter. At least one-half of these should be omitted. 

 It is a great mistake to keep the student lingering over the never- 

 ending questions of conic sections, of maxima and minima, &c., 

 and to give him the habit of solving petty problems, when he 

 should be led forward as soon as possible to the study of the 

 memoirs of those who have created the science. In this con- 

 ned ion ic seems to me a mistake in treating the differential 

 calculus to conSne ourselves rigorously to the notion of a limit. 

 Although the doctrine of limits may be the only logical founda- 

 tion of^this calculus,|the student as he advances must soon become 

 familial with differentials, and it is well that he should make 

 their acquaintance in his text-book. 



4. A defect, perhaps of teaching rather than of text-book, is 

 the ignorance of all American students of numerical and 

 logarithm calculations, and from ' my slight observation I infer 

 that such is the case also with English students. It is not un- 

 common to hear such calculations spoken of with contempt, but 

 there is nothing that gives one a clearer idea of the meaning of 

 analytical formula; than to make a numerical application of them. 

 In this matter it seems to me that the assistance of a teacher is 

 of much more importance than in dealing v^'ith theoretical diffi- 

 culties, since with these a student must generally be left to him- 

 self, while a little advice from a skilful computer will save the 

 beginner much time and trouble. 



5. Finally I mention, as a source of some confusion and per- 

 plexity to the student, the changes of notation and the introduc- 

 tion of new names. Some such change and inventions will be 

 necessary with the progress of science, but any which tendj to 

 mar the symmetry of analytical expressions, and render less easy 

 the reading of the great mass of mathematical literature that we 

 already possess, should be avoided. To call a well-known func- 

 tion a "wonnumetonomy," or a "subcontra-wonnumetonomy," 

 does not of course endow it with any new properties, or make 

 its discussion one whit easier, although we may gain a slight ad- 

 vantage in the way of brevity of reference. For my own part I 

 hope that this introduction of words of thundering sound, and 

 the calculation of almost interminable formulx, for which no 

 more ingenuity is required than for a numerical calculation, is 

 only premonitory to the invention of a calculus of operations 

 which shall furnish us with shorter and more powerful methods 

 of investigation. Asaph Hall „ 



Washington, August 16 



Jeremiah Horrocks 



In the course of research (for literary purposes) concerning 

 Jeremiah Horrocks, the astronomer, born at Toxteth, near 

 Liverpool, i6ig, I have been unable to discover his parentage. 

 Conld any of your readers help me in this matter ? 



London, Aug. 12 E. 



The "Mors Electrique " 

 With reference to your notice of M. Sidot's "Mors Electri- 

 que," I m.iy mention that in India it has been proposed to use 

 Magneto Electricity for the purpose of starting a jibbing horse. 



