We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 29 August 2010
Specifications Ofa Group. (1) If S1, S2, … S6 be any six independent [cf. § 96 (2)] systems of forces, then any system can be written in the form λ1S1+λ2S2+ … λ6S6. Let λ1, λ2, … λ6 be called the co-ordinates of S as referred to the six systems.
Definitions. The assemblage of systems, found from the expression λ1S1+λ2S2 by giving the ratio λ1: λ2 all possible values, will be called a ‘dual group’ of systems. The assemblage of systems, found from the expression λ1S1+λ2S2+ λ3S3 by giving the ratios λ1: λ2: λ3 all possible values, will be called a ‘triple group’ of systems.
The assemblage, found from λ1S1+λ2S2+ λ3S3 + λ4S4 by giving the ratios λ1: λ2: λ3: λ4 all possible values, will be called a ‘quadruple group.’ The assemblage, found from λ1S1+λ2S2+ λ3S3 + λ4S4 + λ5S5 by giving the ratiosλ1: λ2: λ3: λ4: λ5 all possible values, will be called a ‘quintuple group’
(2) A dual group will be said to be of one dimension, a triple group of two dimensions, and so on.
It is obvious that a group of ρ - 1 dimensions (ρ = 2, 3, 4, 5) can be defined by any ρ independent systems belonging to it; and also that not more than ρ independent systems can be found belonging to it.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
