NA TURE 



[November 3, 1892 



a miniature crater as at b, c, d. But the crater vent becoming 

 intermittently choked, the accumulation of gas beneath the crust 

 caused the liquid " lava " to rise through any neighbouring holes 

 as at e,f, giving rise to a ring crater. The pressure of the ac- 

 cumulated gas now drove out the obstruction in a, when the 

 liquid lava receded in e as at^. This intermittent action went 

 on till the crater i was built up— entirely by " rise and fall " (as 

 of a tide), no gas escaping at this hole. 



In the case of the moon the rise and fall would be caused by 

 the tidal motion of the still liquid interior. The solid crust 

 would resist the periodic rise of the liquid interior, and the 

 liquid would well through the crust and recede again as the 

 wave passed. 



When the crust was thin, and the lava very liquid, the large 

 ring structures would be formed, as the lava would flow far ; but 



with a raised floor and a central cone, 2X b z. crater filled to the 

 lip like " Wargentin," while on the plain near b, and round the 

 open crater c, will be seen numerous minute craters, as on the 

 moon's surface in the neighbourhood of "Aristotle" or 

 "Copernicus," while in other photographs are seen walled 

 plains like the "Mare Crisium," so that all the important 

 features of lunar topography are reproduced in this slag, and 

 there are many minor points of agreement which cannot be gone 

 into in the limits of a letter. 



Although I have always considered the tides the cause of the 

 wonderful lunar configuration, I was not satisfied that that cause 

 alone was of sufficient magnitude, till the work of Mr. Darwin 

 placed the matter in such a clear light that I now venture to 

 submit the idea to your readers as a feasible explanation of the 

 familiar lunar features. J. B. Hannay. 



On the Need of a New Geometrical Term — "Conjugate 

 Angles." 



r In geometrical discussions, such as arise out of a great 

 variety of physical problems, it is frequently necessary to refer 

 to an acute or obtuse angle A as being equal to another acute 

 or obtuse angle B, because contained by two straight lines 

 which are respectively perpendicular to those containing the 

 angle B. Such a statement of the reason of the equality is, 

 however, cumbrous. Sometimes, indeed, such angles when 

 acute might be described as equal because they are the comple- 

 ments of equal (because vertically opposite) angles ; but it will 

 often happen that the figure does not show the vertically oppo- 

 site angles that would be referred to. 



I should be glad to know whether there is any term express- 

 ing the relation in question in use among either English or 

 foreign writers, and, in default of such, would suggest that such 

 angles be called cotijugate, or if greater precision is required, 

 rectangularly conjugate, the general term conjugate to be used 

 when we wish to refer to an angle A as equal to an angle B 

 because contained by sides whose directions are the directions of 

 the sides of B, after each has experienced an equal and similar 

 rotation in the plane of the diagram, whether the rotation is 

 through a right angle or not. 



The shorter inclusive term conjugate could always be used for 

 the less general but longer term rectangularly conjugate, when 

 brevity was aimed at. A. M. WORTHINGTON. 



R.N.E. College, Devonport, October 30. 



as the crust got thicker and the lava more viscid, the more 

 striking craters like Copernicus would be built up. When the 

 vent was very small, or the lava very viscid, the exuded lava 

 would build up mountain ranges, or peaks like Pico, as it could 

 not flow far, and would be cooled too much to allow of its flow- 

 ing back with the ebb tide. 



The existence of the cause proposed by Messrs. Nasmyth and 

 Carpenter, viz., expansion on solidification, is very doubtful. 

 The proof they adduced was that a piece of solid slag would 

 float on liquid slag. But when slag solidifies it becomes filled 

 with small cracks, which doubtless contain air, and so aid in the 

 flotation. When I was working at this subject I had some slag 

 poured into an iron mould kept cool by immersion in water. 

 When the slag had cooled a distinct depression was seen on the 

 upper free surface, showing that the slag had contracted during 

 solidification. No doubt its contraction or expansion will de- 

 pend upon its composition, and we do not know the composition 

 of the moon's surface, but we need not depend upon a doubtful 

 property for an explanation when a set of conditions have 

 existed which must have yielded an ample force for the pro- 

 duction of the observed results. 



In the photograph marked Fig. 2, at a can be seen a crater 



NO. 1 201, VOL. 47I 



Printing Mathematics. 



The main features of mathematical work that give trouble in 

 printing are three : the expressing of (i) fractions, (2) powers, 

 (3) roots. 



(i) To simplify the expression of fractions we have the solidus 

 suggested by Sir G. Stokes. But the solidus has been hitherto 

 much less used than it might be, on account of the uncertainty 

 as to how far its influence reaches in any expression more com- 

 plicated than the simplest fractions. This uncertainty can easily 

 be removed, and the usefulness of the solidus greatly extended 

 by defining more definitely its exact meaning. This is done in 

 the simple conventions proposed below. 



(2) To express the process of involution, the sign \, suggested 

 by Mr. C. T. Mitchell in the Electrician, is more concise and 

 clearer than that mentioned by Prof. S. P. Thompson in 

 Nature. And Mr. Mitchell's sign, if defined by conventions 

 similar to those applied below to the solidus, is capable of a like 

 extensive application. 



(3) To express roots we have the sign sj. But, when accom- 

 panied by a horizontal line above to show the extent of its 

 influence, this sign also requires special spacing. But it can be 

 brought into line with the rest by the use of the same conven- 

 tions. 



Taking then for 



o. the sign of division . 

 ^. ,. ,, involution 

 7. ,, ,, evolution . 



/ 



we may use each of these signs in either of two ways : — 



I. Simply as a sign of operation, in which case it can influence 

 only the quantities immediately adjacent to it. 



II. In a double capacity — 

 (i) As a sign of operation. 



