History Of The Airedale Lodge, No. 387,

Phoanix Lodge , Hull , No . 256 , and Allmaun ' s Lodge , Almondbury , No . 594 , had become extinct ; and five lodges , as under , had been removed from the register , either for the same reason , or by erasure of Grand Lodge : No . 323 , Newtonian , Knaresbro ' ... ... ... Erased 3 rd Dec , 1851 . 677 SavileLeeds ... ... ... ... „ „ „ „

„ , , „ 681 , Verity , Ripon . „ 688 , Tudor , Saddleworth . „ 716 , Friendly , Barnsley ... ... ... Erased 3 rd Dec , 1851 . ( To be continued ) .

Descriptive Geometry And Our Ancient Secrets.

DESCRIPTIVE GEOMETRY AND OUR ANCIENT SECRETS .

A Paper read before the Bhoraanm Lodge hy Bro . W . W . Whytehead , M . A ., B . Sc . ( Paris ) . I WILL in a few words explain how my attention has been drawn to the subject of my paper . After a prolonged residence at Paris , I determined to consolidate my acquaintance -with the French and their language by taking a

degree at the University of France . I had , ten years previously , taken a degree in mathematics at the University of Cambridge , and , therefore , decided to read for the degree entitled " Baccalaureat es Sciences , " the programme of which is composed of Latin , literature , history , mathematics , physics , and chemistry . Of the ten subjects of mathematics , several differed in method from what we are generally | iised to in England ; for instance , Euclid , that

foundation of mathematical studies here , has been quite discarded in France , having given place to "Modern Geometry , " which is so far more serviceable than Euclid , and more in harmony with the advanced and practical condition of mathematics of this nineteenth century . But the name , even of one of the subjects , was entirely new to me ; it was called " Descriptive Geometry , " and is the science which forms the basis of architecture , engineering , and map drawing . We have here a good illustration of the advanced state of general scientific education in France , where the study of this subject is obligatory in the case of every mathematical student . Descriptive geometry is the science

of representing on a sheet of paper any machine or construction whatever . There is an important distinction between an ordinary drawing and a plan . Put the former into the hands of anybody and he will be able to picture to himself the object represented ; but the mason , artizan , or carpenter only seeing one side of the object will have to guess what may be the appearances of the other sides ; moreover , the curves , angles , and retreating parts of the object

will be more or less distorted by the effects of perspective , so that the workman will not be able to make use of his rule and compass in order to ascertain the dimensions of the object . On the other hand , the plan does not represent the object except to the skilled eye , but supplies the constructor with the dimensions he has need of . The applications of descriptive geometry are then to be found in architecture , timber cutting , military engineering , and in the

construction of sundials ; and a knowledge of the science , carried to a greater or less extent , is demanded of all candidates for the Government schools of France , as , for instance , those of the army and navy , of civil engineering , of mines , of architecture , of fine arts , of woods and forests . It is the draughtsman who makes a daily use of these principles , which , however , he may never have studied scientifically , and may , therefore , be reduced to working mechanically and by simple routine .